Polar code encoding and rate-matched sequence outputting method and apparatus
Granted 25 Nov 2025 · 4 office actions
Assignee: Huawei Technologies
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Attorney: Attorney · Log in to unlock
Inventors: Rong Li, Huazi Zhang, Xianbin Wang, Wen Tong +4 · Examiner: Justin R Knapp · AU 2112 · TC 2100
Life of the application
9 dated eventsDescription
33 parts›CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of International Patent Application No. PCT/CN2021/101177, filed on Jun. 21, 2021, which claims priority to Chinese Patent Application No. 202010663589.9, filed on Jul. 10, 2020. The disclosures of the aforementioned applications are hereby incorporated by reference in their entireties.
›TECHNICAL FIELD
Embodiments of this application relate to the field of communications technologies, and in particular, to a polar code encoding method and apparatus.
›BACKGROUND
Channel encoding, as a most fundamental radio access technology, is crucial in ensuring reliable data transmission. In an existing wireless communications system, turbo code, low density parity check (LDPC) code, and polar code are usually used to perform channel encoding. The turbo code cannot support information transmission at an excessively low or high code rate. Due to encoding/decoding features of the turbo code and the LDPC code, for medium and short packet transmission, it is difficult for the turbo code and the LDPC code to achieve ideal performance in a case of a limited code length. During implementation, the turbo code and the LDPC code have high computation complexity in an encoding/decoding implementation process. The polar code is high-performance code that has been theoretically proved to be capable of achieving Shannon capacity and that has low encoding/decoding complexity, and therefore is applied increasingly widely.
In a 5th generation (5G) communications system, the polar code is determined as an encoding scheme of a control channel. Because a data amount included in the control channel is usually not large, a code block is not large. In the 3GPP standard, only a reliability ranking sequence whose mother code length is N max =1024 is specified, and is used to sort reliability of 1024 subchannels to select a location of an information bit. For another case in which the mother code length N is less than 1024, a subsequence of the reliability ranking sequence in which N max =1024 may be used as a corresponding reliability ranking sequence. A system design can be simplified by using this sequence nesting feature.
However, during data channel encoding, a long code block needs to be used for encoding in a plurality of cases. In this case, it is not enough to still use the reliability ranking sequence in which N max =1024. Therefore, how to design a long reliability ranking sequence to meet a requirement of a data channel becomes a problem that needs to be resolved.
›SUMMARY · 1 of 2
Embodiments of this application provide a polar code encoding method and apparatus applied to wireless communication, to support polar code encoding of a large data block, and to allow backward compatibility with a reliability ranking sequence supported by an existing NR system. This reuses the conventional technology to a maximum extent.
Specific technical solutions provided in embodiments of this application are as follows.
According to a first aspect, a polar code encoding method is provided, including:
An encoding apparatus obtains K to-be-encoded bits, a mother code length N, and a first sequence, where the first sequence includes sequence numbers of N polarized subchannels, the sequence numbers of the N polarized subchannels are arranged in the first sequence based on reliability of the N polarized subchannels, N=2 n , and K≤N, N is greater than or equal to 32, and K, n, and N are positive integers;
determines, based on the first sequence, K polarized subchannels used to contain the K to-be-encoded bits, and performs polarization encoding on the K to-be-encoded bits to obtain an encoded bit sequence; performs rate matching on the encoded sequence to obtain a rate-matched sequence; and outputs the rate-matched sequence, where the first sequence is any Q sequence whose length is N in the appendix.
This design fits a feature of a large data block, and can be backward compatible with a reliability ranking sequence supported by an existing NR system. This reduces implementation difficulty.
In a possible design, the first sequence is a subsequence of a second sequence, the second sequence includes sequence numbers of N max polarized subchannels, the sequence numbers of the N max polarized subchannels are arranged in the second sequence based on reliability of the N max polarized subchannels, N is less than or equal to N max , and N max =2 n max , where n max is a positive integer, n is less than or equal to n max , and the second sequence is any Q sequence whose length is N max in the appendix.
In a possible design, the K to-be-encoded bits include a cyclic redundancy check bit.
In a possible design, the K to-be-encoded bits include a parity check bit.
In a possible design, the polar encoding method is performed by a network device or a terminal.
In a possible design, the determining, based on the first sequence, K polarized subchannels used to contain the K to-be-encoded bits is: when M is less than or equal to N, mapping the K to-be-encoded bits to the K polarized subchannels with high reliability in M−P non-punctured polarized subchannels to enable reliability of the polarized subchannels containing the K to-be-encoded bits to be higher than reliability of remaining M−P−K polarized subchannels, where M is a target code length, P is a quantity of pre-frozen polarized subchannels, and P is greater than or equal to 0.
In a possible design, the first sequence is prestored.
In a possible design, the sequence numbers of the N polarized subchannels are 0 to (N−1) or 1 to N.
According to a second aspect, a polar code decoding method is provided, including:
A decoding apparatus obtains a to-be-decoded information sequence, where the to-be-decoded information sequence includes K to-be-decoded bits;
determines a mother code length N and a first sequence, where the first sequence includes sequence numbers of N polarized subchannels, the sequence numbers of the N polarized subchannels are arranged in the first sequence based on reliability of the N polarized subchannels, N=2 n , K≤N, N is greater than or equal to 32, and K, n, and N are positive integers; determines, based on the first sequence, K polarized subchannels used to contain the K to-be-decoded bits, and decodes the to-be-decoded information sequence to obtain a decoding result; and outputs the decoding result, where the first sequence is any Q sequence whose length is N in the appendix or a subsequence of any Q sequence whose length is greater than N in the appendix.
This design completely corresponds to the encoding method according to the first aspect, fits a feature of a large data block, and can be backward compatible with a reliability ranking sequence supported by an existing NR system. This reduces implementation difficulty.
In a possible design, the first sequence is a subsequence of a second sequence, the second sequence includes sequence numbers of N max polarized subchannels, the sequence numbers of the N max polarized subchannels are arranged in the second sequence based on reliability of the N max polarized subchannels, N is less than or equal to N max , and N max =2 n max , where n max is a positive integer, n is less than or equal to n max , and the second sequence is any Q sequence whose length is N max in the appendix.
In a possible design, the K to-be-decoded bits include a cyclic redundancy check bit.
In a possible design, the K to-be-decoded bits include a parity check bit.
In a possible design, the polar encoding method is performed by a network device or a terminal.
In a possible design, the determining, based on the first sequence, K polarized subchannels used to contain the K to-be-decoded bits is: when M is less than or equal to N, mapping the K to-be-decoded bits to the K polarized subchannels with high reliability in M−P non-punctured polarized subchannels to enable reliability of the polarized subchannels containing the K to-be-decoded bits to be higher than reliability of remaining M−P−K polarized subchannels, where M is a target code length, P is a quantity of pre-frozen polarized subchannels, and P is greater than or equal to 0.
In a possible design, the first sequence is prestored.
In a possible design, the sequence numbers of the N polarized subchannels are 0 to (N−1) or 1 to N.
According to a third aspect, a polar code encoding apparatus is provided. The apparatus has functions of implementing the method according to any one of the first aspect and the possible designs of the first aspect. The function may be implemented by hardware, or may be implemented by hardware executing corresponding software. The hardware or the software includes one or more modules corresponding to the foregoing function.
›SUMMARY · 2 of 2
In a possible design, when some or all of the functions are implemented by using hardware, the polar code encoding apparatus includes: an input interface circuit, configured to obtain a to-be-encoded bit; a logical circuit, configured to perform the operation according to any one of the first aspect and the possible designs of the first aspect; and an output interface circuit, configured to output a rate-matched sequence.
Optionally, the polar code encoding apparatus may be a chip or an integrated circuit.
In a possible design, when some or all of the functions are implemented by using software, the polar code encoding apparatus includes: a memory, configured to store a program; and a processor, configured to execute the program stored in the memory. When the program is executed, the polar code encoding apparatus may implement the method according to any one of the first aspect and the possible designs of the first aspect.
Optionally, the memory may be a physically independent unit, or may be integrated with the processor.
In a possible design, when some or all of the functions are implemented by using software, the polar code encoding apparatus includes a processor. A memory configured to store a program is located outside of the polar code encoding apparatus, and the processor is connected to the memory through a circuit/cable, and is configured to read and execute the program stored in the memory.
In a possible design, the apparatus is a network device or a terminal.
According to a fourth aspect, a polar code decoding apparatus is provided. The apparatus has functions of implementing the method according to any one of the second aspect and the possible designs of the second aspect. The function may be implemented by hardware, or may be implemented by hardware executing corresponding software. The hardware or the software includes one or more modules corresponding to the foregoing function.
In a possible design, when some or all of the functions are implemented by using hardware, the polar code decoding apparatus includes: an input interface circuit, configured to obtain a to-be-decoded information sequence; a logical circuit, configured to perform the operation according to any one of the second aspect and the possible designs of the second aspect; and an output interface circuit, configured to output a decoding result.
Optionally, the polar code decoding apparatus may be a chip or an integrated circuit.
In a possible design, when some or all of the functions are implemented by using software, the polar code decoding apparatus includes: a memory, configured to store a program; and a processor, configured to execute the program stored in the memory. When the program is executed, the polar code decoding apparatus may implement the method according to any one of the second aspect and the possible designs of the second aspect.
Optionally, the memory may be a physically independent unit, or may be integrated with the processor.
In a possible design, when some or all of the functions are implemented by using software, the polar code decoding apparatus includes a processor. A memory configured to store a program is located outside of the polar code decoding apparatus, and the processor is connected to the memory through a circuit/cable, and is configured to read and execute the program stored in the memory.
In a possible design, the apparatus is a network device or a terminal.
According to a fifth aspect, a communications system is provided. The communications system includes a network device and a terminal. The network device performs the method according to the first aspect and the possible designs of the first aspect, and the terminal performs the method according to the second aspect and the possible designs of the second aspect. Alternatively, the terminal performs the method according to the first aspect and the possible designs of the first aspect, and the network device performs the method according to the second aspect and the possible designs of the second aspect.
According to a sixth aspect, a computer storage medium is provided, where the computer storage medium stores a computer program. The computer program includes instructions used to perform the method according to any one of the first aspect and the possible designs of the first aspect.
According to a seventh aspect, a computer storage medium is provided, where the computer storage medium stores a computer program. The computer program includes instructions used to perform the method according to any one of the second aspect and the possible designs of the second aspect.
According to an eighth aspect, an embodiment of this application provides a computer program product including instructions. When the instructions are run on a computer, the computer is enabled to perform the method in the foregoing aspects.
According to a ninth aspect, a wireless device is provided, including an encoding apparatus and a transceiver that are configured to implement any one of the first aspect and the possible designs of the first aspect.
The transceiver is configured to receive or send a signal.
In a possible design, the wireless device is a terminal or a network device.
According to a tenth aspect, a wireless device is provided, including a decoding apparatus and a transceiver that are configured to implement any one of the second aspect and the possible designs of the second aspect.
The transceiver is configured to receive or send a signal.
In a possible design, the wireless device is a terminal or a network device.
›BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a schematic diagram of an architecture of a communications system to which an embodiment of this application is applied;
FIG. 2 is a schematic flowchart of a polar code encoding method according to an embodiment of this application;
FIG. 3 is a first schematic diagram of a structure of a polar code encoding apparatus according to an embodiment of this application;
FIG. 4 is a second schematic diagram of a structure of a polar code encoding apparatus according to an embodiment of this application;
FIG. 5 is a third schematic diagram of a structure of a polar code encoding apparatus according to an embodiment of this application;
FIG. 6 is a fourth schematic diagram of a structure of a polar code encoding apparatus according to an embodiment of this application;
FIG. 7 is a first schematic diagram of a structure of a polar code decoding apparatus according to an embodiment of this application;
FIG. 8 is a second schematic diagram of a structure of a polar code decoding apparatus according to an embodiment of this application;
FIG. 9 is a third schematic diagram of a structure of a polar code decoding apparatus according to an embodiment of this application; and
FIG. 10 is a fourth schematic diagram of a structure of a polar code decoding apparatus according to an embodiment of this application.
›DESCRIPTION OF EMBODIMENTS · 1 of 6
The following describes in detail embodiments of this application with reference to accompanying drawings.
If a polar code encoding scheme used for a control channel in an existing 5G NR standard is directly applied to data without considering a feature of a data channel, because in the current 5G NR standard, a maximum mother code length of a polar code is 1024, a data packet length that can be supported is limited. Therefore, it is necessary to redesign the polar code encoding scheme, to be more suitable for the data channel. In addition, it is optimal that the polar code encoding scheme is applicable to the control channel.
Embodiments of this application provide a polar code encoding method and apparatus. A sequence number of a polarized subchannel used to send an information bit is selected based on a prestored reliability ranking sequence or a subsequence of the reliability ranking sequence, and polar code encoding is performed based on the selected sequence number of the information polarized subchannel. Then, a rate matching operation is performed on an encoded sequence, and a rate-matched sequence is output, where the rate matching operation includes repetition, puncturing, or shortening. Embodiments of this application are more applicable to the data channel. The following describes in detail the polar code encoding method and apparatus provided in embodiments of the present application with reference to the accompanying drawings.
For convenience of understanding embodiments of this application, polar code is briefly described below.
According to an encoding policy of the polar code, a noiseless channel is used to transmit information useful to a user, while a pure noisy channel is used to transmit agreed information or is not used to transmit information. The polar code is also linear block code. An encoding matrix of the polar code is G N , and an encoding process is x 1 N =u 1 N G N . u 1 N =(u 1 , u 2 , . . . , u N ) is a binary row vector whose length is N (that is, a code length. It can be learned that lengths of the sequences x and u before and after encoding are both N, where N is also referred to as a mother code length). G N is an N×N matrix, and G N =F 2 ⊗(log 2 (N)) . F 2 ⊗(log 2 (N)) is defined as a Kronecker product of log 2 N matrices F 2 . The matrix
F 2 = [ 1 0 1 1 ] .
In some implementations, there may be a transpose matrix in u 1 N and G N . Because polar code performance is not affected essentially, details are not described in this application.
In a polar code encoding process, one part of bits in u 1 N are used to carry information, and are referred to as a set of information bits, where a set of indexes of the bits is denoted as A; and another part of bits are set to a fixed value pre-agreed upon between a receiving end and a transmitting end, and are referred to as a set of fixed bits or a set of frozen bits, where a set of indexes of the bits is indicated by a complementary set A c of A. The polar code encoding process is equivalent to: x 1 N =u A G N ·(A)⊕u A C G N ·(A C ). Herein, G N (A) is a submatrix obtained by using rows corresponding to the indexes in the set A in G N , and G N (A C ) is a submatrix obtained by using rows corresponding to the indexes in the set A c in G N . u A is an information bit set in u 1 N , and a quantity of information bits is K. Usually, various types of check bits including but not limited to a cyclic redundancy check (CRC) bit and a parity check (PC) bit may also be included in the information bit set. u A C is a frozen bit set in u 1 N , a quantity of frozen bits is (N-K), and the frozen bits are known bits. These frozen bits are usually set to 0. However, values of the frozen bits may be set to any value provided that the value is pre-agreed on by the receiving end and the transmitting end. Therefore, an encoding output of the polar code may be simplified as x n N =u A G N (A). Herein, u A is the information bit set in u 1 N , and u A is a row vector of a length K, that is, |A|=K. |⋅| indicates a quantity of elements in the set, K is an information block size, G N (A) is the submatrix obtained by using the rows corresponding to the indexes in the set A in the matrix G N , and G N (A) is a K×N matrix.
After the mother code length N is determined, a polar code construction process is a selection process of the set A, and polar code performance is determined. The polar code construction process is usually as follows: It is determined, based on the mother code length N that N polarized channels co-exist, where the N polarized channels respectively correspond to N rows in an encoding matrix.
When rate matching is not performed, indexes of first K polarized subchannels with high reliability are used as elements of the set A, and indexes corresponding to remaining (N-K) polarized subchannels are used as elements of the index set A c of the frozen bits. The set A determines a location of the information bit, and the set A c determines a location of the frozen bit. A sequence number of a polarized channel is a location index of an information bit or a frozen bit, that is, a location index in u 1 N .
When rate matching is performed, particularly when puncturing or shortening is performed, N−M polarized subchannels that need to be punctured or shortened (that is, deleted) usually are first determined. Herein, M is a target code length, that is, a length of a rate-matched bit sequence, and the N−M polarized subchannels selected herein are used to contain frozen bits. In the 5G NR standard, when puncturing is performed, some pre-frozen polarized subchannels are further additionally determined, and are also used to contain frozen bits. Herein, a quantity of the pre-frozen polarized subchannels are defined as P, and P is greater than or equal to 0 (in 5G NR, when shortening is performed, P is 0, and in this case, P may not need to be considered. This is not limited in this application). Then, the K polarized subchannels with high reliability are selected from remaining M−P polarized subchannels based on reliability to contain K information bits. Certainly, M−P−K subchannels with low reliability may alternatively be first selected to contain frozen bits, and remaining K subchannels are used to contain information bits. Reliability of any one of the K polarized subchannels containing the K information bits is higher than reliability of any one of the M−P−K subchannels containing the frozen bits. In this application, a value of P is not limited. Even when puncturing is performed, P may be 0. Even when shortening is performed, P may be greater than 0. This does not affect implementation of the technical solutions in this application. Regardless of an encoder or a decoder, principles and methods for determining that the K subchannels are used to contain the K information bits are consistent. In the 5G NR standard, for selection of N−M polarized subchannels, a solution is to contain a sequence obtained after subblock interleaving (divided into 32 subblocks) in a circular buffer (equivalent to a rate-matched sequence). If puncturing is performed, reading starts from an (N−M) th location in the circular buffer, and bits from a 0 th location to an (N−M−1) th location are discarded. If shortening is performed, reading starts from a 0 th location to an (M−1) th location in the circular buffer, and bits from an M th location to an (N−1) th location are discarded. Generally, a reliability ranking sequence whose length is the mother code length N is used to represent a relative reliability relationship between different polarized subchannels. The reliability ranking sequence includes sequence numbers (starting from 0 to N−1) of N polarized subchannels, and the sequence numbers may be arranged in descending order or ascending order of reliability. Without loss of generality, this application uses an example in which the sequence numbers are arranged in ascending order of the reliability.
›DESCRIPTION OF EMBODIMENTS · 2 of 6
It should be noted that the relative reliability relationship described herein is based on a specific reliability calculation manner. Different reliability calculation manners may cause a change in the relative reliability relationship between the polarized subchannels. However, methods for selecting polarized subchannels used to contain information bits are the same. In addition to the 5G NR standard, it may also be considered that an information bit is contained by a last punctured or shortened polarized subchannel. In this application, it is not limited that the polarized subchannel containing the information bit needs to be selected according to the 5G NR standard.
In the 5G NR standard, when reliability ranking sequences corresponding to different mother code lengths meet a nesting feature, that is, the mother code length N is less than or equal to a mother code length N′, a relative relationship between reliability of polarized subchannels (polarized subchannels 0, . . . , and N−1) in the reliability ranking sequence corresponding to N is consistent with a relative relationship between the reliability of the polarized subchannels (the polarized subchannels 0, . . . , and N−1) in a reliability ranking sequence corresponding to N′. In other words, in the reliability ranking sequence corresponding to N′, only numbers of polarized subchannels less than N are retained, and a relative ranking relationship between locations of the numbers of the N polarized subchannels is not changed. In this way, the reliability ranking sequence corresponding to N can be obtained. Therefore, the reliability ranking sequence whose length is N may be referred to as a subsequence of the reliability ranking sequence whose length is N′, where N is less than or equal to N′. For example, N′=8, and a reliability ranking sequence 1 is [0, 4, 6, 2, 3, 1, 7, 5]. Correspondingly, if N=4, and a reliability ranking sequence 2 is [0, 2, 3, 1], the sequence 2 is a subsequence of the sequence 1. Therefore, in a specific implementation, reliability ranking sequences of different mother code lengths may be prestored. Alternatively, only a reliability ranking sequence whose length is equal to a maximum mother code length N max may be prestored, and another reliability ranking sequence corresponding to the mother code length N is obtained by retaining only sequence numbers of polarized subchannels less than N in the reliability ranking sequence corresponding to the maximum mother code length. In this way, storage overheads can be reduced. Particularly, a sequence may also be a subsequence of the sequence. Therefore, a largest value of N may be equal to N max .
FIG. 1 is a schematic diagram of a structure of a wireless communications network according to an embodiment of the present invention. FIG. 1 is merely an example, and other wireless networks to which the encoding method or apparatus in embodiments of the present application can be applied shall fall within the protection scope of the present invention.
As shown in FIG. 1 , the wireless communications network 100 includes a network device 110 and a terminal 112 . When the wireless communications network 100 includes a core network 102 , the network device 110 may further be connected to the core network 102 . The network device 110 may further communicate with an IP network 104 such as the Internet, a private IP network, or another data network. The network device provides services for a terminal within coverage. For example, refer to FIG. 1 . The network device 110 provides wireless access for one or more terminals 112 within the coverage of the network device 110 . In addition, coverage of network devices, for example, the network device 110 and a network device 120 , may have an overlapping area. The network devices may further communicate with each other. For example, the network device 110 may communicate with the network device 120 .
The network device may be a device configured to communicate with a terminal device. For example, the network device may be an evolved NodeB (eNB, or eNodeB) in an LTE system, may be a gNB in a 5G network, may be a satellite in satellite communication, a network side device in a future communications system, or the like. Alternatively, the network device may be a relay station, an access point, a vehicle-mounted device, or the like. In a device to device (D2D) communications system, a machine to machine (M2M) communications system, and an Internet of vehicles system, the network device may alternatively be a terminal that functions as a base station.
The terminal may be user equipment (UE), an access terminal, a subscriber unit, a mobile station, a remote station, a remote terminal, a mobile device, a user terminal, a wireless communications device, a user agent, or a user apparatus. The access terminal may be a cellular phone, a cordless phone, a session initiation protocol (SIP) phone, a wireless local loop (WLL) station, a personal digital assistant (PDA), a handheld device having a wireless communications function, a computing device, another processing device connected to a wireless modem, a vehicle-mounted device, a wearable device, or a terminal device in a future communications network.
Based on the architecture of the communications system shown in FIG. 1 , in embodiments of this application, the polar code encoding method may be performed by the foregoing network device or terminal. When the network device or the terminal is used as a transmitting end to send data or information, the polar code encoding method may be used. Correspondingly, when the network device or the terminal serves as a receiving end to receive data or information, the network device or the terminal also needs to determine a reliability ranking sequence according to the method described in the present application and then perform decoding. The following describes in detail the polar code encoding method provided in embodiments of this application.
Based on the architecture of the communications system shown in FIG. 1 , as shown in FIG. 2 , a specific process of a polar code encoding method provided in an embodiment of this application is as follows.
›DESCRIPTION OF EMBODIMENTS · 3 of 6
Operation 210 : Obtain K to-be-encoded bits, a target code length M, a mother code length N, and a first sequence, where the first sequence is a reliability ranking sequence and includes sequence numbers of N polarized subchannels, the sequence numbers of the N polarized subchannels are arranged in the first sequence based on reliability of the N polarized subchannels, N=2 n , and K≤N. In an application scenario of polar code, N may be a value greater than or equal to 32, and M, K, n, and N are positive integers.
The K to-be-encoded bits herein may include only a payload bit, or may include one or more types of other types of non-frozen bits such as a CRC bit and a PC bit in addition to the payload bit.
How to obtain the mother code length N based on factors such as the target code length M and a code rate is specified in the 5G NR system. Because this is not a technical problem to be resolved in this application, the manner of obtaining the mother code length N is directly used, but it is not indicated that only the 5G NR manner can be used to obtain the mother code length N in the solution of this application.
After N is determined, the first sequence whose length is N may be determined. As described above, the first sequence may be prestored, or may be a subsequence whose length is N and that is extracted from a second sequence. The second sequence is a reliability ranking sequence whose length is a maximum mother code length N max . The first sequence may be any Q sequence whose length is N in the appendix or a subsequence of any Q sequence whose length is greater than N in the appendix, the second sequence may be any Q sequence whose length is N max in the appendix, and the first sequence is a subsequence of the second sequence, where N is less than or equal to N max . N max may be any one of 2048, 4096, 8192, and 16384.
In this application, the appendix provides, based on decoding implementation, rate matching, and code block retransmission, eight groups of polar code reliability ranking sequences applicable to long code block encoding. In terms of reliability, each group of sequences includes reliability ranking sequences (Qx_y sequences, which are generally referred to as Q sequences for ease of understanding, where x is any integer from 1 to 8, and y is any value in 2048, 4096, 8192, and 16384. This also applies to the following statements) that are of lengths of 2048, 4096, 8192, and 16384 and that are arranged in ascending order of the reliability, and corresponding reliability location sequences (Zx_y sequences, which are generally referred to as Z sequences for ease of understanding, where x is any integer from 1 to 8, and y is any value in 2048, 4096, 8192, and 16384. This also applies to the following statements). For the Q sequence, each value in the sequence is a sequence number of a polarized subchannel, and a location of the value in the sequence is a reliability order. A higher location indicates lower reliability. For the Z sequence, each value in the sequence is a reliability order of a location of the value (that is, a polarized subchannel containing the value) in reliability of all polarized subchannels. The Q sequence is in a one-to-one correspondence with the Z sequence. In a simple example, if a Q sequence is [0, 4, 6, 2, 3, 1, 7, 5], a corresponding Z sequence is [0, 5, 3, 4, 1, 7, 2, 6], and both the Q sequence and the Z sequence indicate that a polarized subchannel 5 has highest reliability, a polarized subchannel 7 has second highest reliability, and a polarized subchannel 1 has third highest reliability. The rest may be deduced by analogy. A polarized subchannel 0 has lowest reliability. It should be noted that only reliability ranking sequences whose lengths are greater than 1024 is provided in the appendix. This is because the sequences are backward compatible. To be specific, a reliability ranking sequence whose length is N max =1024 and that is specified in the 5G NR protocol is a subsequence of any Qx_y sequence in the appendix. In other words, reliability ranking sequences whose lengths are separately 32, 64, 128, 256, 512, or 1024 and that are used in the 5G NR protocol are subsequences of any Qx_y sequence in the appendix. In an actual implementation, K polarized subchannels are usually selected by using the Q sequence, but may also be selected by using the Z sequence.
Sequence group 1 (Q1_y and Z1_y): A criterion for designing the sequence is to ensure decoding performance and provide a high degree of parallelism for polar decoding, to further reduce a decoding delay.
Sequence group 2 (Q2 y and Z2_y): Currently, in NR, in addition to a repetition rate matching scheme, there are two rate matching schemes based on a code rate: puncturing and shortening. A criterion for designing the sequence is to preferentially optimize performance in the rate matching scheme in which puncturing is performed.
Sequence group 3 (Q3_y and Z3_y): Currently, in NR, in addition to a repetition rate matching scheme, there are two rate matching schemes based on a code rate: puncturing and shortening. A criterion for designing the sequence is to preferentially optimize performance in the rate matching scheme in which shortening is performed.
Sequence group 4 (Q4_y and Z4_y): HARQ needs to be supported in a data channel. Currently, a polar code HARQ solution commonly used in the industry mainly includes IR and IF. A criterion for designing the sequence is to consider both IR (incremental redundancy) HARQ performance and IF (incremental frozen) HARQ performance.
In a high-throughput communications scenario of a data channel, a system defines several fixed MCS formats, and corresponding required mother code lengths are expected to include 2048/4096/8192/16384 and the like. The mother code lengths vary with different subdivided scenarios. Therefore, some reliability ranking sequences are designed for different mother code lengths and modulation schemes in the present invention.
Sequence group 5 (Q5_y and Z5_y): Performance in a 16-QAM modulation scheme is preferentially considered, but it can also be ensured that performance in another modulation scheme can meet a requirement.
›DESCRIPTION OF EMBODIMENTS · 4 of 6
Sequence group 6 (Q6_y and Z6_y): Performance in a 64-QAM modulation scheme is preferentially considered, but it can also be ensured that performance in another modulation scheme can meet a requirement.
Sequence group 7 (Q7_y and Z7_y): Performance of a mother code length 2048 is preferentially considered, but it can also be ensured that performance of another mother code length can meet a requirement.
Sequence group 8 (Q8_y and Z8_y): Performance of a mother code length 4096 is preferentially considered, but it can also be ensured that performance of another mother code length can meet a requirement.
Pay attention to the following points:
1. A reliability ranking sequence whose length is 1024 given in the 5G NR protocol is a subsequence of any Q sequence in the appendix. In this way, a data channel encoding requirement is met, and compatibility with an existing protocol is ensured. Correspondingly, reliability ranking sequences that are used in the 5G NR protocol and whose lengths are separately 32, 64, 128, 256, 512, or 1024 are subsequences of any Q sequence in the appendix.
2. Locations of fewer elements in the sequence are exchanged. For example, a sequence number location may be adjusted by a specified magnitude, for example, the specified magnitude is 5. A location of an element whose sequence number is 10 may be adjusted by left and right five locations.
3. Some elements in the sequence are adjusted, but channel sets that are used to transmit T-bit information and that are selected based on the sequence are consistent or similar.
4. The sequence includes N elements from 0 to N−1, and the N elements from 0 to N−1 represent sequence numbers of N polarized subchannels. Actually, the sequence numbers of the N polarized subchannels may alternatively start from 1 and end with N, that is, 1 is added to the sequence numbers in the foregoing sequence. This is also a sequence number form in the foregoing calculation manner. Certainly, a sequence number or an identifier of the polar subchannel may alternatively be represented in another manner. The specific representation manner does not affect a specific location of the polar subchannel in the sequence.
Operation 220 : Determine, based on the first sequence, the K polarized subchannels used to contain the K to-be-encoded bits, and perform polarization encoding on the K to-be-encoded bits to obtain an encoded bit sequence.
For a specific encoding operation, refer to the foregoing description. A specific scheme of rate matching may be first determined. When puncturing or shortening is performed, polarized subchannels to be punctured or shortened (that is, deleted) and possible P pre-frozen polarized subchannels (P is greater than or equal to 0) are first determined, and the K polarized subchannels with high reliability are selected from remaining M−P polarized subchannels based on reliability to contain K information bits. When repetition is performed, the K polarized subchannels with high reliability are directly selected from the N polarized subchannels based on reliability to contain the K information bits. A decoder may also determine locations of the K information bits in the same manner.
Operation 230 : Perform a rate matching operation on the encoded bit sequence to obtain a rate-matched bit sequence whose length is M.
For a specific rate matching operation, refer to a manner in which block interleaving is first performed and then bits are sequentially fetched in a circular buffer in 5G NR. Alternatively, a specific rate matching operation may be performed by using a preset rate matching sequence. This is not limited herein.
Operation 240 : Output the rate-matched sequence.
It should be noted that if a modulation operation is used, the output herein should be a sequence obtained after modulation is performed on a rate-matched bit sequence. The sequence is a symbol sequence. In this case, a length of the sequence may not be M. If modulation is not used, the rate-matched sequence is a rate-matched bit sequence. For ease of understanding, terms “rate-matched sequence” and “rate-matched bit sequence” are not strictly distinguished in this application.
The embodiment shown in FIG. 2 is an operation of a transmitting end, and an operation of a receiving end is similar. After receiving a to-be-decoded information sequence, a receiver (or a receiving apparatus) also needs to use a similar method. A to-be-decoded information sequence including K to-be-decoded bits, a target code length M, and a mother code length N is obtained, a first sequence is determined, K polarized subchannels used to contain the K to-be-decoded bits are determined based on the first sequence, and a decoding operation is performed on the to-be-decoded information sequence to obtain and output a decoding result. A detailed decoding algorithm is not limited herein.
As shown in FIG. 3 , an embodiment of this application further provides a polar code encoding apparatus 300 . Some or all of the polar code encoding method shown in FIG. 3 may be implemented by hardware, or may be implemented by software.
For the polar code encoding apparatus 300 , based on a same inventive concept as the polar code encoding method shown in FIG. 2 , the polar code encoding apparatus 300 is configured to perform the polar code encoding method shown in FIG. 2 . When some or all of the polar code encoding method is implemented by hardware, the polar code encoding apparatus 300 includes: an input interface circuit 301 , configured to obtain to-be-encoded bits; a logic circuit 302 , configured to perform the polar code encoding method shown in FIG. 2 ; and an output interface circuit 303 , configured to output a rate-matched sequence. Further, the rate-matched sequence is still a modulated sequence, where for details, refer to description in the foregoing method embodiments, and details are not described herein again. The sequence is a modulated symbol sequence, and is output to a transceiver 320 . The transceiver 320 performs corresponding processing (including but not limited to processing such as digital-to-analog conversion and/or frequency conversion) on the modulated sequence, and sends a processed modulated sequence through an antenna 330 . Optionally, in a specific implementation, the polar code encoding apparatus 300 may be a chip or an integrated circuit.
›DESCRIPTION OF EMBODIMENTS · 5 of 6
Optionally, when some or all of the polar code encoding method in the foregoing embodiment is implemented by software, as shown in FIG. 4 , a polar code encoding apparatus 400 includes: a memory 401 , configured to store a program; and a processor 402 , configured to execute the program stored in the memory 401 . When the program is executed, the polar code encoding apparatus 400 can implement the polar code encoding method provided in the foregoing embodiment.
Optionally, the memory 401 may be a physically independent unit. Alternatively, as shown in FIG. 5 , a memory 501 and a processor 502 may be integrated together.
Optionally, when some or all of the encoding method in the foregoing embodiment is implemented by software, the polar code encoding apparatus 400 may alternatively include only the processor 402 . The memory 401 configured to store the program is located outside the polar code encoding apparatus 400 . The processor 402 is connected to the memory 401 through a circuit/cable, and is configured to read and execute the program stored in the memory 401 .
Based on the polar code encoding method shown in FIG. 2 , as shown in FIG. 6 , an embodiment of this application further provides a polar code encoding apparatus 600 . The polar code encoding apparatus 600 is configured to perform the polar code encoding method shown in FIG. 2 . The polar code encoding apparatus 600 includes:
an obtaining unit 601 , configured to obtain K to-be-encoded bits; an encoding unit 602 , configured to: determine a mother code length N and a first sequence (a reliability ranking sequence whose length is N), and perform polar encoding on the K to-be-encoded bits based on the mother code length N to obtain an encoded bit sequence, where for a specific encoding process, refer to operation 220 in the foregoing embodiment; and a rate matching unit 603 , configured to perform a rate matching operation on the encoded bit sequence to obtain a rate-matched bit sequence whose length is M (or a sequence obtained through further modulation on the bit sequence, which is also referred to as a rate-matched sequence), where for a specific rate matching method, refer to operation 230 in the foregoing embodiment.
Corresponding to the transmitting end, an apparatus at the receiving end may also be designed similarly.
As shown in FIG. 7 , a polar code decoding apparatus 700 includes: an input interface circuit 701 , configured to obtain a to-be-decoded information sequence; a logic circuit 702 , configured to perform the foregoing polar code decoding method to obtain a decoded information bit; and an output interface circuit 703 , configured to output decoded information. The polar code decoding apparatus 700 may further include a transceiver 720 that obtains the to-be-decoded information sequence through an antenna 730 . In a specific implementation, the polar code decoding apparatus 700 may be a chip or an integrated circuit.
Optionally, when some or all of the polar code decoding method in the foregoing embodiment is implemented by software, as shown in FIG. 8 , a polar code decoding apparatus 800 includes: a memory 801 , configured to store a program; and a processor 802 , configured to execute the program stored in the memory 801 . When the program is executed, the polar code decoding apparatus 800 can implement the polar code decoding method provided in the foregoing embodiment.
Optionally, the memory 801 may be a physically independent unit. Alternatively, as shown in FIG. 9 , a memory 901 and a processor 902 may be integrated together.
Optionally, when some or all of the decoding method in the foregoing embodiment is implemented by software, the polar code decoding apparatus 800 may alternatively include only the processor 802 . The memory 801 configured to store the program is located outside the polar code decoding apparatus 800 . The processor 802 is connected to the memory 801 through a circuit/cable, and is configured to read and execute the program stored in the memory 801 .
The processor 402 and/or the processor 802 may be a central processing unit (CPU), a network processor (NP), or a combination of the CPU and the NP.
The processor 402 and/or the processor 802 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), generic array logic (GAL), or any combination thereof.
The memory in the foregoing embodiments may include a volatile memory, for example, a random-access memory (RAM). Alternatively, the memory may include a non-volatile memory, such as a flash memory, a hard disk drive (HDD), or a solid-state drive (SSD). Alternatively, the memory may include a combination of the foregoing types of memories.
Based on the foregoing polar code decoding method, as shown in FIG. 10 , an embodiment of this application further provides a polar code decoding apparatus 1000 . The polar code decoding apparatus 1000 is configured to perform the foregoing polar code decoding method. The polar code decoding apparatus 1000 includes:
an obtaining unit 1001 , configured to obtain a to-be-decoded information sequence; and a processing unit 1002 , configured to: determine a first sequence of a mother code length N (a reliability ranking sequence whose length is N), and perform a decoding operation on the to-be-decoded information sequence to obtain and output a decoding result.
An embodiment of this application further provides a computer storage medium that stores computer program instructions. When the computer program instructions are executed by a computer, the foregoing polar code encoding method or polar code decoding method is performed.
An embodiment of this application further provides a computer program product including instructions. When the computer program product runs on a computer, the foregoing polar code encoding method or polar code decoding method is performed.
›DESCRIPTION OF EMBODIMENTS · 6 of 6
A person skilled in the art should understand that embodiments of this application may be provided as a method, a system, or a computer program product. Therefore, this application may use a form of hardware only embodiments, software only embodiments, or embodiments with a combination of software and hardware. In addition, this application may use a form of a computer program product that is implemented on one or more computer-usable storage media (including but not limited to a disk memory, a CD-ROM, an optical memory, and the like) that include computer-usable program code.
This application is described with reference to the flowcharts and/or block diagrams of the method, the device (system), and the computer program product according to embodiments of this application. It should be understood that computer program instructions may be used to implement each process and/or each block in the flowcharts and/or the block diagrams and a combination of a process and/or a block in the flowcharts and/or the block diagrams. The computer program instructions may be provided for a general-purpose computer, a dedicated computer, an embedded processor, or a processor of another programmable data processing device to generate a machine, so that the instructions executed by a computer or a processor of another programmable data processing device generate an apparatus for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
The computer program instructions may be stored in a computer-readable memory that can instruct the computer or another programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate an artifact that includes an instruction apparatus. The instruction apparatus implements a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
The computer program instructions may alternatively be loaded onto a computer or another programmable data processing device, so that a series of operations and steps are performed on the computer or the another programmable device. In this way, computer-implemented processing is generated. Therefore, the instructions executed on the computer or the another programmable device provide steps for implementing a specific function in one or more processes in the flowcharts and/or in one or more blocks in the block diagrams.
Although some example embodiments of this application have been described, a person skilled in the art can make changes and modifications to these embodiments once the person skilled in the art learns of the basic inventive concept. Therefore, the following claims are intended to be construed as to cover the embodiments and all changes and modifications falling within the scope of this application.
Clearly, a person skilled in the art can make various modifications and variations to embodiments of this application without departing from the scope of embodiments of this application. This application is intended to cover these modifications and variations provided that they fall within the scope of protection defined by the following claims and their equivalent technologies.
›APPENDIX · 1 of 21
Sequence Group 1: Q1_2048
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,1024,1025,67, 41,144,28,69,42,516,49,74,272,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,1026,1028,137,82,56,27,97,39,259,84,138,145,261,29,43,98,515,88,1032,1040,140,30,146, 71,262,265,161,576,45,100,640,51,148,46,1056,1027,75,266,273,517,104,162,53,193,1029,1088,1 52,77,1033,1030,164,768,1041,1034,268,274,518,54,83,57,521,112,135,78,289,194,85,276,522,58, 168,139,99,86,60,280,89,290,529,524,196,141,101,147,176,142,530,321,31,200,90,545,292,322,53 2,263,149,102,105,304,296,163,92,47,267,385,546,324,208,386,1042,1152,150,153,165,106,55,32 8,536,577,548,113,154,79,269,108,578,224,1036,1057,166,519,552,195,1089,1044,270,641,523,27 5,580,291,59,169,560,114,277,156,1280,1058,87,197,116,170,61,531,525,642,281,278,526,177,29 3,388,1048,1060,91,584,769,198,1031,1153,172,120,201,336,62,282,1090,1536,143,103,178,294,9 3,644,202,592,323,392,297,770,107,180,1035,1064,151,209,284,648,94,204,298,400,608,352,325, 533,155,210,305,547,300,109,1092,1154,1043,1037,184,534,537,115,167,225,326,306,772,157,65 6,329,1072,1038,110,117,212,171,776,330,226,549,1096,1281,538,387,308,216,1045,1156,416,271, 279,158,337,550,672,118,332,579,540,389,173,121,553,199,784,179,228,338,312,704,1059,1282, 390,174,554,581,393,283,122,448,353,561,203,63,340,394,527,582,556,181,1050,1537,1104,1061, 1049,1046,295,285,232,124,205,182,643,562,286,585,1160,1284,299,354,211,401,1288,1062,1538, 1120,185,396,344,586,1091,1065,1168,1052,645,593,1093,1066,535,240,206,95,327,564,1540,10 73,800,402,356,307,301,417,213,568,832,588,186,646,404,227,896,594,1098,1296,1184,1544,131 2,1552,418,302,649,771,1216,1568,360,539,111,331,214,309,188,449,1094,1068,1155,1105,217,40 8,609,596,551,650,229,159,420,310,541,773,610,657,333,119,600,339,218,368,652,230,391,313,1 074,1097,450,542,1039,1344,334,233,555,774,175,123,1157,1076,658,612,341,777,220,314,424,3 95,673,583,1047,1158,355,287,183,234,125,557,660,616,1408,1100,342,316,241,778,1161,1106,56 3,345,452,397,403,207,1080,1051,674,558,785,432,357,187,1121,1063,1283,1108,236,664,624,58 7,780,705,126,242,565,398,1162,1169,346,456,1285,1053,358,405,303,569,244,595,189,566,676,3 61,1067,1122,706,589,215,786,1539,1112,1164,1054,647,348,419,406,464,680,801,362,590,409,57 0,788,597,572,219,311,1170,1095,1286,1289,708,598,601,651,1185,1600,1069,1124,421,792,802,6 11,602,410,1664,1075,231,688,1172,1070,653,248,369,190,364,654,659,335,1099,1290,480,315,2 21,370,1297,1541,1128,1186,613,422,425,451,614,543,235,412,343,372,1077,1217,775,317,222,4 26,453,237,559,833,1176,1101,1188,1792,1292,1298,804,712,834,661,808,779,617,604,433,720,81 6,836,347,897,1542,1078,1107,1081,243,662,1545,1136,454,318,675,618,898,781,376,428,665,73 6,567,840,625,238,1159,1102,1313,1218,1109,1300,1546,1082,359,457,399,787,591,678,434,677,1 192,1163,1123,1110,349,245,458,666,620,363,127,191,782,407,436,626,1084,1304,1113,1314,155 3,1548,571,465,1220,1165,681,246,707,350,1125,1171,1200,1166,599,668,790,460,1554,1345,105 5,1224,249,682,1114,1569,573,411,803,789,709,365,440,628,689,374,423,466,793,250,371,481,13 16,1346,1556,1287,1173,1126,1129,1328,574,413,603,366,468,655,900,805,1320,1187,1116,1071, 1291,1409,1570,1348,615,684,710,429,1232,1410,794,252,373,605,848,690,1174,1177,713,632,48 2,806,427,904,414,223,1189,1130,663,692,835,619,1079,1352,1560,1601,472,455,796,809,1572,11 37,1178,1103,714,721,1293,1132,837,716,864,810,606,912,722,696,1602,1248,1190,1543,377,435, 817,319,621,812,484,430,838,667,1576,1219,1294,1665,1547,1299,488,239,378,459,622,627,1604, 1315,1083,1193,437,380,818,461,496,669,679,724,841,629,1584,1138,1301,1180,1111,1221,351,4 67,438,737,251,462,442,441,1140,1194,1085,1555,1549,1666,1305,1302,1550,1201,469,247,683,8 42,1317,1412,738,899,670,783,849,820,728,928,791,367,901,630,1115,1608,685,844,1793,1222,6 33,711,1196,1144,1225,1360,253,691,1086,1306,1167,1127,824,902,1202,1318,1117,1668,686,740, 850,375,444,470,483,415,1226,1616,1347,1416,485,905,1321,1794,795,473,1131,1204,1175,1233, 1308,1672,1118,1228,634,744,852,960,1322,1424,1632,1376,1349,1557,1179,1234,865,693,1329, 1571,1324,1133,1208,1558,1561,1139,797,906,715,807,1191,1249,1350,1330,474,636,694,254,717, 575,913,798,1796,1181,1680,1353,811,379,697,431,607,489,866,723,486,908,1134,1141,718,813, 476,856,839,725,1236,1195,1800,1354,698,914,752,868,819,814,439,929,1250,1573,490,623,671, 739,916,463,843,381,497,930,1562,1411,1332,1240,1440,1295,1303,1182,1361,1574,1696,1142,13 56,1603,1564,1413,1197,1145,1577,1223,821,726,1808,1203,1252,1362,1336,1728,961,872,1414, 1198,492,631,1578,1605,729,700,443,741,1417,1307,1146,1472,1377,1585,1227,1087,845,920,38 2,822,1364,1418,1551,1606,1580,1205,1319,1309,1256,1148,851,730,498,880,742,445,471,635,12 29,1206,1667,1586,1310,1609,932,687,1323,1378,903,825,500,846,745,826,1235,1425,1209,1420, 732,446,962,936,475,853,1368,1610,867,637,907,487,1669,1617,1559,1264,695,746,1230,1119,82 8,753,1351,1588,854,857,1824,1426,1380,1331,1325,1441,504,799,255,964,1237,1592,1856,1612, 909,719,1210,1670,1428,1251,1920,1618,477,915,638,748,1442,1326,1673,1795,944,869,491,699, 754,858,1384,1563,478,968,383,910,815,976,1135,1355,870,917,1238,1333,727,493,873,701,1212, 1473,1241,1432,1633,1620,1575,1674,1253,1183,1444,1334,931,756,1565,1797,860,499,731,823, 1634,1681,1357,1143,1624,1363,1242,1392,1676,1254,922,874,1415,1337,918,502,1474,1566,933, 743,760,881,1358,1257,1579,1798,1199,1147,1682,1636,494,702,921,501,1365,1801,1244,1338,1 448,1419,1697,1607,1379,1311,1207,1258,1149,1581,1684,1640,1366,1340,1265,1802,1587,1369, 1476,1421,876,847,992,447,1427,1231,733,827,1698,1582,1809,1456,934,882,937,963,1381,1211, 1260,1688,747,505,855,924,734,829,965,938,1648,1611,1804,1729,884,506,749,945,1150,1266,96 6,755,859,940,1589,1422,1370,1480,1382,1429,1327,1593,1268,1619,830,911,871,639,888,479,12 13,1590,946,750,969,508,861,757,970,919,875,862,758,948,1700,1385,1730,1613,1239,1810,1671, 1372,1443,1430,1488,1704,1825,1386,1614,1433,1594,1812,1621,1596,1243,1335,977,923,1732, 1622,1625,1675,1445,1816,1826,1635,1626,1434,1255,1712,972,761,1677,1272,1393,1214,1388,1 678,1683,1359,1504,1339,1245,1394,877,952,495,703,935,978,883,762,503,925,878,735,1637,144 6,1449,1475,993,885,1638,1567,1259,1436,1367,1396,1799,1341,1246,1450,1477,1261,1583,1857, 1828,1736,1858,1685,1832,1803,939,994,1641,1628,1457,1744,980,926,1840,1860,1371,1921,12 67,1686,1478,1342,1699,1642,764,941,1922,1805,967,886,1400,1452,831,947,1689,1760,1591,18 64,507,889,1649,1262,1383,1481,1423,1811,984,751,1615,1702,1458,1701,1373,1269,1482,1690, 1644,1387,1151,1215,1806,1431,1460,1650,1595,1489,942,996,1705,1270,971,890,1731,1374,162 3,1692,1814,1484,1273,1706,509,949,1597,1435,973,1000,892,950,1827,1813,1733,1389,1464,16 52,1713,1398,1447,1490,863,759,1817,1274,1395,1505,1598,1437,1008,510,1627,1390,1492,1679, 1924,1829,979,953,1639,1708,1734,1453,1818,1276,763,974,1397,1629,1872,1714,954,879,981,9 82,1737,1656,1506,1830,1451,1928,1438,1247,1687,1716,927,995,1859,1643,1496,1479,1820,183 3,1738,1745,765,956,1861,1740,1888,1834,887,985,1630,1936,1746,1720,1401,1459,1841,1343,9 97,986,1645,1836,1508,1454,1862,1691,1512,1263,1402,1483,1646,1651,943,891,1461,1404,998, 766,1842,1485,1520,1693,1703,1748,511,988,1865,1653,1375,1491,1462,1761,1275,1486,1466,14 65,1001,951,1493,1271,1707,1866,1762,1923,1002,893,1694,1807,975,894,1873,1844,1752,1952, 1815,1391,1925,1654,1709,1868,1657,1735,1009,955,1277,1715,1848,1926,1710,1764,1874,1399, 1468,1494,1004,1010,1507,1439,1509,1929,1819,1497,1658,1768,1876,1984,957,983,1889,1717,1 821,1930,1739,1831,1498,1660,958,987,1718,1278,1741,1599,1012,999,1937,1822,1835,1403,172 1,1455,1016,767,1631,1513,1890,1747,1510,1932,1742,1837,1500,1880,1863,1749,1722,1938,989, 1003,1776,1892,1843,1838,1463,1953,1514,1647,1695,1763,1940,1487,1867,1405,990,1005,1521, 1954,1845,1750,1985,1896,1516,1655,1753,1724,1467,1765,1869,1944,1406,1846,1875,1754,152 2,1904,1766,1469,959,1011,1495,1659,1956,1711,1927,1849,1013,895,1524,1870,1769,1850,1756, 1470,1986,1960,1499,1877,1891,1661,1931,1511,1719,1770,1852,1777,1878,1881,1528,1823,127 9,1988,1933,1743,1501,1939,1006,1014,1662,1772,1968,1893,1515,1723,1778,1882,1502,1992,10 17,1018,1407,1934,1839,2000,1894,1941,1751,1517,1897,1725,1955,1780,1884,1523,1755,1847,1 946,1898,1942,1526,1957,1767,1784,1905,1518,1726,1945,1525,1900,1871,991,1020,2016,1471,1 757,1851,1958,1906,1961,1987,1771,1529,1879,1948,1758,1853,1007,1015,1989,1962,1908,1530, 1773,1969,1990,1779,1883,1964,1854,1935,1895,1663,1912,1503,1019,1021,1970,1774,1993,153 2,1885,1781,1994,1943,1899,1886,1782,1972,2001,1947,1996,1785,1901,1976,1519,1727,1959,20 02,1907,1786,1527,1949,1902,1759,2017,1909,1963,2018,2004,1950,1788,1965,1991,1910,1855,1 971,1022,1023,1531,1913,2008,1775,1966,2020,1995,1914,1533,1973,1997,2024,1916,1974,1887, 1783,2032,1534,2003,1977,1787,1998,1978,1903,2005,2006,1951,2019,1789,1980,1911,2009,202 1,2010,1967,1915,2022,1790,153 5,2012,2025,1975,2026,1917,1999,1918,2033,1979,2028,2034,19 81,2007,1982,2011,2036,2023,2040,1791,2013,2027,2014,2029,1983,2035,2037,1919,2030,2038,2 041,2042,2015,2044,2031,2039,2043,2045,2046,2047]
›APPENDIX · 2 of 21
Sequence Group 1: Z1_2048
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,91,59,99,107, 174,6,17,21,40,23,45,51,93,29,57,61,100,73,114,119,189,34,63,76,117,81,128,143,202,90,145,155, 228,160,240,262,369,9,18,26,56,30,60,72,109,36,77,64,122,85,133,149,209,44,75,89,144,95,152,1 59,236,103,162,176,252,188,270,286,417,53,92,101,158,115,168,183,267,126,184,201,278,211,29 9,318,452,147,207,231,307,238,319,341,477,259,347,364,497,385,516,552,728,15,25,31,74,39,80, 83,148,48,88,96,157,106,167,171,266,58,97,108,169,118,182,198,282,132,199,208,294,233,313,33 7,469,66,112,127,187,136,200,216,308,156,229,239,321,258,346,359,496,170,247,268,351,279,37 5,387,514,304,402,432,541,456,568,625,729,70,129,151,219,166,237,255,349,175,260,272,368,28 7,386,416,533,194,283,295,396,320,428,454,576,331,462,480,596,504,634,654,825,213,309,324,4 35,352,468,483,618,384,493,515,646,546,657,701,877,415,524,553,684,566,723,745,921,623,760, 777,906,811,950,1021,1196,20,37,41,94,49,98,110,181,50,111,123,190,140,210,222,335,65,124,14 1,225,153,232,245,336,161,244,263,363,284,383,390,513,68,150,163,227,178,248,269,382,186,27 6,288,394,298,426,445,564,185,296,311,425,330,455,471,597,354,485,505,633,523,653,689,863,7 9,173,179,274,193,292,310,418,203,315,323,453,342,476,492,629,261,338,353,479,370,502,522,6 48,404,529,558,678,583,722,747,902,291,366,395,512,424,540,562,710,450,571,589,727,626,769, 791,935,481,624,635,778,649,812,773,965,694,860,878,1031,887,1069,1122,1228,84,191,195,329, 249,345,358,484,275,362,371,507,403,531,555,712,289,397,423,532,434,563,585,731,463,591,615, 765,647,789,824,969,334,427,444,584,470,610,641,774,506,642,655,822,695,807,867,1033,539,6 74,716,861,732,886,904,1058,770,909,908,1110,966,1139,1163,1323,365,457,488,643,530,656,688, 837,559,711,724,879,755,889,907,1067,586,741,775,903,792,920,967,1140,836,979,1018,1166,10 44,1210,1226,1377,632,779,820,968,866,974,1038,1173,876,1035,1062,1220,1104,1239,1292,144 4,890,1070,1136,1259,1154,1295,1277,1450,1194,1341,1353,1512,1383,1554,1581,1668,27,43,52, 102,62,125,142,217,67,146,154,224,165,242,246,372,69,164,172,241,180,293,305,414,204,306,32 8,451,344,472,489,645,71,177,192,297,206,325,339,466,218,348,360,494,374,517,537,658,230,36 7,389,528,419,554,569,698,429,565,592,740,595,764,788,1023,113,205,212,343,226,361,373,509, 253,391,405,549,431,575,590,714,273,411,437,567,465,594,603,752,478,604,614,790,673,813,852, 1034,290,464,474,613,501,640,644,804,519,672,691,831,726,864,880,1063,548,700,733,881,771, 895,937,1105,819,944,988,1141,1019,1171,1212,1375,116,223,243,388,271,410,433,582,285,446,4 67,605,482,622,627,793,314,475,500,628,518,669,685,828,547,696,725,869,753,891,928,1064,340, 508,536,690,570,717,715,892,587,744,761,922,805,940,962,1149,619,772,815,951,829,1001,1020, 1178,855,1032,1052,1221,1109,1241,1293,1445,355,551,574,746,602,768,806,945,667,818,844,1 012,849,1022,1042,1203,675,845,854,1037,893,1047,1093,1238,932,1108,1135,1260,1162,1326,13 44,1453,697,905,926,1065,963,1111,1138,1281,989,1156,1179,1340,1213,1354,1381,1521,1054,11 83,1222,1359,1255,1385,1390,1573,1282,1429,1449,1596,1498,1626,1661,1755,137,254,277,447, 312,473,495,652,322,503,525,671,550,693,730,929,350,538,577,713,593,767,754,934,611,776,810, 978,838,1010,1025,1195,422,588,612,766,666,795,821,1013,670,839,851,1030,865,1043,1057,12 30,676,862,888,1056,931,1092,1123,1261,956,1153,1157,1327,1182,1345,1372,1506,430,659,668, 830,677,848,868,1046,699,894,923,1068,941,1120,1155,1321,814,930,964,1134,990,1167,1186,13 42,1045,1187,1223,1360,1258,1384,1389,1572,850,1000,1036,1170,1055,1219,1234,1374,1101,12 40,1273,1388,1320,1442,1452,1603,1137,1283,1333,1448,1352,1459,1503,1632,1376,1513,1545,1 657,1560,1689,1693,1819,436,679,692,927,794,936,957,1152,823,975,1011,1172,1039,1202,1229, 1373,853,1024,1053,1211,1066,1235,1276,1387,1121,1294,1272,1415,1343,1451,1487,1616,933,1 059,1071,1254,1148,1280,1332,1446,1165,1334,1347,1480,1361,1499,1540,1656,1218,1355,1380, 1507,1391,1555,1561,1681,1443,1589,1602,1707,1627,1730,1740,1810,991,1100,1164,1335,1197, 1346,1358,1502,1227,1382,1386,1544,1428,1558,1597,1692,1231,1414,1447,1588,1486,1604,160 5,1731,1520,1633,1643,1741,1669,1770,1786,1892,1322,1458,1481,1617,1541,1642,1660,1747,15 59,1680,1688,1771,1718,1787,1848,1908,1580,1706,1719,1811,1746,1818,1849,1909,1754,1860,1 861,1926,1893,1927,1968,1969,54,55,86,121,87,130,135,256,104,134,139,280,214,303,317,490,10 5,138,196,302,221,332,381,510,250,380,376,535,409,561,581,758,120,215,235,356,251,379,399,5 43,281,407,413,572,459,608,621,799,316,421,486,617,499,650,681,832,534,683,709,884,734,912, 952,1119,131,220,264,406,300,412,458,599,326,487,438,630,521,661,703,843,378,461,527,682,54 5,706,721,900,579,736,762,938,798,960,986,1181,401,542,573,720,609,748,785,955,638,786,827, 980,847,1005,1040,1232,687,841,897,1009,910,1041,1083,1265,947,1089,1114,1289,1133,1308,13 56,1532,197,257,301,460,333,498,511,702,392,526,556,719,580,743,751,954,408,557,598,749,620, 784,816,982,660,817,842,998,899,1027,1079,1251,440,606,639,797,662,826,858,1014,718,885,91 1,1049,946,1088,1103,1288,750,919,958,1095,981,1129,1143,1306,1006,1160,1204,1337,1242,137 8,1433,1533,448,651,705,871,742,901,943,1091,759,948,970,1118,987,1142,1180,1325,808,983,99 9,1158,1048,1198,1236,1396,1075,1244,1268,1412,1298,1440,1468,1613,857,1015,1060,1207,109 6,1250,1271,1426,1132,1285,1307,1462,1338,1471,1515,1651,1177,1314,1357,1492,1370,1527,15 43,1683,1431,1552,1575,1676,1595,1708,1743,1842,234,327,357,544,393,560,600,783,398,601,63 1,800,664,846,872,1077,439,636,665,875,707,898,917,1078,735,916,953,1113,984,1131,1146,1305, 442,704,737,883,780,924,959,1130,796,976,992,1150,1004,1192,1215,1368,787,1002,1017,1191,1 074,1237,1253,1413,1098,1275,1299,1439,1313,1467,1495,1641,491,757,781,972,803,996,1016,1 184,833,1029,1051,1233,1084,1264,1284,1437,949,1080,1097,1267,1124,1296,1312,1464,1168,13 17,1364,1490,1399,1526,1547,1672,995,1116,1151,1304,1190,1336,1366,1516,1224,1393,1405,15 31,1434,1565,1583,1699,1269,1432,1441,1576,1465,1598,1569,1715,1504,1638,1652,1751,1659,1 785,1802,1862,520,801,809,1073,925,1087,1102,1274,973,1112,1125,1301,1161,1319,1363,1518,9 93,1159,1189,1324,1206,1367,1401,1535,1245,1407,1425,1557,1463,1579,1612,1721,1076,1193,1 214,1400,1252,1420,1455,1570,1300,1456,1469,1610,1505,1593,1647,1753,1331,1484,1524,1639, 1536,1658,1674,1776,1566,1679,1678,1798,1716,1809,1825,1895,1115,1243,1278,1457,1318,147 0,1494,1621,1365,1517,1528,1653,1551,1663,1677,1783,1402,1539,1571,1673,1584,1682,1717,18 12,1620,1725,1738,1828,1764,1846,1858,1925,1438,1577,1608,1720,1646,1722,1760,1833,1650,1 757,1778,1854,1794,1869,1886,1946,1664,1788,1806,1875,1820,1889,1881,1952,1840,1903,1913, 1970,1931,1978,1987,2008,265,377,400,578,420,637,680,859,441,686,708,874,739,914,918,1126, 443,738,756,913,782,997,1007,1176,834,1008,1072,1225,1086,1256,1279,1461,449,763,802,1003, 840,1061,1081,1248,870,1090,1106,1286,1128,1309,1329,1472,896,1117,1145,1316,1185,1362,13 79,1510,1199,1369,1408,1538,1411,1556,1578,1745,607,835,856,1085,882,1107,1127,1303,939,11 47,1169,1349,1201,1395,1406,1522,971,1175,1209,1371,1247,1410,1417,1548,1266,1418,1424,15 82,1483,1599,1634,1756,994,1246,1262,1423,1291,1454,1460,1590,1311,1482,1497,1619,1530,16 44,1654,1779,1348,1514,1537,1655,1567,1671,1701,1795,1607,1704,1726,1813,1739,1831,1850,1 923,616,873,915,1144,961,1174,1205,1398,985,1216,1249,1419,1270,1430,1435,1585,1028,1263, 1290,1436,1310,1477,1493,1614,1339,1508,1529,1649,1549,1665,1690,1780,1082,1302,1328,149 6,1392,1525,1523,1666,1403,1542,1553,1684,1591,1702,1712,1815,1427,1568,1601,1709,1615,17 33,1742,1834,1637,1752,1768,1855,1797,1871,1887,1947,1099,1351,1394,1546,1416,1564,1592,1 705,1475,1606,1624,1736,1629,1744,1762,1845,1485,1625,1636,1759,1667,1767,1791,1868,1696, 1796,1805,1876,1824,1896,1906,1955,1509,1675,1686,1781,1713,1799,1808,1883,1727,1822,183 5,1902,1851,1914,1929,1973,1772,1837,1856,1917,1873,1933,1938,1985,1884,1943,1951,1990,19 62,1998,2007,2027,663,942,977,1217,1026,1257,1287,1466,1050,1297,1315,1479,1350,1501,1534, 1691,1094,1330,1397,1519,1409,1563,1550,1698,1421,1574,1594,1724,1622,1734,1749,1841,118 8,1404,1422,1562,1474,1587,1609,1737,1478,1623,1631,1750,1645,1763,1775,1864,1488,1640,16 62,1774,1695,1790,1803,1877,1710,1817,1823,1897,1836,1907,1920,1966,1200,1473,1476,1618,1 489,1628,1648,1766,1511,1670,1685,1784,1703,1800,1821,1891,1600,1694,1714,1804,1728,1829, 1838,1904,1765,1839,1857,1918,1874,1932,1937,1984,1630,1732,1758,1830,1773,1853,1866,192 2,1793,1870,1879,1936,1890,1944,1954,1993,1807,1885,1899,1950,1912,1957,1965,2000,1924,19 71,1977,2005,1982,2013,2015,2035,1208,1491,1500,1687,1586,1700,1711,1816,1611,1723,1735,1 832,1761,1844,1863,1921,1635,1748,1769,1847,1782,1867,1880,1935,1801,1888,1878,1941,1905, 1953,1961,1996,1697,1777,1789,1872,1814,1882,1898,1948,1827,1900,1911,1958,1919,1963,197 4,2004,1852,1915,1928,1967,1939,1979,1983,2011,1945,1989,1992,2017,1999,2020,2022,2032,17 29,1792,1826,1901,1843,1910,1916,1964,1859,1930,1934,1976,1942,1980,1991,2014,1865,1940,1 949,1988,1960,1994,1995,2021,1972,2001,2003,2023,2009,2028,2030,2040,1894,1956,1959,1997, 1975,2002,2006,2025,1981,2010,2012,2029,2018,2031,2036,2042,1986,2016,2019,2033,2024,203 4,2037,2043,2026,2038,2039,2044,2041,2045,2046,2047]
›APPENDIX · 3 of 21
Sequence Group 1: Q1_4096
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,1024,1025,67, 41,144,28,69,42,516,49,74,272,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,1026,1028,137,82,56,27,97,39,259,84,138,145,261,29,43,98,515,88,1032,1040,140,30,204 8,2049,2050,2052,146,71,262,265,161,576,45,100,640,51,148,46,1056,1027,75,266,273,517,104,1 62,53,193,1029,1088,152,77,1033,1030,164,768,1041,1034,268,274,518,54,83,57,521,112,135,78, 289,194,85,276,522,58,168,139,99,86,60,280,89,290,529,524,196,141,2056,2064,2080,2051,101,1 47,176,142,530,321,31,200,90,545,292,322,532,263,149,102,105,304,296,163,92,47,267,385,546,3 24,208,386,1042,1152,150,153,2053,2112,2057,2054,165,106,55,328,536,577,548,113,154,79,269, 108,578,224,1036,1057,166,519,552,195,1089,1044,270,641,523,275,580,291,2065,2058,2066,217 6,59,169,560,114,277,156,1280,1058,87,197,116,170,61,531,525,642,2060,2081,2113,2068,281,27 8,526,177,2304,2082,2072,2084,293,388,1048,1060,2055,2177,2114,2560,91,584,769,198,1031,11 53,172,120,201,336,62,282,1090,1536,143,103,178,294,93,644,202,592,323,392,297,770,107,180, 1035,1064,151,209,284,648,94,204,298,400,608,352,325,533,155,210,305,547,300,109,1092,1154, 1043,1037,184,534,537,115,167,225,326,306,772,157,656,329,1072,1038,110,117,212,171,776,330, 226,549,1096,1281,538,387,308,216,1045,1156,416,271,279,158,337,550,672,118,332,579,540,38 9,173,121,553,199,784,179,228,338,312,704,1059,1282,390,174,554,581,393,283,2059,2088,2116, 2178,122,448,353,561,203,63,340,394,527,582,556,181,1050,1537,1104,1061,1049,1046,295,285, 232,124,205,182,643,562,286,585,1160,1284,299,354,2067,2061,2096,2062,211,401,1288,1062,15 38,1120,185,396,2120,2305,2069,2180,344,586,1091,1065,1168,1052,645,593,1093,1066,535,240, 206,95,327,564,1540,1073,800,402,356,307,301,417,2083,2306,2074,2561,213,568,832,588,186,6 46,404,227,896,594,1098,1296,1184,1544,1312,1552,418,302,649,771,1216,1568,360,539,111,331, 214,309,2128,2085,2073,2070,188,449,1094,1068,1155,1105,217,408,2184,2308,2312,2086,609,5 96,551,650,229,159,420,310,541,773,610,657,2562,2144,3072,3073,333,119,600,339,218,368,652, 230,391,313,1074,1097,450,542,1039,1344,334,233,555,774,175,123,1157,1076,658,612,341,777, 2115,2089,2192,2076,220,314,424,395,673,583,1047,1158,355,287,183,234,125,557,660,616,1408, 1100,342,316,241,778,1161,1106,563,345,452,397,403,207,1080,1051,674,558,785,432,2117,2090, 2564,2097,2122,2320,2208,2568,357,187,1121,1063,1283,1108,236,664,624,587,780,705,126,242, 565,398,1162,1169,346,456,1285,1053,358,405,2336,2576,2240,2592,303,569,244,595,189,566,6 76,361,1067,1122,706,589,215,786,1539,1112,2118,2092,2179,2129,1164,1054,647,348,419,406,4 64,680,2098,2121,2063,2368,801,362,590,409,570,788,597,572,219,311,1170,1095,1286,1289,708, 598,601,651,1185,1600,1069,1124,421,792,802,611,602,410,1664,1075,231,688,1172,1070,653,24 8,369,190,364,654,659,335,1099,1290,2181,2100,2071,2182,480,315,221,370,1297,1541,1128,118 6,613,422,425,451,614,543,235,412,343,372,1077,1217,775,317,222,426,453,237,559,833,1176,11 01,1188,1792,1292,1298,804,712,2432,2124,3074,3076,2185,2130,2104,2075,2145,2087,2307,213 2,834,661,808,779,617,604,433,720,816,836,347,897,1542,1078,1107,1081,243,662,1545,1136,21 86,2193,2309,2077,454,318,675,618,898,781,376,428,2091,2146,2563,2136,3080,3088,2188,2078, 665,736,567,840,625,238,1159,1102,2194,2119,2310,2313,2209,2624,2093,2148,1313,1218,1109,1 300,2688,2099,2196,2094,1546,1082,359,457,399,787,591,678,434,677,1192,1163,3104,3075,212 3,2314,1123,1110,349,245,458,666,620,363,127,191,782,407,436,626,1084,1304,1113,1314,1553,1 548,571,465,1220,1165,681,246,707,350,1125,1171,1200,1166,2321,2565,2152,2210,2101,2241,30 77,3136,2200,2125,3081,3078,599,668,790,460,1554,1345,1055,1224,2212,2816,3089,3082,249,6 82,1114,1569,573,411,803,789,709,365,440,628,689,374,423,466,2316,2322,2566,2102,2131,2105, 2569,2160,793,250,371,481,1316,1346,1556,1287,1173,1126,1129,1328,574,413,603,366,468,655, 900,805,1320,1187,1116,1071,1291,1409,1570,1348,615,684,710,429,1232,1410,794,252,373,605, 848,690,1174,1177,713,632,482,806,427,904,2183,2126,2337,2242,414,223,1189,1130,2133,2324, 2570,2106,663,692,835,619,1079,1352,1560,1601,472,455,796,809,2216,2187,2147,2134,1572,11 37,1178,1103,714,721,1293,1132,837,716,864,810,606,912,722,696,1602,1248,1190,1543,2108,23 28,2137,2338,377,435,817,319,621,812,484,430,838,667,1576,1219,1294,1665,1547,1299,2577,25 72,2244,2189,488,239,378,459,622,627,1604,1315,2149,2195,2224,2190,1083,1193,437,380,818,4 61,496,669,679,724,841,629,2578,2369,2079,2248,1584,1138,1301,1180,1111,1221,351,467,438,7 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847,2303,3012,3285,3640,1007,1015,1989,1962,3904,3660,2957,2767,1908,1530,1773,1969,1990, 1779,1883,1964,3258,3718,3476,3299,3968,3666,2525,2963,2686,2796,3490,3374,3721,3843,299 2,2917,2539,2747,2802,2906,1854,1935,1895,1663,3432,3611,2526,3016,2431,2958,2863,3024,31 83,3403,2918,2965,1912,1503,1019,1021,3286,3381,2775,2541,2921,2749,3260,3521,3289,3480,3 681,3668,1970,1774,1993,1532,3623,3722,3301,3231,3492,3382,2979,2804,3613,3845,2908,2547, 1885,1781,1994,1943,2779,2871,3682,3729,3405,3191,3672,3411,1899,1886,1782,1972,2001,194 7,1996,1785,3290,3440,3724,3302,2970,2922,3463,3385,2966,2550,3522,3614,2981,2791,2808,29 29,3406,3305,3627,3846,1901,1976,1519,1727,3247,3195,3730,3684,2542,2750,2969,2549,3413,3 849,3292,3386,3496,3467,3745,3655,1959,2002,1907,1786,3427,3359,3255,3306,3197,3629,3732, 3688,1527,1949,1902,1759,3414,3388,3313,3850,3635,3417,3524,3469,2924,2895,3040,2495,347 5,3279,2781,2875,2017,1909,1963,2018,3746,3630,3857,3504,2982,2930,2985,3011,3429,3259,33 08,3736,2795,2553,2903,2972,2782,2877,3013,2986,3696,3659,3852,3777,2004,1950,1788,1965,2 932,2554,2797,2993,1991,1910,1855,1971,3198,3314,3014,2803,2907,2988,3637,3470,3418,3528, 3430,3477,1022,1023,1531,1913,3375,3641,3316,3667,2878,2959,2919,2687,2936,2527,3261,363 8,2994,2798,3017,2556,2909,2805,3018,2967,2008,1775,1966,2020,2923,2910,2806,2996,3748,34 33,3778,3661,3287,3858,3719,3420,1995,1914,1533,1973,3491,3478,3536,3752,1997,2024,1916,1 974,3873,3434,3662,3481,3642,3860,3669,3644,3291,3383,3025,2971,3780,3670,3673,3723,3493, 3864,3874,3683,3674,3482,3303,3760,1887,1783,2032,1534,3020,2809,3725,3320,3441,3262,343 6,3726,3731,3407,3552,3387,3293,3442,2925,3000,2543,2751,2983,3026,2003,1977,1787,1998,29 31,2810,2551,2973,2926,2783,3685,3494,3497,3523,3041,2933,3686,3615,3307,3484,3415,3444,3 847,3389,1978,1903,2005,2006,3294,3498,3525,3309,3631,3905,3876,3784,3906,3733,3880,3851, 2987,3042,3689,3676,1951,2019,1789,1980,3505,3792,3028,2974,3888,3908,3419,3969,1911,200 9,2021,2010,3315,3734,3526,3390,3747,3690,2812,2989,3970,3853,3015,2934,1967,1915,2022,17 90,3448,3500,2879,2995,3737,3808,3639,3912,2555,2937,3697,3310,3431,3529,3471,3859,3032,2 799,3663,3750,3506,3749,3421,3317,3530,3738,3692,3435,1535,2012,2025,1975,3199,3263,3854, 3479,3508,3698,3643,3537,2990,3044,3753,3318,3019,2938,3779,3422,3671,3740,3862,3532,332 1,3754,2557,2997,3645,3483,3021,3048,2026,1917,1999,1918,2940,2998,3875,3861,3781,3437,35 12,3700,3761,3446,3495,3538,2911,2807,3865,3322,3443,3553,3646,3485,3056,2558,3675,3438,3 540,3727,3972,3877,3027,3001,3687,3756,3782,3501,3866,3324,2811,3022,3445,3677,3920,3762, 3002,2927,2033,1979,2028,2034,3029,3030,3785,3704,3554,3878,3499,3976,3486,3295,3735,376 4,1981,2007,1982,2011,2975,3043,3907,3691,3544,3527,3868,3881,3786,3793,2813,3004,3909,37 88,3936,3882,2935,3033,3678,3984,3794,3768,3449,3507,3889,3391,3045,3034,3693,3884,3556,3 502,3910,3739,3560,3311,3450,3531,3694,3699,2991,2939,3509,3452,3046,2814,3890,3533,3568, 3741,3751,3796,2559,3036,3913,3701,2036,2023,2040,1791,3423,3539,3510,3809,3323,3534,351 4,3513,3049,2999,3541,3319,3755,3914,3810,3971,3050,2941,3742,3855,2013,2027,2014,2029,30 23,2942,3921,3892,3800,4000,3863,3439,3973,3702,3757,3916,3705,3783,3057,3003,3325,3763,3 896,3974,3758,3812,3922,3447,3516,3542,3052,3058,3555,3487,3557,3977,3867,3545,3706,3816, 3924,4032,3005,3031,3937,3765,3869,3978,3787,3879,3546,3708,3006,3035,3766,3326,3789,364 7,3060,3047,3985,3870,3883,3451,1983,2035,2037,1919,3769,3503,3064,2815,3679,3561,3938,37 95,3558,3980,3790,3885,3548,3928,3911,3797,3770,3986,3037,3051,3824,3940,3891,3886,3511,4 001,3562,3695,2030,2038,2041,2042,3743,3811,3988,3535,3915,3453,3038,3053,3569,4002,3893, 3798,4033,3944,3564,3703,3801,3772,3515,3813,3917,3992,3454,3894,3923,3802,3570,3952,381 4,3517,3007,3059,2015,2044,2031,2039,3543,3707,4004,3759,3975,3897,3061,2943,3572,3918,38 17,3898,3804,3518,4034,4008,3547,3925,3939,3709,3979,3559,3767,3818,3900,3825,3926,3929,3 576,3871,3327,4036,3981,3791,3549,3987,3054,3062,3710,3820,4016,3941,3563,3771,3826,3930, 3550,4040,3065,3066,3455,3982,3887,4048,3942,3989,3799,3565,3945,3773,4003,3828,3932,357 1,3803,3895,3994,3946,3990,3574,4005,3815,3832,3953,3566,3774,3993,3573,3948,3919,2043,20 45,2046,2047,3039,3068,4064,3519,3805,3899,4006,3954,4009,4035,3819,3577,3927,3996,3806,3 901,3055,3063,4037,4010,3956,3578,3821,4017,4038,3827,3931,4012,3902,3983,3943,3711,3960, 3551,3067,3069,4018,3822,4041,3580,3933,3829,4042,3991,3947,3934,3830,4020,4049,3995,404 4,3833,3949,4024,3567,3775,4007,4050,3955,3834,3575,3997,3950,3807,4065,3957,4011,4066,40 52,3998,3836,4013,4039,3958,3903,4019,3070,3071,3579,3961,4056,3823,4014,4068,4043,3962,3 581,4021,4045,4072,3964,4022,3935,3831,4080,3582,4051,4025,3835,4046,4026,3951,4053,4054, 3999,4067,3837,4028,3959,4057,4069,4058,4015,3963,4070,3838,3583,4060,4073,4023,4074,396 5,4047,3966,4081,4027,4076,4082,4029,4055,4030,4059,4084,4071,4088,3839,4061,4075,4062,40 77,4031,4083,4085,3967,4078,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095]
›APPENDIX · 4 of 21
Sequence Group 1: Z1_4096
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,91,59,99,107, 182,6,17,21,40,23,45,51,93,29,57,61,100,73,118,123,197,34,63,76,121,81,132,147,214,90,149,159, 244,164,256,290,401,9,18,26,56,30,60,72,113,36,77,64,126,85,137,153,221,44,75,89,148,95,156,1 63,252,103,166,184,280,196,298,314,457,53,92,101,162,119,176,191,295,130,192,213,306,223,32 7,346,496,151,219,247,335,254,347,369,533,287,375,396,553,417,576,620,852,15,25,31,74,39,80, 83,152,48,88,96,161,106,171,179,294,58,97,112,177,122,190,206,310,136,207,220,322,249,341,36 5,521,66,116,131,195,140,212,228,336,160,245,255,349,286,374,387,552,178,267,296,379,307,40 7,419,574,332,438,476,609,504,640,705,853,70,133,155,231,170,253,283,377,183,288,300,400,31 5,418,456,593,202,311,323,432,348,472,498,648,359,510,536,676,564,718,738,977,225,337,352,4 79,380,520,539,698,416,549,575,730,614,741,809,1045,455,584,621,780,638,847,869,1105,703,90 0,925,1082,959,1142,1249,1520,20,37,41,94,49,98,114,189,50,115,127,198,144,222,234,363,65,12 8,145,237,157,248,265,364,165,264,291,391,312,415,422,573,68,154,167,239,186,272,297,414,19 4,304,316,426,326,466,489,636,193,324,339,465,358,499,523,677,382,541,565,717,583,737,789,1 027,79,181,187,302,201,320,338,458,215,343,351,497,370,532,548,709,289,366,381,535,402,558, 582,732,444,589,626,774,659,846,871,1078,319,398,427,572,464,608,630,830,494,643,669,851,70 6,909,939,1127,537,704,719,926,733,960,913,1169,794,1024,1046,1259,1059,1313,1390,1556,84, 199,203,357,273,373,386,540,303,390,403,567,439,591,623,832,317,433,463,592,478,631,661,855, 511,671,695,905,731,937,976,1173,362,467,488,660,522,690,725,914,566,726,739,970,795,955,1 031,1265,599,770,836,1025,856,1058,1080,1298,910,1093,1092,1378,1170,1423,1455,1723,397,5 05,544,727,590,740,788,993,627,831,848,1047,891,1061,1083,1311,662,865,915,1079,940,1104,11 71,1424,992,1183,1246,1458,1284,1538,1554,1809,716,927,968,1172,1030,1178,1270,1465,1044,1 267,1306,1548,1368,1583,1672,1932,1062,1314,1420,1623,1446,1675,1645,1938,1510,1753,1773, 2076,1815,2134,2221,2420,27,43,52,102,62,129,146,229,67,150,158,236,169,258,266,404,69,168, 180,257,188,321,333,454,216,334,356,495,372,524,545,729,71,185,200,325,218,353,367,518,230, 376,388,550,406,577,597,742,246,399,421,588,459,622,641,806,473,637,672,864,675,904,936,125 1,117,217,224,371,238,389,405,569,281,423,445,617,475,647,670,834,301,451,481,639,517,674,6 83,888,534,684,694,938,769,961,1012,1266,318,516,526,693,557,724,728,952,579,768,791,987,85 0,1028,1048,1307,616,808,857,1049,911,1067,1129,1369,967,1136,1192,1425,1247,1463,1540,180 7,120,235,259,420,299,450,477,658,313,490,519,685,538,702,707,941,342,527,556,708,578,765,7 81,984,615,804,849,1033,889,1063,1116,1308,368,568,596,790,642,837,835,1064,663,868,901,110 6,953,1132,1166,1433,699,912,963,1143,985,1221,1248,1482,1015,1264,1292,1549,1377,1585,167 3,1933,383,619,646,870,682,908,954,1137,751,966,1004,1236,1009,1250,1282,1531,771,1005,101 4,1269,1065,1287,1349,1582,1124,1376,1403,1624,1454,1726,1756,1949,805,1081,1110,1309,116 7,1379,1422,1649,1193,1448,1483,1752,1541,1774,1813,2089,1294,1491,1550,1779,1615,1817,18 42,2209,1650,1901,1937,2272,2062,2326,2393,2647,141,282,305,491,340,525,551,736,350,559,58 5,767,618,793,854,1117,378,598,649,833,673,907,890,1126,691,924,958,1182,994,1230,1253,1511, 462,668,692,906,750,943,969,1237,766,995,1011,1258,1029,1283,1297,1558,772,1026,1060,1296, 1119,1348,1391,1625,1152,1445,1449,1727,1490,1757,1804,2070,474,743,764,986,773,1008,1032, 1286,807,1066,1107,1312,1133,1388,1447,1721,962,1118,1168,1402,1194,1459,1494,1754,1285,1 495,1551,1780,1622,1816,1841,2208,1010,1220,1268,1462,1295,1547,1578,1806,1357,1584,1641, 1840,1720,1930,1948,2279,1421,1651,1733,1936,1772,1959,2067,2332,1808,2077,2125,2389,214 0,2453,2457,2767,480,775,792,1111,942,1128,1153,1444,971,1179,1231,1464,1271,1530,1557,180 5,1013,1252,1293,1539,1310,1579,1644,1819,1389,1674,1640,1871,1755,1939,2043,2308,1125,12 99,1315,1614,1432,1648,1732,1934,1457,1734,1759,2036,1781,2063,2116,2388,1546,1775,1812,2 071,1843,2135,2141,2441,1931,2245,2278,2479,2327,2554,2584,2754,1195,1356,1456,1735,1521, 1758,1778,2066,1555,1814,1818,2124,1900,2138,2273,2456,1559,1870,1935,2244,2042,2280,228 1,2555,2088,2333,2347,2585,2421,2682,2706,3024,1722,1958,2037,2309,2117,2346,2392,2591,21 39,2440,2452,2683,2518,2707,2888,3108,2220,2478,2519,2755,2590,2766,2889,3109,2646,2900,2 901,3162,3025,3163,3336,3337,54,55,86,125,87,134,139,284,104,138,143,308,226,331,345,546,10 5,142,204,330,233,360,413,570,274,412,408,595,449,629,657,894,124,227,251,384,275,411,435,6 11,309,447,453,644,507,688,701,947,344,461,542,697,555,734,777,988,594,779,829,1056,858,109 6,1148,1387,135,232,292,446,328,452,506,679,354,543,482,710,581,745,811,1003,410,509,587,77 8,613,822,845,1076,651,860,902,1130,946,1164,1190,1489,437,610,645,844,689,872,933,1151,722, 934,979,1184,1007,1225,1280,1576,783,1001,1073,1229,1094,1281,1339,1629,1139,1345,1382,1 661,1401,1700,1776,2108,205,285,329,508,361,554,571,810,424,586,624,839,656,867,875,1150,4 48,625,678,873,700,932,964,1186,744,965,1002,1210,1075,1255,1335,1611,484,686,723,945,746, 978,1018,1238,838,1057,1095,1289,1138,1344,1359,1660,874,1103,1154,1351,1185,1397,1427,16 98,1226,1452,1532,1737,1586,1810,1913,2109,492,735,821,1035,866,1077,1135,1347,895,1140,11 74,1386,1191,1426,1488,1725,956,1187,1211,1450,1288,1522,1580,1852,1319,1588,1636,1868,16 78,1928,2000,2305,1017,1239,1304,1535,1352,1610,1639,1890,1400,1657,1699,1978,1738,2003,2 079,2367,1481,1706,1777,2048,1790,2095,2119,2443,1903,2132,2211,2436,2271,2480,2587,2858, 250,355,385,612,425,628,680,931,434,681,711,948,748,1006,1036,1333,483,720,749,1039,823,10 74,1101,1334,859,1100,1149,1381,1188,1399,1430,1697,486,820,861,1051,928,1108,1155,1398,94 4,1180,1204,1434,1224,1508,1543,1788,935,1222,1245,1507,1318,1581,1613,1869,1354,1643,167 9,1927,1705,1983,2051,2345,547,893,929,1176,951,1208,1244,1492,989,1257,1291,1577,1340,16 28,1656,1925,1141,1336,1353,1631,1392,1676,1704,1980,1460,1709,1784,2046,1855,2094,2127,2 424,1207,1384,1435,1696,1506,1736,1786,2084,1552,1845,1861,2107,1914,2185,2223,2463,1637, 1912,1929,2216,1981,2274,2201,2511,2068,2342,2372,2643,2391,2705,2746,2902,580,949,957,13 17,1109,1343,1358,1642,1177,1380,1393,1689,1453,1711,1783,2086,1205,1451,1505,1724,1534,1 787,1857,2111,1589,1863,1889,2137,1979,2219,2304,2521,1332,1509,1542,1856,1612,1880,1951, 2202,1688,1956,2001,2298,2069,2269,2359,2645,1731,2040,2092,2343,2112,2390,2426,2688,218 6,2439,2438,2722,2516,2753,2773,3027,1383,1587,1646,1957,1710,2002,2050,2313,1785,2085,21 04,2373,2131,2395,2437,2695,1858,2115,2203,2425,2240,2442,2517,2760,2312,2545,2566,2776,2 668,2886,2898,3161,1926,2217,2296,2520,2358,2522,2664,2781,2366,2653,2690,2894,2718,2917, 3006,3234,2404,2708,2750,2963,2768,3013,2997,3264,2856,3083,3117,3338,3179,3378,3415,354 0,293,409,436,650,460,721,776,1019,485,782,828,1038,863,1098,1102,1394,487,862,892,1097,93 0,1209,1227,1480,990,1228,1316,1553,1342,1620,1647,1977,493,903,950,1223,1000,1305,1337,1 608,1034,1346,1370,1658,1396,1701,1729,2020,1072,1385,1429,1708,1493,1782,1811,2074,1523, 1789,1864,2114,1867,2136,2218,2589,687,991,1016,1341,1050,1371,1395,1691,1131,1431,1461,1 761,1529,1847,1862,2090,1175,1467,1537,1791,1591,1866,1873,2128,1630,1874,1888,2222,2039, 2275,2334,2652,1206,1590,1626,1883,1663,1950,1976,2246,1703,2038,2061,2311,2106,2356,237 4,2691,1760,2078,2113,2375,2187,2423,2469,2719,2283,2476,2546,2761,2567,2779,2890,3147,69 6,1037,1099,1428,1165,1466,1533,1854,1189,1544,1609,1875,1638,1902,1915,2241,1256,1627,16 62,1924,1702,2025,2049,2306,1739,2072,2105,2365,2129,2405,2454,2692,1338,1690,1728,2060,1 844,2093,2091,2406,1859,2118,2133,2444,2247,2470,2508,2763,1891,2200,2277,2481,2307,2561, 2586,2782,2341,2644,2680,2895,2721,2919,3007,3235,1355,1763,1846,2126,1872,2184,2268,247 7,2023,2282,2324,2564,2329,2588,2666,2885,2041,2325,2340,2655,2407,2671,2711,2916,2460,27 20,2749,2972,2772,3040,3090,3267,2073,2427,2446,2693,2509,2723,2752,2999,2547,2770,2783,3 082,2891,3118,3177,3361,2684,2829,2896,3121,2961,3193,3206,3413,3004,3211,3255,3438,3314, 3482,3511,3699,747,1134,1181,1545,1254,1621,1659,1982,1290,1677,1707,2027,1762,2065,2110, 2455,1350,1730,1853,2087,1865,2143,2130,2462,1881,2210,2270,2544,2314,2562,2641,2857,150 4,1860,1882,2142,2022,2243,2297,2565,2026,2315,2331,2642,2357,2667,2687,2904,2044,2344,23 94,2686,2459,2710,2747,2973,2482,2765,2771,3041,2828,3091,3144,3322,1528,2021,2024,2310,2 045,2328,2364,2670,2075,2422,2445,2704,2471,2744,2769,3015,2276,2458,2510,2748,2552,2777, 2830,3088,2669,2831,2897,3122,2962,3192,3205,3412,2330,2560,2654,2778,2685,2893,2906,314 6,2717,2918,2975,3204,3014,3232,3266,3461,2751,3005,3043,3254,3116,3285,3321,3492,3160,33 39,3377,3509,3386,3573,3575,3787,1536,2047,2064,2447,2242,2468,2483,2764,2299,2523,2563,2 780,2665,2884,2903,3145,2335,2640,2681,2887,2694,2907,2996,3195,2745,3012,2974,3209,3089, 3265,3313,3480,2461,2689,2709,2960,2762,2998,3042,3252,2775,3080,3111,3286,3123,3315,336 2,3508,2892,3119,3176,3323,3207,3379,3387,3543,3233,3437,3460,3621,3483,3636,3638,3784,25 53,2716,2774,3081,2859,3110,3120,3320,2899,3178,3194,3376,3210,3384,3439,3574,2905,3208,3 253,3436,3312,3462,3463,3637,3360,3493,3495,3639,3541,3720,3722,3852,3026,3284,3287,3481, 3363,3494,3510,3697,3385,3542,3572,3721,3622,3723,3816,3854,3414,3620,3623,3785,3696,378 6,3817,3855,3698,3818,3819,3936,3853,3937,3938,3939,108,109,110,175,111,208,211,276,172,21 0,241,392,260,429,431,666,173,240,242,428,263,442,503,714,270,502,470,759,563,787,803,1070, 174,261,269,468,271,501,515,761,393,561,601,796,653,818,827,1121,430,603,664,825,713,880,91 9,1162,758,921,983,1260,1020,1300,1366,1653,209,262,278,560,394,600,652,813,440,665,604,84 2,753,885,973,1201,500,655,757,920,763,980,999,1276,799,1022,1084,1328,1120,1406,1438,1769, 529,760,797,998,819,1052,1091,1375,878,1112,1161,1414,1203,1475,1514,1848,923,1199,1263,1 487,1278,1515,1573,1909,1363,1595,1632,1953,1685,1984,2032,2384,243,277,395,654,443,712,7 15,972,512,756,784,997,802,1043,1055,1374,562,785,812,1053,826,1090,1158,1418,884,1159,120 0,1470,1273,1501,1569,1897,606,816,879,1115,896,1160,1216,1496,996,1261,1279,1517,1362,159 4,1607,1952,1054,1323,1404,1599,1415,1667,1687,1974,1484,1742,1820,2013,1876,2096,2193,23 85,634,881,975,1219,1042,1277,1331,1597,1071,1364,1408,1652,1439,1686,1768,2005,1146,1419, 1471,1716,1516,1800,1850,2120,1563,1886,1916,2160,1964,2206,2238,2557,1213,1497,1524,182 3,1600,1896,1919,2182,1684,1945,1975,2230,2018,2249,2337,2625,1767,1992,2033,2292,2082,23 79,2413,2713,2191,2448,2489,2674,2535,2786,2865,3104,268,441,469,762,513,786,814,1089,514, 815,843,1122,916,1202,1234,1567,605,876,917,1241,981,1272,1321,1568,1021,1320,1367,1619,1 436,1683,1694,1973,632,974,1023,1243,1086,1324,1405,1682,1114,1412,1440,1714,1474,1798,18 33,2080,1113,1472,1499,1797,1562,1851,1899,2161,1602,1921,1965,2205,1991,2237,2301,2611,6 67,1069,1087,1410,1145,1468,1498,1770,1163,1503,1519,1849,1574,1908,1944,2197,1365,1570,1 601,1911,1654,1962,1990,2232,1744,1997,2054,2286,2147,2378,2415,2662,1443,1634,1715,1972, 1796,2012,2058,2354,1838,2099,2153,2383,2194,2473,2503,2735,1917,2192,2207,2490,2233,253 6,2485,2801,2318,2608,2626,2875,2635,2941,3010,3152,752,1123,1147,1561,1325,1593,1606,192 0,1411,1618,1655,1967,1743,1999,2035,2360,1441,1717,1795,2004,1822,2059,2149,2387,1887,21 55,2179,2465,2231,2501,2556,2805,1566,1799,1832,2148,1898,2174,2225,2486,1966,2226,2239,2 550,2319,2531,2615,2877,2011,2266,2368,2609,2396,2634,2672,2930,2474,2677,2676,2990,2802, 3035,3063,3279,1633,1877,1940,2227,1998,2248,2300,2577,2055,2355,2380,2627,2431,2637,267 5,2939,2150,2409,2487,2663,2504,2712,2803,3036,2576,2815,2862,3066,2912,3130,3150,3349,22 04,2491,2548,2804,2614,2810,2882,3073,2624,2879,2934,3140,2984,3167,3240,3432,2638,2942,3 032,3191,3054,3243,3221,3442,3102,3301,3317,3520,3355,3566,3597,3692,279,471,528,798,602, 877,918,1217,607,922,982,1240,1041,1302,1322,1664,633,1040,1068,1301,1088,1469,1485,1766, 1196,1486,1560,1839,1592,1904,1941,2229,635,1085,1144,1473,1198,1525,1571,1894,1218,1596, 1616,1946,1666,1985,2009,2250,1262,1635,1693,1996,1771,2034,2097,2322,1801,2081,2156,240 8,2159,2464,2500,2867,817,1197,1212,1575,1242,1617,1665,1969,1329,1695,1745,2029,1803,210 3,2154,2362,1409,1751,1825,2083,1893,2158,2167,2428,1910,2168,2178,2502,2265,2537,2600,28 78,1442,1892,1906,2177,1961,2224,2228,2528,1987,2264,2303,2571,2382,2612,2628,2935,2028,2 336,2397,2629,2475,2651,2737,2985,2543,2756,2824,3037,2863,3071,3132,3347,824,1235,1303,1 692,1407,1750,1821,2146,1437,1834,1895,2169,1918,2190,2195,2505,1502,1907,1960,2196,1986, 2261,2293,2568,2019,2320,2381,2617,2429,2639,2728,2936,1572,1968,2008,2302,2098,2369,236 3,2648,2151,2412,2449,2714,2529,2740,2798,3049,2183,2484,2539,2787,2569,2841,2864,3078,26 03,2876,2924,3141,2989,3169,3241,3433,1603,2031,2102,2414,2166,2472,2530,2757,2259,2542,2 592,2852,2597,2866,2910,3115,2267,2593,2602,2881,2649,2915,2969,3166,2732,2988,3031,3196, 3062,3282,3304,3445,2321,2673,2726,2937,2799,2991,3034,3225,2825,3056,3079,3300,3133,331 8,3353,3529,2926,3087,3142,3327,3187,3357,3366,3589,3226,3417,3441,3612,3502,3650,3685,37 91,897,1330,1413,1835,1500,1905,1947,2236,1518,1963,1993,2263,2030,2317,2386,2729,1598,20 10,2121,2361,2157,2467,2430,2734,2175,2488,2534,2814,2578,2850,2869,3103,1794,2152,2176,2 466,2258,2507,2549,2853,2262,2579,2599,2874,2613,2911,2929,3154,2284,2610,2636,2928,2731, 2968,3011,3197,2792,3053,3057,3283,3086,3305,3344,3514,1802,2251,2260,2570,2285,2596,261 6,2914,2323,2650,2715,2940,2741,3008,3055,3277,2538,2730,2800,3030,2826,3067,3094,3302,29 13,3095,3143,3328,3190,3356,3365,3588,2598,2840,2880,3070,2927,3139,3158,3346,2981,3168,3 217,3364,3276,3430,3444,3619,3033,3227,3293,3440,3316,3451,3507,3656,3348,3521,3557,3681, 3576,3717,3725,3863,1824,2287,2316,2727,2506,2736,2793,3052,2551,2811,2851,3072,2883,311 4,3153,3345,2601,2868,2925,3131,2938,3159,3220,3359,3009,3242,3216,3399,3303,3443,3487,36 40,2733,2931,2943,3186,3048,3224,3292,3434,3065,3294,3307,3476,3329,3503,3552,3680,3138,3 319,3352,3515,3367,3567,3577,3709,3431,3605,3618,3739,3651,3762,3772,3850,2827,2980,3064, 3295,3105,3306,3326,3506,3151,3354,3358,3556,3416,3570,3613,3724,3155,3398,3435,3604,348 6,3624,3625,3763,3528,3657,3667,3773,3693,3806,3826,3940,3278,3450,3477,3641,3553,3666,36 84,3779,3571,3708,3716,3807,3750,3827,3892,3956,3596,3738,3751,3851,3778,3862,3893,3957,3 790,3904,3905,3974,3941,3975,4016,4017,530,531,754,841,755,882,887,1360,800,886,899,1416,1 214,1479,1513,1942,801,898,1156,1478,1233,1564,1681,1970,1326,1680,1668,2007,1749,2057,21 45,2434,840,1215,1275,1604,1327,1671,1719,2015,1417,1747,1765,2100,1879,2172,2189,2515,15 12,1793,1922,2181,1955,2234,2289,2572,2006,2291,2353,2632,2398,2696,2788,3003,883,1232,13 72,1746,1476,1764,1878,2163,1526,1923,1826,2198,1989,2253,2339,2583,1670,1885,1995,2290,2 017,2350,2377,2660,2123,2400,2450,2738,2514,2796,2822,3085,1741,2014,2101,2376,2173,2416, 2497,2791,2214,2498,2559,2816,2595,2845,2908,3156,2295,2581,2657,2849,2678,2909,2955,320 1,2759,2965,2994,3237,3029,3260,3324,3544,1157,1361,1477,1884,1565,1954,1971,2338,1712,19 94,2052,2371,2144,2411,2419,2790,1748,2053,2162,2417,2188,2496,2540,2818,2252,2541,2582,2 838,2659,2871,2951,3183,1828,2170,2215,2513,2254,2558,2606,2854,2370,2633,2679,2921,2758, 2964,2983,3236,2418,2703,2794,2971,2817,3021,3039,3258,2846,3060,3124,3297,3170,3350,342 1,3545,1836,2235,2349,2619,2410,2661,2743,2967,2435,2784,2806,3002,2823,3038,3084,3281,25 32,2819,2839,3058,2920,3106,3164,3372,2947,3172,3212,3396,3246,3428,3464,3633,2605,2855,2 932,3127,2976,3182,3215,3410,3028,3229,3259,3454,3298,3467,3523,3675,3077,3270,3325,3496, 3342,3535,3555,3711,3419,3564,3591,3704,3611,3740,3775,3886,1274,1527,1605,2016,1713,205 6,2164,2495,1718,2165,2199,2524,2256,2594,2620,2949,1827,2212,2257,2623,2351,2658,2701,29 50,2399,2700,2789,2993,2820,3023,3046,3257,1830,2348,2401,2631,2492,2724,2795,3022,2512,2 812,2832,3050,2844,3100,3135,3340,2499,2842,2861,3099,2946,3165,3185,3397,2978,3219,3247, 3427,3269,3459,3499,3665,1943,2433,2493,2808,2527,2836,2860,3092,2573,2873,2923,3157,295 6,3200,3228,3425,2785,2952,2977,3203,3016,3244,3268,3456,3068,3273,3332,3490,3375,3534,35 59,3700,2835,3000,3051,3256,3098,3296,3334,3524,3148,3369,3389,3539,3422,3581,3599,3731,3 213,3420,3429,3592,3457,3614,3585,3747,3512,3662,3676,3783,3683,3825,3842,3906,1988,2525, 2533,2945,2725,2959,2982,3218,2809,2992,3017,3249,3061,3275,3331,3526,2833,3059,3097,328 0,3126,3335,3381,3547,3173,3391,3409,3569,3455,3595,3632,3753,2948,3101,3134,3380,3184,34 04,3447,3586,3248,3448,3465,3630,3513,3609,3671,3789,3291,3484,3532,3663,3548,3682,3702,3 812,3582,3707,3706,3838,3748,3849,3869,3943,2995,3171,3222,3449,3274,3466,3498,3645,3333, 3525,3536,3677,3563,3687,3705,3823,3382,3551,3587,3701,3600,3710,3749,3856,3644,3757,377 0,3872,3800,3890,3902,3973,3426,3593,3628,3752,3670,3754,3796,3877,3674,3793,3814,3898,38 34,3913,3930,3994,3688,3828,3846,3919,3864,3933,3925,4000,3884,3951,3961,4018,3979,4026,4 035,4056,1373,1669,1740,2122,1792,2213,2288,2607,1829,2294,2352,2622,2403,2698,2702,3018, 1831,2402,2432,2697,2494,2837,2847,3076,2574,2848,2944,3149,2958,3188,3223,3453,1837,245 1,2526,2843,2580,2933,2953,3180,2618,2966,2986,3230,3020,3261,3289,3468,2656,3001,3045,32 72,3093,3330,3351,3518,3107,3341,3392,3550,3395,3568,3594,3777,2171,2575,2604,2957,2630,2 987,3019,3251,2739,3047,3069,3309,3113,3371,3390,3530,2807,3075,3129,3343,3175,3394,3401, 3560,3202,3402,3408,3598,3479,3615,3658,3792,2834,3174,3198,3407,3239,3446,3452,3606,326 3,3478,3501,3643,3538,3668,3678,3815,3308,3522,3549,3679,3583,3695,3733,3835,3627,3736,37 58,3857,3771,3875,3894,3971,2180,2621,2699,3044,2797,3074,3125,3374,2821,3136,3181,3403,3 214,3418,3423,3601,2872,3199,3238,3424,3262,3473,3497,3634,3299,3516,3537,3673,3561,3689, 3718,3820,2954,3250,3288,3500,3368,3533,3531,3690,3383,3554,3565,3712,3607,3734,3744,385 9,3411,3584,3617,3741,3635,3765,3774,3878,3661,3788,3804,3899,3837,3915,3931,3995,2979,33 11,3370,3558,3400,3580,3608,3737,3471,3626,3648,3768,3653,3776,3798,3889,3485,3649,3660,3 795,3691,3803,3831,3912,3728,3836,3845,3920,3868,3944,3954,4003,3517,3703,3714,3821,3745, 3839,3848,3927,3759,3866,3879,3950,3895,3962,3977,4021,3808,3881,3900,3965,3917,3981,398 6,4033,3928,3991,3999,4038,4010,4046,4055,4075,2255,2742,2813,3137,2870,3189,3231,3458,29 22,3245,3271,3475,3310,3505,3546,3719,2970,3290,3373,3527,3393,3579,3562,3730,3405,3590,3 610,3756,3646,3766,3781,3885,3096,3388,3406,3578,3470,3603,3629,3769,3474,3647,3655,3782, 3669,3799,3811,3908,3488,3664,3686,3810,3727,3830,3843,3921,3742,3861,3867,3945,3880,395 5,3968,4014,3112,3469,3472,3642,3489,3652,3672,3802,3519,3694,3713,3824,3735,3840,3865,39 35,3616,3726,3746,3844,3760,3873,3882,3952,3801,3883,3901,3966,3918,3980,3985,4032,3654,3 764,3794,3874,3809,3897,3910,3970,3833,3914,3923,3984,3934,3992,4002,4041,3847,3929,3947, 3998,3960,4005,4013,4048,3972,4019,4025,4053,4030,4061,4063,4083,3128,3491,3504,3715,360 2,3732,3743,3860,3631,3755,3767,3876,3797,3888,3907,3969,3659,3780,3805,3891,3822,3911,39 24,3983,3841,3932,3922,3989,3953,4001,4009,4044,3729,3813,3829,3916,3858,3926,3946,3996,3 871,3948,3959,4006,3967,4011,4022,4052,3896,3963,3976,4015,3987,4027,4031,4059,3993,4037, 4040,4065,4047,4068,4070,4080,3761,3832,3870,3949,3887,3958,3964,4012,3903,3978,3982,402 4,3990,4028,4039,4062,3909,3988,3997,4036,4008,4042,4043,4069,4020,4049,4051,4071,4057,40 76,4078,4088,3942,4004,4007,4045,4023,4050,4054,4073,4029,4058,4060,4077,4066,4079,4084,4 090,4034,4064,4067,4081,4072,4082,4085,4091,4074,4086,4087,4092,4089,4093,4094,4095]
›APPENDIX · 5 of 21
Sequence Group 1: Q1_8192
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,1024,1025,67, 41,144,28,69,42,516,49,74,272,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,1026,1028,137,82,56,27,97,39,259,84,138,145,261,29,43,98,515,88,1032,1040,140,30,204 8,2049,2050,2052,146,71,262,265,161,576,45,100,640,51,148,46,1056,1027,75,266,273,517,104,1 62,53,193,1029,1088,152,77,1033,1030,164,768,1041,1034,268,274,518,54,83,57,521,112,135,78, 289,194,85,276,522,58,168,139,99,86,60,280,89,290,529,524,196,141,2056,2064,2080,2051,101,1 47,176,142,530,321,31,200,90,545,292,322,532,263,149,102,105,304,296,163,92,47,267,385,546,3 24,208,386,1042,1152,150,153,2053,2112,2057,2054,165,106,55,328,4096,4097,4098,4100,4104,4 112,4128,4099,536,577,548,113,154,79,269,108,578,224,1036,1057,166,519,552,195,1089,1044,2 70,641,523,275,580,291,2065,2058,2066,2176,59,169,560,114,277,156,1280,1058,87,197,116,170, 61,531,525,642,2060,2081,2113,2068,281,278,526,177,2304,2082,2072,2084,293,388,1048,1060,2 055,2177,2114,2560,91,584,769,198,1031,1153,172,120,201,336,62,282,1090,1536,143,103,178,2 94,93,644,202,592,323,392,297,770,107,180,1035,1064,151,209,284,648,94,204,298,400,608,352, 325,533,155,210,305,547,300,109,1092,1154,1043,1037,184,534,537,115,4101,4160,4105,4102,41 13,4106,4114,4224,167,225,326,306,772,157,656,329,1072,1038,110,117,212,171,776,330,226,549, 1096,1281,538,387,308,216,1045,1156,416,271,279,158,337,550,672,118,332,579,540,389,173,12 1,553,199,784,179,228,338,312,704,1059,1282,390,174,554,581,393,283,2059,2088,2116,2178,12 2,448,353,561,4108,4129,4161,4116,4352,4130,4120,4132,203,63,340,394,527,582,556,181,1050, 1537,1104,1061,1049,1046,295,285,232,124,205,182,643,562,286,585,1160,1284,299,354,2067,20 61,2096,2062,211,401,1288,1062,1538,1120,185,396,2120,2305,2069,2180,344,586,1091,1065,116 8,1052,645,593,1093,1066,535,240,4103,4225,4162,4608,4107,4136,4164,4226,206,95,327,564,15 40,1073,800,402,356,307,301,417,2083,2306,2074,2561,213,568,832,588,186,646,404,227,896,59 4,1098,1296,1184,1544,1312,1552,4115,4109,4144,4110,4168,4353,4117,4228,418,302,649,771,12 16,1568,360,539,4131,4354,4122,4609,4176,4133,4121,4118,111,331,214,309,2128,2085,2073,207 0,4232,4356,4360,4134,4610,4192,5120,5121,188,449,1094,1068,1155,1105,217,408,2184,2308,2 312,2086,609,596,551,650,229,159,420,310,541,773,610,657,2562,2144,3072,3073,333,119,600,3 39,218,368,652,230,391,313,1074,1097,450,542,1039,1344,334,233,555,774,175,123,1157,1076,6 58,612,341,777,2115,2089,2192,2076,220,314,424,395,673,583,1047,1158,355,287,183,234,125,5 57,660,616,1408,1100,342,316,241,778,1161,1106,563,345,452,397,403,207,1080,1051,674,558,78 5,432,2117,2090,2564,2097,2122,2320,2208,2568,357,187,1121,1063,1283,1108,236,664,624,587, 780,705,126,242,565,398,1162,1169,346,456,1285,1053,358,405,2336,2576,2240,2592,303,569,24 4,595,189,566,676,361,1067,1122,706,589,215,786,1539,1112,2118,2092,2179,2129,1164,1054,64 7,348,419,406,464,680,2098,2121,2063,2368,801,362,590,409,570,788,597,572,219,311,1170,109 5,1286,1289,708,598,601,651,1185,1600,1069,1124,421,792,802,611,602,410,1664,1075,231,688,1 172,1070,653,248,369,190,364,654,659,335,1099,1290,2181,2100,2071,2182,480,315,221,370,129 7,1541,1128,1186,613,422,425,451,4163,4137,4240,4124,4165,4138,4612,4145,614,543,235,412,3 43,372,1077,1217,775,317,222,426,453,237,559,833,1176,1101,1188,1792,1292,1298,804,712,243 2,2124,3074,3076,2185,2130,2104,2075,2145,2087,2307,2132,834,661,808,779,617,604,433,720,8 16,836,347,897,1542,1078,1107,1081,243,662,1545,1136,2186,2193,2309,2077,454,318,675,618,4 170,4368,4256,4616,4384,4624,4288,4640,898,781,376,428,2091,2146,2563,2136,3080,3088,2188, 2078,665,736,567,840,4166,4140,4227,4177,4146,4169,4111,4416,625,238,1159,1102,2194,2119, 2310,2313,2209,2624,2093,2148,1313,1218,1109,1300,2688,2099,2196,2094,1546,1082,359,457,3 99,787,591,678,434,677,1192,1163,3104,3075,2123,2314,1123,1110,349,245,458,666,620,363,127, 191,782,407,4229,4148,4119,4230,4480,4172,5122,5124,436,626,1084,1304,1113,1314,1553,1548, 571,465,1220,1165,681,246,707,350,1125,1171,1200,1166,2321,2565,2152,2210,2101,2241,3077,3 136,2200,2125,3081,3078,599,668,790,460,1554,1345,1055,1224,2212,2816,3089,3082,249,682,1 114,1569,573,411,803,789,709,365,440,628,4233,4178,4152,4123,4193,4135,4355,4180,689,374,4 23,466,2316,2322,2566,2102,2131,2105,2569,2160,793,250,371,481,4234,4241,4357,4125,4139,4 194,4611,4184,1316,1346,1556,1287,1173,1126,1129,1328,574,413,603,366,468,655,900,805,1320, 1187,1116,1071,1291,1409,1570,1348,5128,5136,4236,4126,6144,6145,6146,6148,615,684,710,42 9,1232,1410,794,252,373,605,848,690,1174,1177,713,632,482,806,427,904,2183,2126,2337,2242, 414,223,1189,1130,2133,2324,2570,2106,663,692,835,619,1079,1352,1560,1601,472,455,796,809, 2216,2187,2147,2134,1572,1137,1178,1103,714,721,1293,1132,4242,4167,4358,4361,4257,4672,4 141,4196,837,716,864,810,606,912,722,696,1602,1248,1190,1543,2108,2328,2137,2338,377,435,8 17,319,621,812,484,430,838,667,1576,1219,1294,1665,1547,1299,2577,2572,2244,2189,488,239,3 78,459,622,627,1604,1315,2149,2195,2224,2190,1083,1193,437,380,818,461,496,669,679,724,841, 629,2578,2369,2079,2248,1584,1138,1301,1180,1111,1221,351,467,4736,4147,4244,4142,5152,51 23,4171,4362,4369,4613,4200,4258,4149,4289,5125,5184,438,737,251,462,2138,2593,2340,2370, 2580,2311,2197,2150,442,441,1140,1194,1085,1555,1549,1666,1305,1302,1550,1201,469,247,683, 842,1317,1412,738,899,2153,2352,2344,2211,670,783,849,820,2140,2095,2315,2433,728,928,791, 367,4248,4173,5129,5126,4260,4864,5137,5130,901,630,1115,1608,685,844,1793,1222,633,711,11 96,1144,1225,1360,253,691,2594,2372,2256,2434,1086,1306,1167,1127,824,902,1202,1318,3090,3 200,2198,2201,4364,4370,4614,4150,4179,4153,4617,4208,2213,2154,2103,2376,1117,1668,686,7 40,850,375,444,470,483,415,1226,1616,4231,4174,4385,4290,4181,4372,4618,4154,1347,1416,48 5,905,1321,1794,795,473,1131,1204,1175,1233,1308,1672,1118,1228,634,744,852,960,2584,2625, 2596,2161,2202,2127,2317,2156,1322,1424,1632,1376,1349,1557,1179,1234,2626,2272,3084,310 5,2214,2567,2600,2243,865,693,1329,1571,1324,1133,1208,1558,1561,1139,797,906,3137,3092,2 318,2689,715,807,1191,1249,2571,2323,2628,2339,1350,1330,474,636,694,254,717,575,913,798,1 796,1181,1680,1353,811,379,2107,2217,2608,2162,4264,4235,4195,4182,4156,4376,4185,4386,69 7,431,607,489,866,723,486,908,2325,2204,3328,3106,2135,2245,2164,2218,1134,1141,718,813,47 6,856,839,725,1236,1195,1800,1354,698,914,752,868,819,814,439,929,2109,2579,2573,2690,1250, 1573,490,623,671,739,916,463,843,381,497,930,1562,1411,1332,1240,2329,2326,2574,2225,2341, 2436,3096,3108,2139,2632,2817,2246,1440,1295,1303,1182,4625,4620,4292,4237,6152,6160,617 6,6147,4197,4243,4272,4238,4626,4417,4127,4296,4186,4641,4388,4418,4628,4359,4245,4198,13 61,1574,1696,1142,1356,1603,1564,1413,1197,1145,1577,1223,821,726,1808,1203,1252,1362,133 6,1728,961,872,1414,1198,3079,3201,2220,2168,2249,2384,2110,2330,492,631,1578,1605,3138,3 584,2191,2151,4201,4400,4392,4259,4188,4143,4363,4481,729,700,443,741,1417,1307,1146,1472, 1377,1585,1227,1087,845,920,382,822,4642,4420,4304,4482,5138,5248,4246,4249,6149,6208,61 53,6150,4261,4202,4151,4424,1364,1418,1551,1606,1580,1205,1319,1309,1256,1148,851,730,222 6,2342,2141,2692,4632,4673,4644,4209,4250,4175,4365,4204,4674,4320,5132,5153,4262,4615,46 48,4291,2250,2640,2371,2440,2345,2818,2155,2228,5185,5140,4366,4737,4619,4371,4676,4387,3 083,3112,2199,2257,498,880,742,445,471,635,1229,1206,1667,1586,1310,1609,932,687,1323,137 8,2332,2696,2142,2252,6161,6154,6162,6272,4155,4265,4656,4210,2346,2448,2656,2400,903,825, 500,846,745,826,1235,1425,1209,1420,732,446,962,936,475,853,1368,1610,867,637,907,487,166 9,1617,2373,2581,2203,2258,2353,2595,2348,2157,3140,3202,3091,3085,1559,1264,695,746,2232, 2582,2585,2163,1230,1119,828,753,1351,1588,854,857,2215,2273,2374,2354,2820,2205,2704,23 77,4373,4252,5376,5154,4183,4293,4212,4266,4157,4627,4621,4738,6156,6177,6209,6164,4377,4 374,4622,4273,6400,6178,6168,6180,1824,1426,1380,1331,1325,1441,504,799,3120,3086,2158,21 65,2260,2219,2824,2378,4389,4484,5144,5156,6151,6273,6210,6656,255,964,1237,1592,2274,259 7,3144,3329,1856,1612,909,719,1210,1670,1428,1251,1920,1618,477,915,638,748,1442,1326,167 3,1795,944,869,491,699,754,858,4187,4680,4865,4294,5127,5249,4268,4216,4297,4432,4158,437 8,5186,5632,4239,4199,1384,1563,478,968,383,910,815,976,2586,2435,2356,2264,3093,3204,246 4,2319,2327,2206,2385,2598,2720,2166,2380,2627,1135,1355,870,917,1238,1333,727,493,873,70 1,1212,1473,1241,1432,1633,1620,2588,2437,2221,2169,2601,2247,2832,2227,2276,2386,2360,27 52,3107,3330,2438,2222,1575,1674,1253,1183,1444,1334,931,756,2602,2629,2441,2331,1565,179 7,860,499,731,823,1634,1681,1357,1143,1624,1363,2170,2496,2401,2609,1242,1392,1676,1254,9 22,874,1415,1337,918,502,1474,1566,4274,4390,4189,4740,4298,4688,4419,4488,933,743,760,88 1,2251,2111,2388,2442,4393,4866,4203,4276,5131,5160,4247,4305,1358,1257,1579,1798,1199,11 47,1682,1636,2575,2630,2604,2229,3098,3585,3152,3109,494,702,921,501,1365,1801,1244,1338, 4380,4744,4190,4300,4394,4496,4704,4448,3097,3094,2343,2333,2280,2172,2253,2230,1448,141 9,1697,1607,2691,2610,2334,2633,1379,1311,1207,1258,1149,1581,1684,1640,1366,1340,1265,18 02,1587,1369,1476,1421,3208,3332,2347,2402,2259,2449,3336,3110,4421,4629,4251,4306,4401,4 643,4396,4205,876,847,992,447,1427,1231,733,827,1698,1582,1809,1456,934,882,937,963,1381,1 211,1260,1688,3586,3168,2233,2444,2392,2634,3139,3113,3216,3100,2693,2641,5188,5250,5139, 5133,4280,4630,4633,4211,747,505,855,924,734,829,965,938,1648,1611,1804,1729,3141,3114,258 3,2288,4263,4321,4422,4402,4868,4253,4752,4425,2254,2143,2375,2612,884,506,749,945,1150,1 266,966,755,859,940,1589,1422,1370,1480,1382,1429,1327,1593,1268,1619,5168,5134,4206,4213, 4308,4267,4872,4426,3588,3121,2848,2450,2404,2355,2349,2465,2261,2616,2880,2636,830,911, 871,639,888,479,1213,1590,946,750,969,508,4322,4645,5192,5377,4634,4483,4404,4312,5141,52 52,4512,4367,4375,4254,4433,4646,861,757,970,919,2234,2694,2452,2275,2944,2642,3146,3344, 3232,3592,3360,3600,2466,2350,2697,2819,3264,3616,2408,2587,875,862,758,948,1700,1385,173 0,1613,2159,2379,2262,2357,1239,1810,1671,1372,4768,4214,4428,4675,4636,4485,4269,4217,14 43,1430,1488,1704,1825,1386,1614,1433,4649,4295,4880,4275,4324,4434,4408,4800,1594,1812,1 621,1596,1243,1335,977,923,1732,1622,1625,1675,2236,2497,3142,3116,1445,1816,1826,1635,32 03,3153,2265,2456,1626,1434,1255,1712,2657,2644,2599,2698,2277,2207,2468,2358,972,761,167 7,1272,5155,5378,4486,4270,4650,4677,4489,4379,2589,2821,2658,2705,2381,2167,2648,2387,13 93,1214,1388,1678,2266,2416,2700,2278,6155,6184,6212,6274,4218,4544,4449,4657,4299,4159,4 436,4490,4623,4678,4652,4277,2439,2361,3122,3145,1683,1359,1504,1339,1245,1394,877,952,49 5,703,935,978,883,762,503,925,2498,2590,3087,3392,2382,2281,2603,2822,878,735,1637,1446,22 23,2171,3205,3124,1449,1475,993,885,2706,2660,2389,2825,2268,2362,2472,2443,2721,2631,309 5,3206,2403,2335,2231,2282,1638,1567,1259,1436,1367,1396,1799,1341,5146,5633,5200,5157,51 45,5142,4391,4381,4328,4220,4301,4278,4739,4658,4382,4681,2173,2605,2708,2664,3456,3148,2 390,2364,2289,2826,3209,3154,2611,2393,2500,2445,5256,5380,4395,4450,6163,6157,6192,6158, 4307,4497,5384,5158,5634,5216,4281,4492,1246,1450,1477,1261,2451,2255,3128,3099,2722,260 6,2833,2480,2405,2235,3169,3111,3331,3156,2284,2712,1583,1857,1828,1736,6216,6401,6165,62 76,4440,4682,5187,5161,1858,1685,1832,1803,2672,2635,2828,2753,5264,5148,4741,4689,5189,5 162,4631,4336,2174,2290,2613,2446,939,994,1641,1628,1457,1744,980,926,1840,1860,1371,1921, 1267,1686,1478,1342,3210,3217,2394,2504,3333,3101,2406,2453,1699,1642,764,941,4302,4191, 4423,4660,5636,5169,4896,4498,1922,1805,967,886,1400,1452,831,947,1689,1760,1591,1864,507, 889,1649,1262,4452,4403,4397,4513,6179,6402,6170,6657,4309,4664,4928,4684,4282,4742,4500, 4323,2351,2617,2292,2643,1383,1481,1423,1811,984,751,1615,1702,1458,1701,1373,1269,2237, 2614,2724,2409,3115,3170,2754,2637,1482,1690,1644,1387,1151,1215,1806,1431,1460,1650,159 5,1489,942,996,1705,1270,4992,4690,5194,5392,5280,5640,5408,5648,2263,2834,3587,3160,971, 890,1731,1374,1623,1692,1814,1484,1273,1706,509,949,1597,1435,973,1000,892,950,1827,1813, 3212,3102,2695,2396,2467,2454,2512,2728,4514,4398,4745,4867,5312,5664,4456,4635,4207,442 7,4310,4405,6224,6181,6169,6166,4284,4545,5190,5164,5251,5201,4313,4504,2849,2410,2638,24 57,2618,2836,2645,2620,2267,2359,3218,3143,3334,3337,2756,2646,2649,2699,3233,3648,3117,3 172,2469,2840,2850,2659,2650,2458,3712,3123,2279,2736,1733,1389,1464,1652,3220,3118,2701, 2296,2417,2238,2412,2702,2707,2383,3147,3338,1713,1398,1447,1490,2528,2363,2269,2418,628 0,6404,6408,6182,4705,4692,4647,4746,4325,4255,4516,4406,4637,4869,4706,4753,863,759,1817, 1274,3345,3589,3176,3234,6658,6240,7168,7169,4429,4215,4696,4435,1395,1505,1598,1437,100 8,510,1627,1390,2661,2470,2473,2499,2662,2591,2283,2460,2391,2420,3125,3265,2823,2365,227 0,2474,1492,1679,1924,1829,979,953,1639,1708,2501,2285,2607,2881,3224,3149,3236,3840,3340, 3346,2852,2760,2882,2709,2856,2827,2665,2652,2481,2768,1734,1453,1818,1276,4314,4464,474 8,4326,4487,4409,5170,5193,4546,4638,5135,5440,4430,4329,4651,4870,4271,4219,5253,5172,47 54,4708,4437,4873,6211,6185,6288,6172,4316,4410,4520,4491,763,974,1397,1629,1872,1714,954, 879,981,982,1737,1656,2864,2884,2395,2945,3590,3126,3155,3129,2291,2710,3593,3184,1506,1 830,1451,1928,2502,2366,2723,2666,4769,4679,5143,5254,4451,4383,4279,4330,4221,4653,4756, 4712,5504,5196,4438,4412,1438,1247,1687,1716,927,995,1859,1643,1496,1479,1820,1833,2946,2 829,2424,2476,2713,2784,2615,2888,1738,1745,765,956,1861,1740,1888,1834,887,985,1630,1936, 2673,2286,3207,3150,1746,1720,1401,1459,1841,1343,997,986,3361,3266,3157,3348,4337,4874, 5257,5202,4659,4441,4548,4493,4499,4303,5176,5147,4770,4654,4881,4528,6213,6186,6660,619 3,6218,6416,6304,6664,3594,3130,2407,2505,1645,1836,1508,1454,4453,4283,5217,5159,5379,52 04,4332,4760,2447,2835,2639,2726,1862,1691,1512,1263,2482,2725,3240,3211,1402,1483,1646,1 651,4720,4683,4876,4801,4222,4338,4661,4494,5258,5265,4442,4552,5381,5149,4454,4501,3171, 3158,2397,2293,2506,2714,2668,2411,2175,2239,2830,2455,943,891,1461,1404,6432,6672,6336,6 688,4399,4665,4340,4691,4285,4662,4772,4457,5163,5218,4802,4685,998,766,1842,1485,2484,26 74,3132,3352,4311,4882,5635,5208,6214,6188,6275,6225,3161,3362,3601,3596,1520,1693,1703,1 748,2619,2513,3268,3213,2729,2294,2755,2398,3173,3219,3248,3214,511,988,1865,1653,1375,14 91,1462,1761,2647,2716,2838,2508,3602,3393,3103,3272,1275,1486,1466,1465,1001,951,1493,12 71,1707,1866,1762,1923,2297,2730,3162,3617,1002,893,1694,1807,975,894,1873,1844,1752,1952, 1815,1391,5260,5150,4743,4444,4515,4502,4560,4776,6194,6217,6159,6464,4897,4458,4686,450 5,4666,4884,4693,4668,4315,4407,5266,5191,5382,5385,4804,4694,4697,4747,5281,5696,2621,24 59,2851,2837,1925,1654,1709,1868,2757,2413,2488,2676,1657,1735,1009,955,1277,1715,1848,19 26,2737,2422,2471,2514,2841,2298,2419,2529,3364,3394,3604,3335,5165,5220,4517,4888,4898,4 707,4698,4506,5760,5171,4327,4784,5268,5166,4749,4344,4465,4286,4460,4750,4755,4431,5195, 5386,6277,6196,6167,6278,4576,4411,4317,4466,3221,3174,3177,3376,2622,2461,2651,2414,251 6,2703,2948,2853,1710,1764,1874,1399,5393,5637,5224,5282,4709,4518,4521,4547,3368,3235,31 64,3119,1468,1494,1004,1010,1507,1439,1509,1929,3339,3457,3618,3396,2663,2732,2758,2477,3 280,3458,2842,2300,4710,4639,4331,4508,4439,4468,5173,5313,2421,2653,2896,2738,3222,3225, 2761,2680,1819,1497,1658,1768,2530,2854,2475,2952,1876,1984,957,983,2462,2271,3237,3178,1 889,1717,1821,1930,1739,1831,1498,1660,4871,4413,4318,4522,4549,4333,4655,4929,2711,2740, 2883,2667,3127,3400,3608,3649,2520,2503,2844,2857,3620,3185,3226,3151,5272,5197,5284,588 8,5388,5394,4900,4808,6528,6220,7170,7172,6281,6226,6200,6171,958,987,1718,1278,1741,1599, 1012,999,2762,2769,3341,3180,2885,2764,2912,2858,6241,6183,6403,6228,4930,4757,4904,4875, 4713,4700,4529,4816,4912,4932,4443,4993,2654,2960,2770,2744,3650,3296,3238,3591,5638,517 4,5203,5177,4339,4758,5641,5232,2425,2483,2865,2367,2669,2860,2532,2478,2886,2715,3624,32 67,3342,3713,3595,3347,2536,2287,2426,2507,2670,2675,3652,3363,3131,3241,2485,2428,2866,2 509,2544,2717,6282,6289,6405,6173,4550,4414,4771,4714,4994,4877,4472,4524,6187,6242,6659, 6232,1937,1822,1835,1403,1721,1455,1016,767,2727,2772,2889,2677,1631,1513,1890,1747,3632, 3186,3349,3228,3159,3269,2399,2515,1510,1932,1742,1837,1500,1880,1863,1749,2486,2785,229 9,2510,2490,2489,3188,3242,7176,7184,6284,6174,4761,4832,4663,4936,4721,4334,5255,5198,62 90,6215,6406,6409,6305,6720,6189,6244,5409,5314,5205,5396,1722,1938,989,1003,1776,1892,18 43,1838,1463,1953,1514,1647,1695,1763,1940,1487,3133,3603,3597,3714,3353,3350,3598,3249,6 784,6195,6292,6190,5642,5178,4455,4553,4495,4883,4687,4774,4530,4773,5288,5259,1867,1405, 990,1005,1521,1954,1845,1750,2517,2295,2731,2890,1985,1896,1516,1655,1753,1724,1467,1765, 3365,3460,2786,2947,2718,2831,2897,2868,2776,2976,2839,2415,2949,2678,3163,3656,2733,289 2,3841,3270,7200,7171,6219,6410,5219,5206,4445,4341,4554,4762,4716,4459,4223,4287,4878,45 03,4532,4722,5180,5400,5209,5410,5649,5644,1869,1944,1406,1846,1875,1754,1522,1904,1766,1 469,959,1011,2681,2759,3244,3192,1495,1659,1956,1711,1927,1849,1013,895,1524,1870,1769,18 50,1756,1470,1986,1960,4667,4561,5316,5261,4777,4342,4803,4446,5221,5267,5296,5262,6417,6 661,6248,6306,6197,6337,7173,7232,6296,6221,7177,7174,4695,4764,4886,4556,5650,5441,5151, 5320,6308,6912,7185,7178,4345,4778,5210,5665,1499,1877,1891,1661,1931,1511,1719,1770,327 3,3408,2301,2739,3134,3354,3215,3175,4669,4507,4899,4885,4805,4461,4536,4724,2872,2950,32 50,3366,3165,3716,2734,2788,2898,2423,2492,2518,2531,2463,3274,3664,3395,3464,2533,2953,3 369,3842,2843,2521,3179,3252,3223,3281,3356,3720,3166,3276,2682,2792,2900,3008,1852,1777, 1878,1881,3370,3472,3680,3424,3397,3605,3227,3282,4785,4470,4519,4562,6412,6418,6662,619 8,2913,2741,3377,3619,3372,3181,3256,3606,6227,6201,6665,6256,4889,4346,4467,4577,3609,31 87,2845,2954,2763,2855,3239,3297,5412,5442,5652,5383,5269,5222,5225,5424,4670,4509,4699,4 462,4564,4751,4996,4901,1528,1823,1279,1988,3398,3378,2522,2684,5416,5283,5212,5167,5387, 5505,5666,5444,4711,4780,4806,4525,5328,5506,4890,4348,2742,2302,2765,2623,2961,2846,384 4,3229,4469,4701,4944,4786,5270,5273,4809,4728,4578,4902,4523,5000,6279,6222,6433,6338,37 28,3401,2859,2427,2745,2479,2655,2537,2914,2771,2534,2956,1933,1743,1501,1939,1006,1014,1 662,1772,1968,1893,1515,1723,1778,1882,1502,1992,1017,1018,1407,1934,4510,4319,5285,5226, 6229,6420,6666,6202,4759,4788,4931,4715,5175,5448,5656,5697,1839,2000,1894,1941,3182,318 9,2766,2861,4568,4551,4892,4905,6312,6283,6243,6230,2524,2904,2887,2773,1751,1517,1897,17 25,5668,5233,5274,5199,4810,4817,5389,5228,4933,4812,4960,4906,4702,5008,4818,4792,5698,5 344,5286,5639,6204,6424,6233,6434,4473,4531,4913,4415,4717,4908,4580,4526,3284,3243,3848, 3402,2746,2962,2800,2916,2867,2862,2487,2977,3298,3621,2538,2671,4934,4763,5672,5315,539 0,5761,5643,5395,6673,6668,6340,6285,4584,4335,4474,4555,4718,4723,5700,5411,6245,6291,63 20,6286,5179,5289,4533,4476,4914,4557,4592,4765,2719,2787,2964,2511,2891,2429,2545,2978,4 775,4820,4937,4725,6674,6465,6175,6344,5680,5234,5397,5276,5207,5317,4447,4563,4534,4833, 4347,4558,6234,6689,6436,6466,6676,6407,6293,6246,4538,4537,5236,5290,3610,3459,3380,328 8,3488,3343,3351,3230,3409,3622,3744,3190,3404,3651,3612,3461,5181,5651,5645,5762,5401,53 98,5646,5297,4565,4343,4779,4938,5413,5508,4834,4995,1955,1780,1884,1523,3245,3193,3625,3 271,2869,2774,3856,3251,1755,1847,1946,1898,3300,3410,3384,3776,3009,2920,3462,3246,2540, 2679,3626,3653,2777,2748,2491,2789,6249,6448,6440,6307,4766,4879,4945,4916,6236,6191,641 1,6529,4824,5024,4887,4463,3465,3355,3194,3520,1942,1526,1957,1767,3425,3633,3275,3135,17 84,1905,1518,1726,2893,2968,2430,2870,1945,1525,1900,1871,3412,3466,3599,3654,3628,3253,3 367,3357,991,1020,2016,1471,3304,3196,2899,2778,4997,4726,5211,5704,4781,4940,5889,5318,2 546,2928,2790,2493,2519,2683,3277,3254,1757,1851,1958,1906,3715,3634,3358,3657,2980,2735, 3371,3426,2951,2873,2548,2894,4729,4807,5292,5240,5321,5456,4349,4787,6690,6468,6352,653 0,5182,5402,5263,5223,2793,2874,3283,3473,3257,3468,2780,2494,3010,2984,2523,2901,3416,36 58,2915,2685,2955,2535,3717,3665,3607,3312,2743,2794,1961,1987,1771,1529,3278,3167,2876,2 801,4920,4998,5298,5414,7186,7296,6294,6297,1879,1948,1758,1853,3399,3636,2902,2905,3872, 3474,3428,3379,3373,3489,2552,2847,2303,3012,3285,3640,1007,1015,1989,1962,3904,3660,295 7,2767,1908,1530,1773,1969,1990,1779,1883,1964,3258,3718,3476,3299,6309,6250,6199,6472,52 13,5764,4782,4836,4946,4471,4540,4566,4579,4511,5322,5712,5443,5512,4581,5001,5417,5890,4 891,4569,5227,5300,5271,5329,5404,5768,5214,5324,4730,4840,4948,5056,6680,6721,6692,6257, 6298,6223,6413,6252,5418,5520,5728,5472,5445,5653,5275,5330,6722,6368,7180,7201,6310,666 3,6696,6339,4961,4789,5425,5667,5420,5229,5304,5654,5657,5235,4893,5002,7233,7188,6414,67 85,4811,4903,5287,5345,3968,3666,2525,2963,2686,2796,3490,3374,6667,6419,6724,6435,5446,5 426,4570,4732,4790,4350,4813,4671,5009,4894,5892,5277,5776,5449,4907,4475,6203,6313,6704, 6258,3721,3843,2992,2917,2539,2747,2802,2906,4793,4527,4703,4585,4962,4819,4582,5004,185 4,1935,1895,1663,3432,3611,2526,3016,6421,6300,7424,7202,6231,6341,6260,6314,2431,2958,28 63,3024,3183,3403,2918,2965,1912,1503,1019,1021,3286,3381,2775,2541,5230,5237,4814,4909,4 572,4952,4935,4821,5332,5291,5896,5450,4794,5010,4848,4964,4915,4910,4535,5025,6205,6675, 6669,6786,5346,5669,4586,4719,4767,4835,5012,4559,2921,2749,3260,3521,3289,3480,3681,366 8,1970,1774,1993,1532,3623,3722,3301,3231,4939,4477,4593,5026,5658,5507,5428,5336,6425,64 22,6670,6321,6437,6532,7192,7204,6235,6728,6913,6342,5536,5391,5399,5278,5457,5670,5792,5 238,5452,5699,5660,5509,5293,5241,5673,5319,4917,4822,5904,5299,3492,3382,2979,2804,3613, 3845,2908,2547,1885,1781,1994,1943,2779,2871,3682,3729,3405,3191,3672,3411,1899,1886,178 2,1972,2001,1947,1996,1785,3290,3440,3724,3302,5348,5458,5432,5824,5057,4968,5510,5294,71 75,7297,6316,6264,6345,6480,6206,6426,4588,4727,5674,5701,7234,7680,6287,6247,2970,2922,3 463,3385,2966,2550,3522,3614,4825,4796,4539,4837,5513,5403,5242,5568,2981,2791,2808,2929, 3406,3305,3627,3846,1901,1976,1519,1727,3247,3195,3730,3684,2542,2750,2969,2549,3413,384 9,3292,3386,5473,5681,5323,5183,4941,5016,4478,4918,5460,5514,5647,5702,5676,5301,5415,54 05,3496,3467,3745,3655,1959,2002,1907,1786,3427,3359,3255,3306,3197,3629,3732,3688,1527,1 949,1902,1759,3414,3388,3313,3850,5352,5244,4947,4826,6322,6438,6237,6788,3635,3417,3524, 3469,2924,2895,3040,2495,3475,3279,2781,2875,2017,1909,1963,2018,6346,6736,6467,6536,644 1,6914,6251,6324,7179,7208,6295,6353,4594,4976,4838,4541,3746,3630,3857,3504,2982,2930,29 85,3011,4567,4731,5325,5302,5763,5682,5406,5705,3429,3259,3308,3736,2795,2553,2903,2972,5 028,4783,5419,5474,6428,6792,6238,6348,2782,2877,3013,2986,3696,3659,3852,3777,6442,6544, 6752,6496,4999,4921,4596,4942,4841,4922,5331,5521,5305,5516,4828,4542,5058,5032,4571,494 9,5464,5706,4963,4733,2004,1950,1788,1965,2932,2554,2797,2993,1991,1910,1855,1971,3198,33 14,3014,2803,5003,4583,5765,5713,6469,6677,6299,6354,6449,6691,6444,6253,7236,7298,7187,7 181,2907,2988,3637,3470,3418,3528,3430,3477,5655,5360,4791,4842,6328,6678,6681,6259,5326, 5215,4924,4849,5447,5684,4950,4953,6311,6369,6470,6450,6916,6301,6800,6473,1022,1023,153 1,1913,3375,3641,3316,3667,2878,2959,2919,2687,2936,2527,3261,3638,5920,5522,5476,5427,54 21,5537,4600,4895,7216,7182,6254,6261,6356,6315,6920,6474,2994,2798,3017,2556,2909,2805,3 018,2967,2008,1775,1966,2020,2923,2910,2806,2996,3748,3433,3778,3661,3287,3858,3719,3420, 4351,5060,5333,5688,6370,6693,7240,7425,1995,1914,1533,1973,3491,3478,3536,3752,1997,202 4,1916,1974,3873,3434,3662,3481,3642,3860,3669,3644,3291,3383,3025,2971,5952,5708,5005,48 15,5306,5766,5524,5347,3780,3670,3673,3723,3493,3864,3874,3683,6016,5714,4573,5011,4734,4 844,5538,5422,3674,3482,3303,3760,1887,1783,2032,1534,3020,2809,3725,3320,3441,3262,3436, 3726,5769,5891,5040,4965,4587,4795,4850,4954,5480,5659,4574,5064,4479,5006,4911,5072,668 2,6531,6452,6360,7189,7300,6560,6415,6423,6302,6481,6694,6816,6262,6476,6723,5231,5451,49 66,5013,5334,5429,4823,4589,4969,4797,5308,5569,5337,5528,5729,5716,3731,3407,3552,3387,3 293,3442,2925,3000,6684,6533,6317,6265,6697,6343,6928,6323,2543,2751,2983,3026,2003,1977, 1787,1998,2931,2810,2551,2973,2926,2783,3685,3494,6372,6482,6456,6848,7203,7426,6534,631 8,5671,5770,5349,5279,5540,5430,5027,4852,6698,6725,6537,6427,5661,5893,4956,4595,4827,49 19,5730,5777,5453,5239,5720,5459,6266,6592,6497,6705,5338,5488,5772,5350,3497,3523,3041,2 933,3686,3615,3307,3484,5018,4970,5511,5433,5014,4598,5570,5662,3415,3444,3847,3389,1978, 1903,2005,2006,5029,4839,4856,4977,6347,6207,6484,6538,3294,3498,3525,3309,3631,3905,387 6,3784,3906,3733,3880,3851,2987,3042,3689,3676,5454,5353,5675,5894,5295,5243,5778,5732,66 71,6726,6700,6325,7194,7681,7248,7205,4590,4798,5017,4597,5461,5897,5340,5434,7193,7190,6 439,6429,6376,6268,6349,6326,1951,2019,1789,1980,3505,3792,3028,2974,3888,3908,3419,3969, 1911,2009,2021,2010,5544,5515,5793,5703,6787,6706,6430,6729,5475,5407,5303,5354,5245,567 7,5780,5736,5462,5436,5361,5898,5683,5465,5572,5517,7304,7428,6443,6498,6355,6545,7432,72 06,4972,4943,5088,4543,5523,5327,4829,4923,5794,5678,5905,5552,5030,4978,5033,5059,5477,5 307,5356,5784,7682,7264,6329,6540,6488,6730,7235,7209,7312,7196,6789,6737,4843,4601,4951, 5020,4830,4925,5061,5034,5744,5707,5900,5825,7237,7210,6679,6384,6350,6239,6471,6708,498 0,4602,4845,5041,5246,5362,5062,4851,4955,5036,5685,5518,3315,3734,3526,3390,3747,3690,28 12,2989,3970,3853,3015,2934,1967,1915,2022,1790,5466,5576,5478,5525,5423,5689,5364,5715,3 448,3500,2879,2995,3737,3808,3639,3912,7684,7217,6944,6546,6500,6451,6445,6561,6357,6712, 6976,6732,4926,5007,4967,4735,2555,2937,3697,3310,3431,3529,3471,3859,3032,2799,3663,375 0,3506,3749,3421,3317,4984,4575,5309,5686,5042,4846,5065,4604,4957,4853,5066,5015,6330,67 90,6548,6371,3530,3738,3692,3435,1535,2012,2025,1975,3199,3263,3854,3479,3508,3698,3643,3 537,2990,3044,3753,3318,3019,2938,3779,3422,3671,3740,3862,3532,3321,3754,2557,2997,7040, 6738,7242,7440,7328,7688,7456,7696,6562,6446,6793,6915,7360,7712,6504,6683,3645,3483,302 1,3048,2026,1917,1999,1918,2940,2998,3875,3861,3781,3437,3512,3700,4971,4958,4854,5044,57 96,5481,5826,5709,3761,3446,3495,3538,2911,2807,3865,3322,3443,3553,3646,3485,3056,2558,3 675,3438,6255,6475,6358,6453,5335,5906,5767,5468,5539,5526,5584,5800,5921,5482,5710,5529, 5690,5908,5717,5692,5339,5431,5073,5019,5828,5718,5721,5771,6332,6593,7238,7212,5541,591 2,5922,5731,7299,7249,6361,6552,3540,3727,3972,3877,3027,3001,3687,3756,3782,3501,3866,33 24,2811,3022,3445,3677,3920,3762,3002,2927,2033,1979,2028,2034,5722,5530,5351,5808,6753,6 740,6695,6794,3029,3030,3785,3704,3554,3878,3499,3976,3486,3295,3735,3764,1981,2007,1982, 2011,2975,3043,3907,3691,3544,3527,3868,3881,3786,3793,2813,3004,3909,3788,3936,3882,293 5,3033,3678,3984,3794,3768,3449,3507,3889,3391,3045,3034,3693,3884,3556,3502,6373,6303,65 64,6454,5068,4857,5773,5368,6685,6917,6754,6801,6477,6263,6744,6483,5489,5310,5484,5774,6 362,6512,6796,6374,6535,6457,7218,7241,5779,5455,5600,5435,5341,5490,4973,5048,4591,4799, 5031,5074,4979,4858,4599,5021,6594,6686,7183,7488,6478,6377,6699,6918,4974,4831,5733,554 2,6319,6267,7301,7220,5545,5571,5089,4981,6802,6756,6485,6921,6364,6458,6568,6539,6817,67 27,7191,7302,6499,6431,6327,6378,5734,5663,5355,5532,5463,5492,5895,5437,3910,3739,3560,3 311,3450,3531,3694,3699,6269,6701,6804,6760,7552,7244,6486,6460,6385,6922,7305,7250,6707, 6489,6596,6541,5342,5546,5573,5357,6547,6351,7224,7195,6818,6702,6929,6576,6501,6331,726 5,7207,7427,7252,6380,6808,5679,5953,5924,5832,5954,5781,5928,5899,6768,6731,6924,6849,29 91,2939,3509,3452,3046,2814,3890,3533,6270,6386,6709,6542,5035,5090,5737,5724,5553,5840,5 076,5022,5936,5956,5467,6017,5363,5782,5574,5438,7306,7313,6490,6600,7429,7197,6502,6549, 5795,5738,4860,5037,6018,5901,5063,4982,5496,5548,4927,5043,5785,5856,5687,5960,4603,498 5,5745,5358,3568,3741,3751,3796,2559,3036,3913,3701,2036,2023,2040,1791,3423,3539,3510,38 09,3323,3534,3514,3513,3049,2999,3541,3319,3755,3914,3810,3971,3050,2941,3742,3855,2013,2 027,2014,2029,3023,2942,3921,3892,3800,4000,3863,3439,3973,3702,3757,3916,6447,6713,6388, 6739,5479,5577,5519,5907,5080,4847,5711,5798,5554,5797,5469,5365,3705,3783,3057,3003,332 5,3763,3896,3974,6333,6710,6820,6505,7211,7266,6850,6733,5578,5786,5740,5483,5247,5311,59 02,5527,5556,5746,5691,5585,5038,5092,5801,5366,6359,6930,7683,7256,5067,4986,5827,5470,5 719,5788,5910,5580,5369,5802,4605,5045,5693,5531,5069,5096,4988,5046,5923,5909,7308,7198, 6791,6492,6563,6550,6608,6824,6945,6506,6734,6553,6714,6932,6741,6716,6363,6455,7314,723 9,7430,7433,6852,6742,6745,6795,7329,7744,7213,7268,6565,6936,3758,3812,3922,3447,3516,35 42,3052,3058,6946,6755,6746,6554,7808,7219,6375,6832,5829,5485,5560,5748,7316,7214,6797,6 392,3555,3487,3557,3977,3867,3545,3706,3816,6513,6334,6508,6798,6803,6479,7243,7434,5809, 5494,5543,5586,6624,6459,6365,6514,4959,4855,5913,5370,7441,7685,7272,7330,5491,5601,569 4,5533,5104,4606,5723,5486,6757,6566,6569,6595,6758,6687,6379,6556,3924,4032,3005,3031,39 37,3765,3869,3978,6487,6516,7221,7361,6919,6461,6366,6570,3787,3879,3546,3708,3006,3035,3 766,3326,5588,5775,6020,5925,5075,5049,5735,5804,3789,3647,3060,3047,3985,3870,3883,3451, 6597,6381,6703,6977,7320,7245,7332,7936,7436,7442,6948,6856,6978,6805,6952,6923,1983,203 5,2037,1919,3769,3503,3064,2815,6761,6748,6577,6864,5830,5549,5914,5372,4859,5070,5493,57 25,5968,5810,5050,4975,5077,5078,5833,5752,6960,6980,6491,7041,3679,3561,3938,3795,3558,3 980,3790,3885,7686,7222,7251,7225,6387,6806,7689,7280,5602,5926,5547,6024,6598,6462,6819, 6762,5534,5343,5783,5812,5023,5091,5955,5739,5592,5575,5916,5929,7042,6925,6520,6572,680 9,6880,6711,6984,5834,5841,4861,5052,5957,5836,5984,5930,4983,5081,5726,6032,6769,6382,73 03,7246,5842,5816,5497,5555,5937,5439,5093,5082,7457,7362,7253,7444,7690,7226,6503,6601,5 741,5932,5604,5550,3548,3928,3911,3797,3770,3986,3037,3051,6543,6931,6735,6822,5958,5787, 5608,5359,3824,3940,3891,3886,3511,4001,3562,3695,6578,6821,7336,7307,5498,5579,5742,574 7,7267,7254,6493,6389,6602,6810,6764,6507,6271,6335,6926,6551,5039,4987,5557,5500,5094,48 62,5938,5581,6580,6770,7228,7448,2030,2038,2041,2042,3743,3811,3988,3535,7257,7458,7697,7 692,5616,5789,5799,5844,3915,3453,3038,3053,3569,4002,3893,3798,4033,3944,3564,3703,3801, 3772,3515,3813,6715,6609,7364,7309,6825,6390,6851,6494,7269,7315,7344,7310,4607,5084,596 1,5749,5471,5587,5558,5857,6743,6812,6934,6604,7698,7489,7199,7368,5371,5582,5562,5561,50 97,5047,5589,5367,5803,5962,5858,6019,3917,3992,3454,3894,3923,3802,3570,3952,6393,6826,7 258,7713,5098,4989,5790,5903,5071,4990,5969,5940,5848,6048,5911,5487,6717,6555,6947,6933, 6021,5750,5805,5964,3814,3517,3007,3059,2015,2044,2031,2039,6853,6509,6584,6772,5753,583 1,5105,5051,5373,5811,5944,6022,6833,6518,6567,6610,6937,6394,6515,6625,7460,7490,7700,74 31,3543,3707,4004,3759,3975,3897,3061,2943,7317,7270,7273,7472,6718,6557,6747,6510,6612,6 799,7044,6949,5806,5860,5970,5495,7464,7331,7260,7215,5564,5590,5100,5106,3572,3918,3817, 3898,3804,3518,4034,4008,5603,5535,5605,6025,7435,7553,7714,7492,6759,6828,6854,6573,737 6,7554,6938,6396,3547,3925,3939,3709,3979,3559,3767,3818,3900,3825,3926,3929,3576,3871,33 27,4036,6517,6749,6992,6834,7318,7321,6857,6776,5915,5593,5754,5864,6626,6950,6571,7048,5 972,6080,5053,5079,6558,6367,7333,7274,5985,5813,5917,6026,5835,5927,5594,5756,6807,6836, 6979,6763,7223,7496,7704,7745,3981,3791,3549,3987,3054,3062,3710,3820,6616,6599,6940,695 3,7716,7281,7322,7247,5054,5083,5814,5374,5837,5695,5108,5095,6858,6865,7437,7276,6981,68 60,7008,6954,6750,7056,6866,6840,7746,7392,7334,7687,4016,3941,3563,3771,3826,3930,3550,4 040,6521,6579,6961,6463,6765,6956,6628,6574,6982,6811,7720,7363,7438,7809,7691,7443,3065, 3066,3455,3982,3887,4048,3942,3989,6632,6383,6522,6603,6766,6771,7748,7459,7227,7337,658 1,6524,6962,6605,6640,6813,6033,5918,5931,5499,5817,5551,5112,4863,6823,6868,6985,6773,57 27,5609,5986,5843,3799,3565,3945,3773,4003,3828,3932,3571,7728,7282,7445,7324,7255,7365,6 495,6611,5606,6028,5838,5933,5596,5976,5959,5845,6582,6881,6395,6606,6586,6585,7284,7338, 5818,6034,5085,5099,5872,5988,5939,5934,5559,6049,5610,5743,5791,5859,6036,5583,7229,769 9,7693,7810,7449,7446,7694,7345,3803,3895,3994,3946,3990,3574,4005,3815,5963,5501,5086,51 01,5617,6050,5941,5846,3832,3953,3566,3774,3993,3573,3948,3919,6613,6391,6827,6986,6081,5 992,5612,5751,5849,5820,5563,5861,7461,7556,6882,7043,6814,6927,6993,6964,6872,7072,6935, 6511,2043,2045,2046,2047,3039,3068,4064,3519,7045,6774,7259,7752,6829,6988,7937,7366,596 5,6040,5502,5942,5971,5850,5618,6000,5862,5565,5055,5107,6777,6855,7340,7288,5591,5755,60 52,5807,6023,5945,5109,4991,5620,5966,5865,5946,5852,5566,6082,6056,3805,3899,4006,3954,4 009,4035,3819,3577,5595,5973,5987,5757,6027,5607,5815,5866,7369,7504,6397,6835,7230,7450, 7311,7271,6968,7046,7346,7462,7261,7812,6830,6884,3927,3996,3806,3901,3055,3063,4037,401 0,6994,6519,6588,6614,6627,6559,7370,7760,3956,3578,3821,4017,4038,3827,3931,4012,7491,75 60,6629,7049,7465,7938,6939,6617,7275,7348,7319,7377,7452,7816,7262,7372,6778,6888,6996,7 104,5948,5873,5974,5977,7466,7568,7776,7520,7493,7701,7323,7378,7009,6837,7473,7715,7468, 7277,7352,7702,7705,7283,6941,7050,6859,6951,7335,7393,3902,3983,3943,3711,3960,3551,306 7,3069,5624,5919,5375,6084,7494,7474,6618,6780,6838,6398,6861,6719,7057,6942,7940,7325,78 24,7497,6955,6523,6841,6575,6751,6633,7010,6867,6630,7052,6029,5839,5597,6035,5102,5110,5 758,5868,6064,5989,5611,5819,4018,3822,4041,3580,3933,3829,4042,3991,5874,5978,5598,6088, 5113,5114,5503,6030,5935,6096,5990,6037,7278,7285,6862,6957,6620,7000,6983,6869,5847,561 3,5993,5821,7380,7339,7944,7498,6842,7058,6896,7012,6963,6958,6583,7073,7394,7717,6634,67 67,3947,3934,3830,4020,4049,3995,4044,3833,6815,6883,7060,6607,6987,6525,6641,7074,7706,7 555,7476,7384,7584,7439,7447,7326,7505,7718,7840,7286,7500,7747,7708,7557,6051,5876,5980, 5619,7341,7289,7721,7367,3949,4024,3567,3775,4007,4050,3955,3834,6965,6870,7952,7347,585 1,5943,6042,5994,7396,7506,7480,7872,7105,7016,7558,7342,3575,3997,3950,3807,4065,3957,40 11,4066,6636,6775,7722,7749,6873,6844,6587,6885,7561,7451,7290,7616,6038,5622,6053,5863,7 521,7729,7371,7231,5880,6001,5614,5822,4052,3998,3836,4013,4039,3958,3903,4019,6989,7064, 6526,6966,6041,5621,5996,5967,7508,7562,7695,7750,7724,7349,7463,7453,5087,5116,6112,556 7,7400,7292,6995,6874,6642,7024,6886,6589,6615,6779,7373,7350,5853,5947,6054,6002,7811,77 30,7454,7753,7076,6831,7467,7522,7047,6969,6644,6990,6889,6970,7379,7569,7353,7564,6876,6 590,3070,3071,3579,3961,4056,3823,4014,4068,7106,7080,6619,6997,7512,7754,7011,6781,7051, 6631,7813,7761,7703,7408,6839,6890,6057,6083,5867,5625,7374,7263,6972,6897,5975,6044,585 4,5949,7495,7732,6998,7001,7968,7570,7524,7475,7469,7585,6648,6943,6399,7108,7381,7736,51 03,5111,6085,6058,8000,7756,7053,6863,6004,5626,5869,6065,4043,3962,3581,4021,4045,4072,3 964,4022,6086,5875,5979,6060,7354,7814,7572,7395,8064,7762,6621,7059,6782,6892,7586,7470, 7817,7939,7088,7013,6635,6843,6898,7002,5950,6031,5991,5759,7528,7707,6622,7112,6527,705 4,6959,7120,7279,7499,7014,7061,6008,5599,5115,5117,7382,7477,6871,6637,7017,6845,7356,76 17,7385,7576,7777,7764,6066,5870,6089,5628,7719,7818,7397,7327,7588,7478,7075,6900,7709,7 941,7004,6643,5981,5877,6090,6039,6875,6967,7778,7825,7501,7287,7768,7507,5995,5982,5878, 6068,3935,3831,4080,3582,4051,4025,3835,4046,6097,6043,6092,5881,7386,7536,7820,7398,706 6,7018,7559,7481,7062,6646,7618,7710,7077,6887,6904,7025,7502,7401,7723,7942,4026,3951,40 53,4054,3999,4067,3837,4028,5997,6072,5615,5823,7343,7291,7826,7780,6638,6846,7065,6645,7 509,7945,7388,7482,7592,7563,7841,7751,6055,6098,6003,5882,7523,7455,7351,7402,7293,7725, 7828,7784,5623,6045,5998,5855,7510,7484,7409,7946,7731,7513,7620,7565,7020,6991,7136,659 1,7571,7375,6877,6971,6113,6005,6059,6114,7842,7726,7953,7600,7078,7026,7081,7107,7525,73 55,7404,7832,6891,6649,6999,7068,6878,6973,7109,7082,7792,7755,7948,7873,6100,6046,5884,6 061,7028,6650,6893,7089,6087,6006,5951,6067,7294,7410,7110,6899,7003,7084,7733,7566,7514, 7624,7526,7573,5118,5119,5627,6009,7471,7737,7412,7763,3959,4057,4069,4058,4015,3963,407 0,3838,6974,7055,7015,6783,7032,6623,7357,7734,7090,6894,7113,6652,7005,6901,7114,7063,61 04,5871,6062,6116,7019,7006,6902,7092,7844,7529,7874,7757,7383,7954,7815,7516,6091,6010,5 629,6069,7587,7574,7632,7848,3583,4060,4073,4023,4074,3965,4047,3966,6093,6120,6012,6070, 7969,7530,7758,7577,7738,7956,7765,7740,7387,7479,7121,7067,7876,7766,7769,7819,7589,796 0,7970,7779,7770,7578,7399,7856,5983,5879,6128,5630,7116,6905,7821,7416,7537,7358,7532,78 22,7827,7503,7648,7483,7389,7538,7021,7096,6639,6847,7079,7122,6099,6073,5883,6094,7027,6 906,6647,7069,7022,6879,7781,7590,7593,7619,7137,7029,7782,7711,7403,7580,7511,7540,7943, 7485,6074,5999,6101,6102,7390,7594,7621,7405,7727,8001,7972,7880,8002,7829,7976,7947,708 3,7138,7785,7772,6047,6115,5885,6076,7601,7888,7124,7070,7984,8004,7515,8065,6007,6105,61 17,6106,7411,7830,7622,7486,7843,7786,6908,7085,4081,4027,4076,4082,4029,4055,4030,4059,8 066,7949,7111,7030,6063,6011,6118,5886,7544,7596,6975,7091,7833,7904,7735,8008,6651,7033, 7793,7406,7527,7625,7567,7955,7128,6895,7759,7846,7602,7845,7517,7413,7626,7834,7788,753 1,5631,6108,6121,6071,7295,7359,7950,7575,7604,7794,7739,7633,7086,7140,7849,7414,7115,70 34,7875,7518,4084,4071,4088,3839,4061,4075,4062,4077,7767,7836,7958,7628,7417,7850,6653,7 093,7741,7579,7117,7144,6122,6013,6095,6014,7036,7094,7971,7957,7877,7533,7608,7796,7857, 7542,7591,7634,7007,6903,7961,7418,7539,7649,7742,7581,7152,6654,7771,7534,7636,7823,806 8,7973,7123,7097,7783,7852,7878,7597,7962,7420,6907,7118,7541,7773,8016,7858,7098,7023,61 29,6075,6124,6130,4031,4083,4085,3967,4078,4086,4089,4090,7125,7126,7881,7800,7650,7974,7 595,8072,7582,7391,7831,7860,6077,6103,6078,6107,7071,7139,8003,7787,7640,7623,7964,7977, 7882,7889,6909,7100,8005,7884,8032,7978,7031,7129,7774,8080,7890,7864,7545,7603,7985,748 7,7141,7130,7789,7980,7652,7598,8006,7835,7656,7407,7546,7627,7790,7795,7087,7035,7605,75 48,7142,6910,7986,7629,7664,7837,7847,7892,6655,7132,8009,7797,6132,6119,6136,5887,7519,7 635,7606,7905,7419,7630,7610,7609,7145,7095,7637,7415,7851,8010,7906,8067,7146,7037,7838, 7951,6109,6123,6110,6125,7119,7038,8017,7988,7896,8096,7959,7535,8069,7798,7853,8012,780 1,7879,7153,7099,7421,7859,7992,8070,7854,7908,8018,7543,7612,7638,7148,7154,7651,7583,76 53,8073,7963,7641,7802,7912,8020,8128,7101,7127,8033,7861,7965,8074,7883,7975,7642,7804,7 102,7131,7862,7422,7885,7743,7156,7143,8081,7966,7979,7547,4063,4092,4079,4087,4091,4093, 4094,4095,6079,6131,6133,6015,7865,7599,7160,6911,7775,7657,8034,7891,7654,8076,7886,798 1,7644,8024,8007,7893,7866,8082,7133,7147,7920,8036,7987,7982,7607,8097,7658,7791,6126,61 34,6137,6138,7839,7907,8084,7631,8011,7549,7134,7149,7665,8098,7989,7894,8129,8040,7660,7 799,7897,7868,7611,7909,8013,8088,7550,7990,8019,7898,7666,8048,7910,7613,7103,7155,6111, 6140,6127,6135,7639,7803,8100,7855,8071,7993,7157,7039,7668,8014,7913,7994,7900,7614,813 0,8104,7643,8021,8035,7805,8075,7655,7863,7914,7996,7921,8022,8025,7672,7967,7423,8132,80 77,7887,7645,8083,7150,7158,7806,7916,8112,8037,7659,7867,7922,8026,7646,8136,7161,7162,7 551,8078,7983,8144,8038,8085,7895,7661,8041,7869,8099,7924,8028,7667,7899,7991,8090,8042, 8086,7670,8101,7911,7928,8049,7662,7870,8089,7669,8044,8015,6139,6141,6142,6143,7135,716 4,8160,7615,7901,7995,8102,8050,8105,8131,7915,7673,8023,8092,7902,7997,7151,7159,8133,81 06,8052,7674,7917,8113,8134,7923,8027,8108,7998,8079,8039,7807,8056,7647,7163,7165,8114,7 918,8137,7676,8029,7925,8138,8087,8043,8030,7926,8116,8145,8091,8140,7929,8045,8120,7663, 7871,8103,8146,8051,7930,7671,8093,8046,7903,8161,8053,8107,8162,8148,8094,7932,8109,813 5,8054,7999,8115,7166,7167,7675,8057,8152,7919,8110,8164,8139,8058,7677,8117,8141,8168,80 60,8118,8031,7927,8176,7678,8147,8121,7931,8142,8122,8047,8149,8150,8095,8163,7933,8124,8 055,8153,8165,8154,8111,8059,8166,7934,7679,8156,8169,8119,8170,8061,8143,8062,8177,8123, 8172,8178,8125,8151,8126,8155,8180,8167,8184,7935,8157,8171,8158,8173,8127,8179,8181,806 3,8174,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191]
›APPENDIX · 6 of 21
Sequence Group 1: Z1_8192
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,91,59,99,107, 182,6,17,21,40,23,45,51,93,29,57,61,100,73,118,123,197,34,63,76,121,81,132,147,214,90,149,159, 252,164,264,298,425,9,18,26,56,30,60,72,113,36,77,64,126,85,137,153,229,44,75,89,148,95,156,1 63,260,103,166,184,288,196,306,322,489,53,92,101,162,119,176,191,303,130,192,213,314,231,33 5,362,544,151,227,255,343,262,363,385,589,295,391,412,609,441,632,676,932,15,25,31,74,39,80, 83,152,48,88,96,161,106,171,179,302,58,97,112,177,122,190,206,318,136,207,228,330,257,357,38 1,577,66,116,131,195,140,212,236,352,160,253,263,365,294,390,403,608,178,275,304,395,315,43 1,443,630,340,462,508,665,560,696,761,933,70,133,155,239,170,261,291,393,183,296,308,424,32 3,442,488,649,202,319,331,456,364,504,546,704,375,566,592,732,620,774,802,1089,233,353,368, 511,396,576,595,754,440,605,631,794,670,805,889,1165,479,640,677,844,694,927,957,1241,759,9 88,1021,1218,1071,1286,1409,1800,20,37,41,94,49,98,114,189,50,115,127,198,144,230,242,379,6 5,128,145,245,157,256,273,380,165,272,299,407,320,439,446,629,68,154,167,247,186,280,305,43 8,194,312,324,450,334,498,529,692,193,332,355,497,374,547,579,733,398,597,621,773,639,801,8 53,1147,79,181,187,310,201,328,354,490,215,359,367,545,386,588,604,765,297,382,397,591,426, 614,638,796,468,645,682,838,715,926,959,1198,327,414,451,628,496,664,686,910,534,699,725,93 1,762,997,1043,1263,593,760,775,1022,797,1072,1009,1321,866,1144,1166,1419,1179,1481,1590, 1852,84,199,203,373,281,389,402,596,311,406,427,623,463,647,679,912,325,457,495,648,510,687, 717,935,567,727,751,993,795,1041,1088,1325,378,499,528,716,578,746,781,1010,622,782,803,10 82,867,1067,1151,1433,655,834,916,1145,944,1178,1216,1466,998,1229,1228,1578,1322,1663,170 3,2051,413,561,600,783,646,804,852,1105,683,911,928,1167,979,1181,1219,1479,718,953,1011,11 99,1044,1240,1323,1664,1104,1343,1406,1706,1452,1818,1850,2161,772,1023,1080,1324,1150,13 38,1438,1713,1164,1435,1474,1828,1560,1879,1984,2340,1182,1482,1660,1919,1694,1987,1941,2 346,1782,2089,2117,2540,2167,2622,2757,3076,27,43,52,102,62,129,146,237,67,150,158,244,169, 266,274,428,69,168,180,265,188,329,341,478,224,342,372,535,388,580,601,793,71,185,200,333,2 26,369,383,574,238,392,404,606,430,633,653,806,254,415,445,644,491,678,697,878,505,693,728, 952,731,992,1040,1411,117,225,232,387,246,405,429,625,289,447,469,673,507,703,726,914,309,4 75,513,695,573,730,739,976,590,740,750,1042,833,1073,1132,1434,326,572,582,749,613,780,792, 1064,635,832,855,1099,930,1148,1168,1475,672,888,945,1169,999,1187,1273,1561,1079,1280,135 2,1665,1407,1711,1820,2159,120,243,267,444,307,474,509,714,321,530,575,741,594,758,763,104 5,358,583,612,764,634,829,845,1096,671,876,929,1153,977,1183,1252,1476,384,624,652,854,698, 917,915,1184,719,956,989,1242,1065,1276,1318,1673,755,1008,1075,1287,1097,1381,1408,1730, 1135,1432,1460,1829,1577,1881,1985,2341,399,675,702,958,738,996,1066,1281,815,1078,1116,13 96,1129,1410,1450,1811,835,1117,1134,1437,1185,1455,1541,1878,1260,1576,1619,1920,1702,20 54,2092,2357,877,1217,1246,1477,1319,1579,1662,1953,1353,1696,1731,2088,1821,2118,2165,25 69,1462,1739,1830,2123,1911,2185,2210,2737,1954,2285,2345,2840,2518,2910,3041,3447,141,29 0,313,531,356,581,607,800,366,615,641,831,674,865,934,1253,394,654,705,913,729,995,978,1262, 747,1020,1070,1342,1106,1390,1413,1783,494,724,748,994,814,1047,1081,1397,830,1107,1131,1 418,1149,1451,1465,1854,836,1146,1180,1464,1255,1540,1591,1921,1296,1693,1697,2055,1738,2 093,2156,2534,506,807,828,1098,837,1128,1152,1454,879,1186,1243,1480,1277,1588,1695,2049,1 074,1254,1320,1618,1354,1707,1742,2090,1453,1743,1831,2124,1918,2184,2209,2736,1130,1380, 1436,1710,1463,1827,1874,2158,1549,1880,1937,2208,2048,2338,2356,2847,1661,1955,2061,234 4,2116,2367,2531,2916,2160,2541,2613,3021,2628,3109,3113,3631,512,839,864,1247,1046,1272, 1297,1692,1083,1339,1391,1712,1439,1810,1853,2157,1133,1412,1461,1819,1478,1875,1940,218 7,1589,1986,1936,2255,2091,2347,2499,2892,1261,1467,1483,1910,1672,1952,2060,2342,1705,20 62,2095,2492,2125,2519,2596,3020,1826,2119,2164,2535,2211,2623,2629,3097,2339,2781,2846,3 167,2911,3290,3344,3618,1355,1548,1704,2063,1801,2094,2122,2530,1851,2166,2186,2612,2284, 2626,2841,3112,1855,2254,2343,2780,2498,2848,2849,3291,2568,2917,2931,3345,3077,3506,354 6,4152,2050,2366,2493,2893,2597,2930,3040,3351,2627,3096,3108,3507,3246,3547,3864,4268,27 56,3166,3247,3619,3350,3630,3865,4269,3446,3876,3877,4442,4153,4443,4840,4841,54,55,86,12 5,87,134,139,292,104,138,143,316,234,339,361,602,105,142,204,338,241,376,437,626,282,436,43 2,651,473,685,713,982,124,235,259,400,283,435,459,667,317,471,477,700,563,744,757,1051,360, 493,598,753,611,798,841,1100,650,843,909,1176,946,1232,1292,1587,135,240,300,470,336,476,56 2,735,370,599,514,766,637,809,891,1115,434,565,643,842,669,902,925,1196,707,948,990,1274,10 50,1316,1350,1737,461,666,701,924,745,960,1037,1295,778,1038,1091,1344,1119,1385,1448,187 2,847,1113,1193,1389,1230,1449,1531,1925,1283,1537,1582,1973,1617,2020,2120,2588,205,293,3 37,564,377,610,627,890,448,642,680,919,712,955,963,1294,472,681,734,961,756,1036,1076,1346, 808,1077,1114,1370,1195,1415,1503,1907,516,742,779,1049,810,1090,1138,1398,918,1177,1231,1 457,1282,1536,1551,1972,962,1239,1298,1543,1345,1613,1667,2018,1386,1700,1812,2065,1882,2 162,2305,2589,532,799,901,1155,954,1197,1279,1539,983,1284,1326,1586,1351,1666,1736,2053, 1068,1347,1371,1698,1456,1802,1876,2220,1487,1884,1932,2252,1990,2336,2440,2889,1137,139 9,1472,1815,1544,1906,1935,2274,1616,1969,2019,2386,2066,2443,2543,2983,1729,2026,2121,25 04,2134,2575,2599,3099,2287,2620,2739,3092,2807,3168,3347,3802,258,371,401,668,449,684,73 6,1035,458,737,767,1052,812,1118,1156,1501,515,776,813,1159,903,1194,1237,1502,947,1236,12 93,1581,1348,1615,1670,2017,518,900,949,1171,1032,1244,1299,1614,1048,1340,1364,1674,1384, 1780,1823,2132,1039,1382,1405,1779,1486,1877,1909,2253,1546,1939,1991,2335,2025,2391,250 7,2929,603,981,1033,1336,1055,1368,1404,1740,1101,1417,1459,1873,1532,1924,1968,2333,1285, 1528,1545,1927,1608,1988,2024,2388,1708,2029,2128,2502,2223,2574,2615,3080,1367,1584,167 5,2016,1778,2064,2130,2564,1848,2213,2237,2587,2306,2697,2759,3119,1933,2304,2337,2752,23 89,2842,2713,3231,2532,2926,2988,3443,3023,3545,3610,3878,636,1053,1069,1485,1245,1535,15 50,1938,1337,1580,1609,2009,1701,2031,2127,2566,1365,1699,1777,2052,1814,2131,2233,2591,1 885,2239,2273,2625,2387,2755,2888,3249,1500,1781,1822,2232,1908,2264,2359,2714,2008,2364, 2441,2866,2533,2805,2967,3445,2059,2496,2572,2927,2592,3022,3082,3512,2698,3095,3094,356 2,3244,3617,3637,4155,1583,1883,1942,2365,2030,2442,2506,2897,2129,2565,2584,2989,2619,30 43,3093,3519,2234,2595,2715,3081,2776,3098,3245,3624,2896,3281,3302,3680,3468,3862,3874,4 441,2334,2753,2864,3248,2966,3250,3464,3685,2982,3453,3514,3870,3558,3917,4134,4618,3060, 3548,3614,4075,3632,4141,4125,4664,3800,4235,4277,4842,4491,4906,4959,5364,301,433,460,70 6,492,777,840,1139,517,846,908,1158,951,1234,1238,1610,519,950,980,1233,1034,1369,1387,172 8,1102,1388,1484,1849,1534,1916,1943,2385,533,991,1054,1383,1112,1473,1529,1904,1154,1538, 1562,1970,1612,2021,2057,2460,1192,1585,1669,2028,1741,2126,2163,2538,1803,2133,2248,259 4,2251,2624,2754,3349,743,1103,1136,1533,1170,1563,1611,2011,1275,1671,1709,2097,1809,221 5,2238,2570,1327,1715,1817,2135,1887,2250,2257,2616,1926,2258,2272,2758,2495,2843,2918,34 52,1366,1886,1922,2267,1975,2358,2384,2782,2023,2494,2517,2895,2586,2964,2990,3515,2096,2 542,2593,2991,2699,3079,3157,3559,2851,3164,3282,3625,3303,3683,3866,4419,752,1157,1235,1 668,1317,1714,1813,2222,1349,1824,1905,2259,1934,2286,2307,2777,1416,1923,1974,2332,2022, 2473,2505,2890,2067,2536,2585,2981,2617,3061,3110,3516,1530,2010,2056,2516,2212,2573,257 1,3062,2235,2598,2621,3100,2783,3158,3228,3627,2275,2712,2845,3169,2891,3297,3346,3686,29 25,3444,3504,3871,3561,3919,4135,4619,1547,2099,2214,2614,2256,2696,2804,3165,2463,2850,2 908,3300,2913,3348,3466,3861,2497,2909,2924,3455,3063,3471,3551,3916,3116,3560,3613,4084, 3636,4176,4250,4667,2537,3083,3102,3517,3229,3563,3616,4127,3283,3634,3687,4234,3867,427 8,4489,4881,3508,3741,3872,4281,4073,4545,4558,4957,4132,4563,4655,5038,4778,5170,5295,57 79,811,1278,1341,1825,1414,1917,1971,2390,1458,1989,2027,2475,2098,2529,2590,3111,1542,20 58,2221,2567,2249,2631,2618,3118,2265,2738,2806,3280,2898,3298,3441,3801,1776,2236,2266,2 630,2462,2779,2865,3301,2474,2899,2915,3442,2965,3467,3511,3896,2500,2928,3042,3510,3115, 3550,3611,4085,3170,3629,3635,4177,3740,4251,4416,4786,1808,2461,2472,2894,2501,2912,298 0,3470,2539,3078,3101,3544,3159,3608,3633,4143,2844,3114,3230,3612,3288,3681,3742,4248,34 69,3743,3873,4282,4074,4544,4557,4956,2914,3296,3454,3682,3509,3869,3898,4418,3557,3918,4 087,4556,4142,4616,4666,5109,3615,4133,4179,4654,4276,4693,4785,5180,4440,4843,4905,5293, 4914,5413,5415,6051,1816,2503,2528,3103,2778,3156,3171,3628,2867,3251,3299,3684,3465,386 0,3879,4417,2919,3440,3505,3863,3518,3899,4124,4547,3609,4140,4086,4561,4249,4665,4777,51 68,3117,3513,3549,4072,3626,4126,4178,4652,3639,4232,4271,4694,4283,4779,4882,5292,3868,4 279,4488,4787,4559,4907,4915,5367,4617,5037,5108,5509,5171,5532,5534,6048,3289,3556,3638, 4233,3803,4270,4280,4784,3875,4490,4546,4904,4562,4912,5039,5414,3897,4560,4653,5036,477 6,5110,5111,5533,4880,5181,5183,5535,5365,5800,5802,6324,4154,4692,4695,5169,4883,5182,52 94,5777,4913,5366,5412,5801,5510,5803,6216,6326,4958,5508,5511,6049,5776,6050,6217,6327,5 778,6218,6219,6672,6325,6673,6674,6675,108,109,110,175,111,208,211,284,172,210,249,408,268, 453,455,722,173,248,250,452,271,466,551,770,278,550,502,823,619,851,875,1190,174,269,277,50 0,279,549,571,825,409,617,657,868,709,898,907,1257,454,659,720,905,769,968,1015,1314,822,10 17,1095,1420,1140,1468,1558,1957,209,270,286,616,410,656,708,893,464,721,660,922,817,973,1 085,1361,548,711,821,1016,827,1092,1111,1444,871,1142,1220,1496,1256,1622,1678,2113,585,82 4,869,1110,899,1172,1227,1567,966,1248,1313,1646,1363,1723,1786,2216,1019,1359,1423,1735,1 446,1787,1869,2301,1555,1891,1928,2361,2005,2408,2488,3016,251,285,411,710,467,768,771,10 84,568,820,848,1109,874,1163,1175,1566,618,849,892,1173,906,1226,1302,1658,972,1303,1360,1 718,1441,1749,1865,2281,662,896,967,1251,984,1312,1376,1744,1108,1421,1447,1789,1554,1890, 1903,2360,1174,1491,1620,1895,1647,1979,2007,2382,1732,2070,2188,2453,2260,2576,2705,301 7,690,969,1087,1379,1162,1445,1499,1893,1191,1556,1640,1956,1679,2006,2112,2445,1290,1659, 1719,2036,1788,2152,2218,2608,1859,2270,2308,2672,2372,2718,2774,3293,1373,1745,1804,219 1,1896,2280,2311,2694,2004,2353,2383,2766,2458,2785,2921,3409,2103,2416,2489,2860,2562,30 11,3069,3553,2703,3104,3177,3474,3263,3690,3825,4264,276,465,501,826,569,850,894,1225,570, 895,923,1258,1012,1362,1394,1863,661,964,1013,1401,1093,1440,1489,1864,1141,1488,1559,191 5,1676,2003,2014,2381,688,1086,1143,1403,1222,1492,1621,2002,1250,1644,1688,2034,1722,215 0,2201,2560,1249,1720,1747,2149,1858,2219,2283,2673,1898,2329,2373,2717,2415,2773,2869,33 95,723,1189,1223,1642,1289,1716,1746,2114,1315,1751,1791,2217,1870,2300,2352,2709,1557,18 66,1897,2303,1958,2370,2414,2768,2072,2421,2510,2854,2635,3010,3071,3462,1691,1930,2035,2 380,2148,2452,2514,2962,2206,2579,2665,3015,2706,3161,3223,3575,2309,2704,2719,3178,2769, 3272,3173,3713,2902,3392,3410,3851,3419,4005,4138,4432,816,1259,1291,1857,1493,1889,1902, 2328,1643,1914,1959,2375,2071,2423,2491,2976,1689,2037,2147,2444,2190,2515,2637,3019,227 1,2667,2691,3153,2767,3221,3292,3717,1862,2151,2200,2636,2282,2686,2761,3174,2374,2762,27 75,3286,2903,3259,3399,3853,2451,2802,2984,3393,3044,3418,3472,3962,3162,3477,3476,4102,3 714,4171,4215,4687,1929,2261,2348,2763,2422,2784,2868,3321,2511,2963,3012,3411,3087,3421, 3475,4003,2638,3065,3175,3463,3224,3552,3715,4172,3320,3727,3806,4218,3912,4370,4422,485 3,2716,3179,3284,3716,3398,3722,3858,4225,3408,3855,3966,4404,4096,4447,4624,5032,3422,40 06,4168,4543,4190,4627,4597,5042,4262,4733,4781,5328,4875,5390,5445,5772,287,503,584,870, 658,965,1014,1377,663,1018,1094,1400,1161,1470,1490,1976,689,1160,1188,1469,1224,1717,173 3,2102,1356,1734,1856,2207,1888,2296,2349,2765,691,1221,1288,1721,1358,1805,1867,2278,137 8,1892,1912,2354,1978,2409,2449,2786,1422,1931,2013,2420,2115,2490,2577,2906,2153,2561,26 68,3064,2671,3152,3220,3827,897,1357,1372,1871,1402,1913,1977,2377,1497,2015,2073,2477,21 55,2583,2666,2978,1641,2079,2193,2563,2277,2670,2679,3084,2302,2680,2690,3222,2801,3273,3 376,3854,1690,2276,2298,2689,2369,2760,2764,3256,2411,2800,2871,3315,3014,3396,3412,3967, 2476,2920,3045,3413,3163,3451,3577,4097,3279,3620,3736,4173,3807,4223,4372,4851,904,1395, 1471,2012,1623,2078,2189,2634,1677,2202,2279,2681,2310,2702,2707,3225,1750,2299,2368,270 8,2410,2797,2861,3312,2459,2904,3013,3401,3085,3423,3568,4000,1868,2376,2448,2870,2578,29 85,2979,3448,2639,3068,3105,3554,3257,3580,3710,4185,2695,3172,3275,3691,3313,3761,3824,4 230,3379,3852,3956,4405,4101,4481,4625,5033,1899,2479,2582,3070,2678,3160,3258,3621,2795, 3278,3352,3780,3357,3826,3902,4275,2803,3353,3378,3857,3449,3915,4081,4446,3572,4100,415 9,4548,4214,4690,4744,5045,2905,3473,3566,4001,3711,4103,4170,4609,3737,4208,4231,4732,43 73,4782,4873,5337,3958,4239,4406,4791,4539,4877,4886,5437,4610,4961,5041,5500,5286,5546,5 717,6055,985,1498,1645,2203,1748,2297,2355,2772,1790,2371,2417,2799,2478,2901,3018,3569,1 894,2450,2609,2977,2669,3155,3086,3574,2687,3176,3262,3726,3322,3778,3829,4263,2146,2664, 2688,3154,2794,3227,3285,3781,2798,3323,3359,3850,3397,3903,3961,4434,2852,3394,3420,396 0,3571,4080,4139,4549,3704,4189,4209,4691,4238,4745,4848,5306,2154,2787,2796,3314,2853,33 56,3400,3914,2907,3450,3555,4004,3581,4136,4191,4685,3274,3570,3712,4158,3738,4219,4254,4 734,3913,4255,4407,4808,4542,4876,4885,5436,3358,3760,3856,4222,3959,4403,4438,4850,4093, 4480,4593,4884,4684,5022,5044,5507,4169,4611,4717,5040,4780,5091,5291,5552,4852,5329,538 1,5713,5416,5797,5805,6359,2192,2855,2900,3567,3226,3576,3705,4188,3287,3723,3779,4224,38 59,4274,4433,4849,3377,3828,3957,4371,4002,4439,4596,4879,4137,4626,4592,4927,4735,5043,5 175,5536,3573,3963,4007,4538,4184,4608,4716,5034,4217,4718,4747,5132,4809,5287,5376,5712, 4402,4783,4872,5307,4887,5391,5417,5789,5023,5493,5506,5835,5547,5994,6012,6322,3739,409 2,4216,4719,4265,4746,4790,5290,4423,4874,4878,5380,4960,5410,5501,5804,4435,4926,5035,54 92,5174,5520,5521,5995,5336,5553,5563,6013,5773,6166,6234,6676,4686,5090,5133,5537,5377,5 562,5716,6027,5411,5788,5796,6167,5926,6235,6468,6756,5444,5834,5927,6323,6026,6358,6469, 6757,6054,6528,6529,6830,6677,6831,7080,7081,586,587,818,921,819,970,975,1552,872,974,987, 1656,1374,1727,1785,2350,873,986,1300,1726,1393,1860,2001,2378,1494,2000,1980,2447,2077,2 513,2633,3090,920,1375,1443,1900,1495,1983,2039,2455,1657,2075,2101,2580,2263,2684,2701,3 243,1784,2145,2330,2693,2363,2770,2857,3316,2446,2859,2961,3416,3046,3520,3692,4131,971,1 392,1564,2074,1724,2100,2262,2675,1806,2331,2194,2710,2413,2789,2923,3327,1982,2269,2419, 2858,2457,2934,3009,3460,2611,3056,3106,3578,3242,3708,3734,4237,2069,2454,2581,3008,268 5,3072,3217,3695,2742,3218,3295,3728,3355,3765,3900,4436,2863,3325,3457,3777,3478,3901,40 51,4553,3623,4077,4122,4621,4157,4660,4788,5368,1301,1553,1725,2268,1861,2362,2379,2922,2 032,2418,2508,2987,2632,3067,3075,3694,2076,2509,2674,3073,2700,3216,3276,3730,2788,3277, 3326,3750,3459,3831,4047,4495,2196,2682,2743,3241,2790,3294,3382,3782,2986,3417,3479,395 3,3622,4076,4095,4620,3074,3527,3706,4083,3729,4149,4175,4658,3766,4212,4284,4729,4482,48 54,4965,5369,2204,2771,2933,3403,3066,3461,3583,4079,3091,3688,3718,4130,3735,4174,4236,4 689,3260,3731,3751,4210,3952,4266,4444,4892,4043,4484,4564,4924,4630,5020,5120,5529,3381, 3783,3964,4287,4088,4494,4567,4954,4156,4613,4659,5094,4730,5123,5331,5659,4229,4670,478 9,5280,4846,5343,5379,5791,4963,5388,5439,5784,5499,5836,6015,6422,1442,1807,1901,2456,20 33,2512,2676,3183,2038,2677,2711,3252,2792,3354,3404,4045,2195,2740,2793,3407,2935,3458,3 525,4046,3047,3524,3693,4121,3732,4151,4182,4657,2198,2932,3057,3415,3180,3564,3707,4150, 3240,3724,3744,4186,3764,4260,4375,4844,3219,3762,3805,4259,4042,4445,4537,4925,4090,459 5,4631,5019,4669,5107,5283,5561,2351,3089,3181,3720,3255,3748,3804,4252,3317,3849,3955,44 37,4052,4552,4612,5017,3689,4048,4089,4555,4144,4628,4668,5104,4220,4681,4812,5178,4895,5 342,5383,5780,3747,4128,4187,4656,4258,4728,4814,5332,4420,4889,4917,5363,4966,5421,5447, 5811,4565,4964,5021,5440,5105,5502,5433,5923,5304,5558,5660,6031,5715,6233,6290,6530,241 2,3253,3261,4041,3565,4055,4094,4594,3721,4120,4145,4649,4213,4683,4811,5334,3745,4211,42 57,4688,4286,4815,4909,5371,4485,4919,4953,5409,5095,5443,5528,5945,4044,4261,4374,4908,4 536,4940,5047,5434,4648,5088,5121,5526,5305,5497,5567,6053,4715,5172,5340,5559,5372,5714, 5782,6180,5422,5787,5786,6246,5924,6321,6389,6679,4123,4483,4598,5089,4682,5122,5282,554 1,4813,5333,5360,5661,5387,5719,5785,6223,4910,5375,5435,5781,5488,5790,5925,6352,5540,59 49,6010,6408,6160,6466,6510,6829,5018,5441,5524,5944,5566,5946,6084,6413,5658,6081,6182,6 506,6242,6569,6642,6962,5768,6236,6294,6575,6384,6645,6629,6984,6420,6727,6769,7082,6875, 7146,7243,7440,1565,1981,2068,2610,2144,2741,2856,3383,2197,2862,2960,3406,3059,3522,352 6,4146,2199,3058,3088,3521,3182,3749,3767,4228,3318,3776,4040,4421,4054,4540,4599,5093,22 05,3107,3254,3763,3324,3965,4049,4492,3402,4078,4098,4614,4148,4661,4713,5124,3456,4129,4 181,4680,4253,4810,4855,5310,4267,4845,4920,5374,4923,5408,5442,6025,2683,3319,3380,4053, 3414,4099,4147,4651,3579,4183,4221,4749,4273,4891,4918,5338,3719,4227,4369,4847,4487,492 2,4937,5384,4554,4938,4952,5446,5135,5503,5554,6080,3746,4486,4550,4943,4623,5046,5092,54 94,4663,5134,5285,5539,5362,5564,5662,6183,4748,5330,5373,5663,5423,5775,5813,6243,5523,5 832,5950,6353,6011,6411,6470,6827,2692,3405,3523,4180,3709,4226,4285,4894,3733,4400,4493, 4939,4566,4962,4967,5489,3848,4551,4622,5016,4662,5129,5281,5530,4731,5308,5361,5657,538 5,5769,5798,6220,4050,4650,4712,5284,4888,5341,5339,5770,4911,5378,5389,5792,5495,5814,59 20,6355,4955,5432,5505,5837,5531,5997,6014,6414,5557,6052,6164,6507,6245,6571,6643,6963,4 091,4751,4890,5382,4936,5420,5496,5833,5127,5522,5544,6008,5549,6024,6086,6465,5173,5545, 5556,6083,5771,6163,6239,6568,5808,6244,6293,6624,6388,6720,6754,6987,5309,5783,5794,622 1,5921,6247,6320,6631,5951,6386,6415,6726,6471,6770,6873,7085,6176,6417,6508,6773,6573,68 77,6922,7241,6640,6927,6967,7246,7018,7278,7399,7635,2791,3582,3725,4401,3830,4541,4615,5 106,3954,4629,4671,5131,4750,5289,5370,5799,4082,4714,4893,5335,4921,5419,5386,5810,4941, 5438,5498,5948,5542,5998,6029,6421,4256,4916,4942,5418,5126,5491,5525,6009,5130,5543,555 1,6030,5565,6087,6179,6532,5176,5560,5718,6178,5807,6238,6291,6625,5838,6357,6387,6721,64 16,6755,6824,7022,4272,5125,5128,5538,5177,5548,5656,6162,5311,5774,5793,6232,5815,6288,6 385,6647,5504,5806,5922,6292,5992,6409,6418,6752,6161,6419,6509,6774,6574,6876,6921,7240, 5550,5996,6082,6410,6177,6505,6534,6826,6241,6570,6627,6920,6646,6960,6986,7273,6295,664 1,6723,6966,6768,6989,7021,7392,6828,7083,7145,7397,7150,7445,7447,7707,4368,5179,5288,57 95,5490,5812,5839,6356,5527,5947,5999,6412,6085,6464,6531,6825,5555,6028,6165,6467,6222,6 535,6628,6879,6289,6644,6626,6925,6753,6985,7017,7276,5809,6181,6237,6572,6354,6630,6722, 6964,6391,6724,6759,6990,6775,7019,7086,7396,6504,6771,6872,7023,6923,7147,7151,7443,696 1,7245,7272,7569,7279,7572,7574,7704,5993,6240,6390,6725,6423,6758,6772,7020,6511,6874,68 78,7144,6926,7148,7247,7446,6533,6924,6965,7244,7016,7274,7275,7573,7084,7393,7395,7575,7 441,7636,7638,7872,6678,6988,6991,7277,7087,7394,7398,7633,7149,7442,7444,7637,7570,7639, 7708,7874,7242,7568,7571,7705,7632,7706,7709,7875,7634,7710,7711,7876,7873,7877,7878,787 9,216,217,218,223,219,344,347,480,220,346,349,484,416,521,523,886,221,348,350,520,419,526,5 43,938,422,542,538,1003,787,1027,1059,1518,222,417,421,536,423,541,555,1005,485,785,789,10 28,881,1126,1203,1573,522,791,884,1201,937,1212,1307,1606,1002,1309,1335,1684,1428,1760,1 842,2321,345,418,482,784,486,788,880,1121,524,885,856,1206,941,1265,1329,1629,540,883,1001, 1308,1007,1332,1427,1756,1031,1430,1520,1832,1572,1946,1994,2521,557,1004,1029,1426,1127, 1512,1527,1847,1210,1568,1605,1962,1631,2047,2138,2648,1311,1627,1687,2087,1758,2139,222 5,2749,1839,2231,2316,2825,2401,2880,2996,3596,351,481,487,882,527,936,939,1328,552,1000,1 024,1425,1058,1507,1515,1846,786,1025,1120,1513,1202,1526,1598,1966,1264,1599,1628,2042,1 753,2109,2181,2729,858,1124,1211,1571,1268,1604,1636,2104,1424,1685,1759,2141,1838,2230,2 291,2824,1514,1771,1944,2243,1963,2327,2403,2878,2084,2438,2556,2969,2656,3032,3201,3597, 862,1213,1331,1639,1506,1757,1835,2241,1519,1840,1948,2320,1995,2402,2520,2945,1594,1967, 2043,2432,2140,2552,2650,3048,2175,2662,2808,3140,2836,3214,3306,3881,1633,2105,2168,255 9,2244,2728,2811,3194,2400,2821,2879,3266,2974,3309,3489,3981,2487,2936,2997,3388,3030,35 91,3645,4065,3199,3676,3773,4026,3823,4198,4385,4896,420,525,537,1006,553,1026,1122,1525, 554,1123,1207,1574,1304,1630,1650,2179,857,1208,1305,1653,1333,1752,1769,2180,1429,1768,1 843,2295,1992,2399,2406,2877,860,1330,1431,1655,1522,1792,1945,2398,1570,1960,1996,2426,2 046,2546,2641,3028,1569,2044,2107,2545,2174,2651,2731,3141,2246,2813,2837,3213,2887,3305, 3429,3947,887,1517,1523,1950,1593,2040,2106,2522,1607,2111,2143,2649,2226,2748,2820,3205, 1841,2182,2245,2751,2322,2830,2886,3268,2468,2941,3002,3374,3123,3590,3647,4022,1999,231 8,2427,2876,2544,2968,3006,3534,2646,3035,3133,3595,3202,3701,3795,4119,2809,3200,3215,37 74,3269,3832,3753,4297,3434,3944,3982,4395,3995,4497,4638,4980,940,1575,1595,2173,1793,22 29,2290,2812,1951,2294,2323,2839,2439,2943,2999,3536,1997,2433,2527,2944,2558,3007,3125,3 599,2663,3135,3191,3697,3267,3793,3880,4301,2178,2547,2640,3124,2730,3186,3237,3754,2838, 3238,3307,3842,3435,3819,3951,4409,2951,3370,3540,3945,3600,3994,4024,4466,3702,4037,403 6,4602,4298,4711,4767,5219,2317,2657,2816,3239,2942,3308,3428,3905,3003,3535,3592,3983,36 67,3997,4027,4479,3126,3641,3755,4023,3796,4064,4299,4720,3904,4311,4382,4770,4452,4946,4 978,5345,3212,3775,3840,4300,3950,4306,4414,4793,3980,4411,4474,4972,4584,5007,5152,5604, 3998,4498,4708,5071,4758,5155,5101,5610,4862,5249,5269,5764,5351,5878,5981,6260,483,539,5 56,1030,790,1209,1306,1637,859,1310,1334,1652,1505,1762,1770,2324,861,1504,1516,1761,1524, 2041,2085,2486,1624,2086,2172,2647,2228,2732,2817,3265,863,1521,1592,2045,1626,2169,2183, 2726,1638,2240,2292,2822,2326,2881,2949,3310,1686,2319,2405,2940,2523,2998,3033,3486,255 3,3029,3136,3640,3139,3696,3792,4387,1125,1625,1632,2227,1654,2293,2325,2873,1833,2407,24 69,2993,2555,3039,3134,3538,1949,2483,2601,3031,2725,3138,3147,3664,2750,3148,3190,3794,3 369,3833,3932,4410,1998,2724,2734,3189,2829,3236,3264,3816,2883,3368,3431,3891,3594,3948, 3984,4475,2992,3488,3601,3985,3703,4011,4161,4585,3839,4192,4320,4721,4383,4775,4948,532 7,1200,1651,1763,2404,1947,2482,2557,3122,1993,2642,2727,3149,2810,3198,3203,3797,2110,27 35,2828,3204,2882,3365,3389,3888,2975,3484,3593,3969,3665,3999,4108,4476,2224,2872,2948,3 430,3034,3541,3539,4008,3127,3644,3677,4066,3817,4164,4294,4737,3195,3752,3835,4199,3889, 4349,4384,4818,3935,4408,4460,4973,4601,5009,5153,5605,2247,2995,3038,3646,3146,3700,381 8,4193,3335,3838,3924,4364,3929,4386,4450,4931,3371,3925,3934,4413,4009,4455,4533,5006,41 16,4600,4675,5072,4766,5222,5252,5621,3485,4025,4070,4477,4295,4603,4710,5113,4321,4760,4 819,5248,4949,5270,5349,5825,4462,4827,4974,5275,5063,5353,5426,5969,5114,5573,5609,6064, 5750,6126,6209,6559,1269,1834,1961,2643,2108,2733,2823,3304,2142,2831,2937,3367,2994,343 3,3598,4109,2242,2950,3049,3537,3137,3699,3666,4118,3187,3772,3822,4310,3906,4358,4389,48 63,2526,3132,3188,3698,3334,3799,3841,4365,3366,3907,3931,4394,3949,4451,4465,4982,3372,3 946,3996,4464,4111,4532,4639,5073,4240,4757,4761,5223,4826,5253,5324,5758,2554,3311,3364, 3890,3373,3928,3968,4454,3487,4010,4067,4496,4165,4636,4759,5217,3834,4110,4296,4674,432 2,4771,4830,5250,4453,4831,4975,5276,5070,5352,5425,5968,3930,4348,4412,4774,4463,4971,50 02,5326,4573,5008,5097,5424,5216,5602,5620,6071,4709,5115,5229,5608,5268,5631,5755,6132,5 344,5765,5869,6205,5884,6301,6305,6711,2600,3375,3432,4071,3798,4160,4241,4756,3843,4307, 4359,4792,4415,4930,4981,5325,3933,4388,4461,4947,4478,5003,5100,5355,4637,5154,5096,547 1,5251,5611,5731,6108,4117,4467,4499,5062,4736,5112,5228,5606,4769,5230,5255,5724,5277,57 51,5860,6204,4970,5271,5348,5759,5427,5879,5885,6281,5603,6021,6070,6335,6127,6442,6480,6 698,4323,4572,4768,5231,4897,5254,5274,5754,4979,5350,5354,5868,5572,5882,6065,6304,4983, 5470,5607,6020,5730,6072,6073,6443,5824,6133,6147,6481,6261,6602,6634,7040,5218,5630,572 5,6109,5861,6146,6208,6487,5883,6280,6300,6603,6382,6635,6864,7132,5980,6334,6383,6699,64 86,6710,6865,7133,6558,6884,6885,7194,7041,7195,7384,7385,558,559,942,1205,943,1214,1267, 1836,1056,1266,1271,1964,1634,2083,2137,2818,1057,1270,1596,2082,1649,2176,2397,2874,179 4,2396,2392,2947,2481,3005,3121,3670,1204,1635,1755,2288,1795,2395,2435,2971,1965,2471,24 85,3036,2659,3184,3197,3811,2136,2525,2814,3193,2827,3270,3385,3892,2946,3387,3533,3992,3 602,4056,4204,4635,1215,1648,1844,2470,2080,2484,2658,3143,2170,2815,2602,3206,2885,3329, 3491,3923,2394,2661,2939,3386,2973,3502,3589,4020,3051,3604,3678,4162,3810,4292,4318,482 5,2437,2970,3037,3588,3185,3648,3789,4207,3234,3790,3883,4312,3927,4353,4448,5000,3391,39 21,4017,4357,4038,4449,4523,5077,4195,4529,4606,5141,4673,5196,5272,5852,1597,1837,2081,2 660,2177,2826,2875,3490,2424,2938,3000,3543,3120,3643,3651,4206,2480,3001,3142,3649,3196, 3788,3836,4314,3328,3837,3922,4338,4019,4391,4519,5059,2604,3150,3235,3809,3330,3882,393 8,4366,3542,3993,4039,4457,4194,4528,4575,5140,3650,4063,4242,4535,4313,4645,4723,5194,43 54,4764,4932,5233,5010,5346,5585,5853,2644,3271,3501,3971,3642,4021,4167,4531,3671,4196,4 302,4634,4319,4722,4824,5221,3820,4315,4339,4762,4456,4898,5004,5452,4503,5012,5084,5468, 5158,5600,5680,6105,3937,4367,4472,4935,4568,5058,5087,5514,4672,5137,5195,5650,5234,568 3,5767,6175,4817,5202,5273,5736,5302,5831,5863,6283,5575,5876,5971,6276,6063,6336,6483,68 34,1754,2171,2289,2972,2425,3004,3144,3787,2434,3145,3207,3812,3332,3926,3972,4517,2603,3 232,3333,3975,3503,4018,4061,4518,3603,4060,4205,4605,4316,4647,4726,5193,2606,3500,3605, 3987,3784,4068,4243,4646,3808,4308,4332,4738,4352,4860,4951,5300,3791,4350,4381,4859,450 2,5005,5061,5469,4570,5099,5159,5599,5201,5655,5739,6145,2819,3669,3785,4304,3815,4336,43 80,4828,3893,4393,4459,5001,4524,5076,5136,5597,4197,4520,4569,5079,4640,5156,5200,5652,4 772,5205,5296,5734,5455,5830,5871,6264,4335,4632,4739,5192,4858,5232,5298,5820,4976,5429, 5461,5851,5586,5937,5983,6311,5085,5584,5601,5976,5653,6066,5961,6375,5756,6142,6188,655 5,6207,6633,6690,6886,2884,3813,3821,4501,4069,4527,4574,5098,4305,4604,4641,5185,4765,52 07,5279,5822,4333,4763,4857,5220,4934,5299,5457,5855,5013,5463,5513,5881,5651,5979,6104,6 393,4516,4861,4950,5456,5060,5480,5623,5962,5184,5628,5681,6098,5757,6061,6159,6557,5227, 5728,5828,6143,5856,6206,6266,6608,5938,6279,6278,6658,6380,6697,6717,7043,4607,5011,510 2,5629,5206,5682,5738,6113,5297,5821,5848,6189,5875,6211,6277,6615,5458,5859,5963,6265,60 16,6282,6381,6704,6112,6433,6454,6728,6588,6862,6882,7193,5598,5977,6096,6392,6158,6394,6 584,6733,6174,6565,6610,6870,6654,6901,7014,7282,6228,6636,6694,6955,6712,7029,7005,7312, 6832,7107,7141,7386,7211,7434,7479,7612,1845,2393,2436,3050,2524,3233,3384,3939,2605,339 0,3532,3974,3607,4058,4062,4642,2607,3606,3668,4057,3786,4337,4355,4816,3894,4356,4500,49 77,4526,5068,5103,5649,2645,3679,3814,4351,3920,4473,4521,5056,3970,4530,4586,5138,4644,5 197,5225,5700,4016,4633,4725,5204,4829,5278,5347,5762,4899,5301,5464,5858,5467,5880,5978, 6485,3151,3895,3936,4525,3986,4587,4643,5187,4163,4727,4773,5257,4929,5431,5462,5826,430 3,4795,4945,5303,5015,5466,5473,5872,5078,5474,5512,5982,5727,6067,6134,6564,4334,5014,50 74,5483,5143,5622,5648,6022,5199,5726,5749,6111,5850,6156,6190,6611,5256,5766,5857,6191,5 939,6263,6317,6655,6075,6332,6434,6705,6455,6731,6866,7179,3192,3973,4059,4724,4293,4794, 4933,5454,4317,4968,5057,5475,5086,5574,5587,6017,4392,5075,5142,5596,5198,5705,5737,610 6,5235,5760,5849,6173,5873,6229,6302,6612,4522,5186,5224,5748,5428,5829,5827,6230,5459,58 62,5877,6284,6023,6318,6372,6707,5515,5960,6069,6337,6107,6449,6482,6734,6141,6556,6600,6 871,6657,6903,7015,7283,4571,5259,5430,5870,5472,5936,6060,6333,5703,6074,6124,6452,6129, 6484,6586,6861,5729,6125,6140,6567,6231,6591,6639,6900,6308,6656,6693,6972,6716,7056,711 4,7315,5761,6267,6286,6613,6373,6659,6696,7007,6435,6714,6735,7106,6867,7142,7209,7417,66 04,6797,6880,7153,6953,7225,7238,7477,7012,7251,7303,7502,7362,7546,7583,7787,3331,4166,4 309,4969,4390,5069,5139,5654,4458,5157,5203,5707,5258,5753,5854,6303,4534,5226,5453,5823, 5465,5887,5874,6310,5481,5970,6062,6432,6114,6450,6553,6833,4856,5460,5482,5886,5702,601 9,6097,6453,5706,6115,6131,6554,6157,6587,6607,6888,5732,6144,6210,6606,6307,6638,6691,69 73,6338,6709,6715,7057,6796,7115,7176,7370,4928,5701,5704,6110,5733,6128,6172,6590,5763,6 262,6285,6632,6319,6688,6713,7031,6068,6306,6374,6692,6440,6729,6798,7112,6589,6799,6881, 7154,6954,7224,7237,7476,6130,6448,6566,6730,6605,6869,6890,7178,6653,6902,6975,7236,703 0,7280,7314,7525,6695,7013,7059,7302,7140,7333,7369,7556,7192,7387,7433,7581,7450,7653,76 55,7883,4944,5735,5752,6287,6018,6316,6339,6708,6099,6395,6451,6732,6585,6860,6887,7177,6 135,6552,6601,6863,6614,6891,7004,7227,6689,7028,6974,7249,7113,7313,7361,7544,6309,6609, 6637,6952,6706,7006,7058,7300,6719,7104,7135,7334,7155,7363,7418,7580,6868,7143,7208,737 1,7239,7435,7451,7615,7281,7501,7524,7701,7547,7724,7726,7880,6441,6652,6718,7105,6835,71 34,7152,7368,6883,7210,7226,7432,7250,7448,7503,7654,6889,7248,7301,7500,7360,7526,7527,7 725,7416,7557,7559,7727,7613,7808,7810,7948,7042,7332,7335,7545,7419,7558,7582,7785,7449, 7614,7652,7809,7702,7811,7912,7950,7478,7700,7703,7881,7784,7882,7913,7951,7786,7914,791 5,8032,7949,8033,8034,8035,1060,1061,1062,1511,1063,1600,1603,1796,1508,1602,1681,2312,17 64,2429,2431,3130,1509,1680,1682,2428,1767,2466,2655,3210,1774,2654,2550,3343,2835,3427,3 483,4014,1510,1765,1773,2548,1775,2653,2723,3361,2313,2833,2953,3436,3053,3498,3531,4113, 2430,2955,3128,3529,3209,3656,3759,4290,3342,3769,3887,4396,3940,4468,4582,5117,1601,176 6,1798,2832,2314,2952,3052,3493,2464,3129,2956,3586,3337,3661,3845,4329,2652,3055,3341,37 68,3363,3884,3911,4428,3439,3942,4028,4512,4112,4678,4742,5265,2745,3360,3437,3910,3499,3 988,4035,4591,3654,4104,4289,4702,4331,4803,4866,5448,3771,4327,4399,4823,4430,4867,4997, 5581,4579,5027,5080,5625,5165,5664,5720,6200,1683,1797,2315,3054,2467,3208,3211,3844,272 0,3340,3424,3909,3482,3979,3991,4590,2834,3425,3492,3989,3530,4034,4246,4706,3660,4247,43 28,4798,4425,4837,4993,5569,2958,3496,3655,4107,3672,4288,4344,4832,3908,4397,4431,4869,4 578,5026,5055,5624,3990,4507,4676,5031,4703,5147,5167,5646,4820,5238,5356,5693,5476,5840, 5953,6201,3026,3657,3847,4347,3978,4429,4515,5029,4015,4580,4696,5116,4743,5166,5264,568 5,4202,4707,4799,5212,4868,5320,5450,5864,4987,5486,5588,5904,5636,5966,6006,6445,4341,48 33,4900,5359,5048,5568,5591,5934,5164,5617,5647,5990,5698,6033,6137,6537,5263,5672,5721,6 092,5818,6195,6253,6649,5943,6296,6345,6594,6407,6738,6841,7128,1772,2465,2549,3362,2721, 3426,3494,4033,2722,3495,3587,4114,3756,4330,4362,4991,2957,3652,3757,4377,3885,4424,450 5,4992,3941,4504,4583,5067,4740,5163,5190,5645,3024,3846,3943,4379,4030,4508,4677,5162,41 06,4700,4752,5210,4802,5318,5401,5816,4105,4800,4835,5317,4986,5451,5571,5905,5050,5593,5 637,5965,5671,6005,6101,6515,3131,4013,4031,4698,4201,4796,4834,5266,4291,4839,4871,5449, 4998,5580,5616,5957,4581,4994,5049,5583,5118,5634,5670,6000,5240,5677,5742,6078,5891,619 4,6255,6582,4755,5082,5211,5644,5316,5692,5746,6154,5406,5843,5897,6199,5954,6329,6367,66 71,5589,5952,5967,6346,6001,6424,6341,6761,6118,6512,6538,6851,6547,6933,7026,7184,3336,4 115,4203,4985,4509,5025,5054,5592,4699,5066,5119,5639,5239,5679,5723,6168,4753,5213,5315, 5684,5358,5747,5893,6203,5487,5899,5931,6313,5991,6365,6444,6765,4990,5319,5400,5892,557 0,5918,5985,6342,5638,5986,6007,6438,6119,6403,6519,6853,5691,6058,6184,6513,6212,6546,65 92,6914,6330,6597,6596,6998,6762,7051,7079,7327,5081,5477,5612,5987,5678,6032,6100,6473,5 743,6155,6196,6539,6271,6549,6595,6931,5894,6249,6343,6583,6368,6648,6763,7052,6472,6783, 6838,7090,6896,7162,7182,7405,5964,6347,6436,6764,6518,6778,6858,7097,6536,6855,6918,717 2,6992,7199,7288,7496,6550,6934,7048,7223,7070,7291,7261,7506,7126,7349,7365,7592,7411,76 46,7677,7780,1799,2551,2744,3438,2954,3653,3758,4345,2959,3770,3886,4376,3977,4470,4506,5 144,3025,3976,4012,4469,4032,4797,4821,5262,4324,4822,4984,5407,5024,5576,5613,5989,3027, 4029,4200,4801,4326,4901,4995,5518,4346,5028,5064,5618,5146,5665,5689,6034,4398,5083,518 9,5676,5267,5722,5841,6122,5321,5817,5900,6248,5903,6312,6364,6843,3497,4325,4340,4999,43 78,5065,5145,5641,4513,5191,5241,5709,5323,5847,5898,6170,4697,5247,5393,5819,5517,5902,5 911,6268,5582,5912,5930,6366,6057,6425,6496,6854,4754,5516,5578,5929,5633,5984,5988,6400, 5667,6056,6103,6459,6198,6516,6540,6919,5708,6136,6213,6541,6331,6563,6681,6993,6431,670 0,6792,7053,6839,7095,7164,7403,3528,4363,4471,5188,4679,5246,5357,5890,4741,5402,5519,59 13,5590,5942,5955,6369,4838,5579,5632,5956,5666,6045,6093,6456,5699,6120,6197,6521,6269,6 551,6664,6928,4996,5640,5688,6102,5842,6185,6171,6560,5895,6252,6297,6650,6401,6684,6750, 7065,5935,6340,6427,6739,6457,6809,6840,7102,6499,6852,6908,7173,6997,7201,7289,7497,505 1,5711,5846,6254,5910,6328,6402,6701,6043,6430,6488,6820,6493,6842,6894,7139,6059,6489,64 98,6857,6561,6899,6969,7198,6668,6996,7047,7228,7078,7330,7352,7509,6121,6593,6662,6929,6 751,6999,7050,7265,6793,7072,7103,7348,7165,7366,7409,7601,6910,7111,7174,7375,7219,7413, 7422,7669,7266,7481,7505,7692,7566,7738,7773,7887,3673,4514,4701,5403,4836,5577,5619,600 4,4870,5635,5673,6047,5710,6117,6202,6665,5030,5690,5865,6169,5901,6315,6270,6670,5919,63 44,6406,6782,6474,6818,6845,7127,5314,5896,5928,6314,6042,6371,6437,6821,6046,6475,6495,6 850,6517,6895,6913,7186,6076,6514,6548,6912,6667,6968,7027,7229,6744,7069,7073,7331,7110, 7353,7400,7586,5322,6035,6044,6458,6077,6492,6520,6898,6123,6562,6651,6932,6685,7024,707 1,7325,6426,6666,6760,7046,6794,7091,7118,7350,6897,7119,7175,7376,7222,7412,7421,7668,64 94,6808,6856,7094,6911,7171,7190,7402,6981,7200,7257,7420,7324,7494,7508,7699,7049,7267,7 341,7504,7364,7515,7579,7744,7404,7593,7629,7769,7656,7805,7813,7959,5392,6079,6116,6663, 6370,6680,6745,7068,6439,6779,6819,7096,6859,7138,7185,7401,6497,6844,6909,7163,6930,719 1,7260,7415,7025,7290,7256,7463,7351,7507,7551,7728,6669,6915,6935,7218,7064,7264,7340,74 98,7089,7342,7355,7540,7377,7567,7624,7768,7170,7367,7408,7587,7423,7647,7657,7797,7495,7 685,7698,7827,7739,7850,7860,7946,6795,6980,7088,7343,7129,7354,7374,7578,7183,7410,7414, 7628,7480,7650,7693,7812,7187,7462,7499,7684,7550,7712,7713,7851,7600,7745,7755,7861,778 1,7902,7922,8036,7326,7514,7541,7729,7625,7754,7772,7867,7651,7796,7804,7903,7838,7923,79 88,8052,7676,7826,7839,7947,7866,7958,7989,8053,7886,8000,8001,8070,8037,8071,8112,8113,2 746,2747,3338,3585,3339,3658,3663,4576,3480,3662,3675,4704,4342,4807,4865,5614,3481,3674, 4244,4806,4361,4988,5161,5642,4510,5160,5148,5687,5245,5745,5889,6274,3584,4343,4427,505 2,4511,5151,5215,5695,4705,5243,5261,5844,5479,5916,5941,6379,4864,5313,5594,5933,5627,60 02,6089,6460,5686,6091,6153,6544,6214,6616,6740,7011,3659,4360,4588,5242,4804,5260,5478,5 907,4902,5595,5394,5958,5669,6037,6139,6479,5150,5485,5675,6090,5697,6150,6193,6580,5867, 6224,6298,6682,6378,6748,6790,7109,5237,5694,5845,6192,5917,6256,6361,6743,5974,6362,644 7,6784,6491,6813,6892,7188,6095,6477,6577,6817,6598,6893,6947,7233,6703,6957,7002,7285,70 45,7308,7372,7616,4245,4577,4805,5484,4989,5626,5643,6138,5208,5674,5740,6187,5888,6251,6 259,6742,5244,5741,5906,6257,5940,6360,6428,6786,6036,6429,6478,6806,6579,6847,6943,7215, 5396,5914,5975,6377,6038,6446,6502,6822,6186,6545,6599,6905,6702,6956,6983,7284,6258,662 3,6746,6971,6785,7037,7055,7306,6814,7076,7156,7345,7202,7406,7485,7617,5404,6003,6149,65 23,6250,6581,6687,6959,6275,6736,6766,7010,6791,7054,7108,7329,6404,6787,6807,7074,6904,7 130,7196,7428,6939,7204,7252,7460,7294,7492,7528,7721,6501,6823,6916,7159,6976,7214,7255, 7474,7044,7269,7307,7518,7346,7531,7595,7763,7101,7318,7373,7560,7390,7607,7627,7799,748 3,7644,7671,7792,7691,7828,7863,7982,4426,4903,5053,5696,5209,5744,5908,6351,5214,5909,59 59,6396,6040,6490,6524,6941,5395,5972,6041,6527,6151,6578,6621,6942,6215,6620,6741,7001,6 788,7039,7062,7305,5398,6148,6225,6543,6348,6660,6747,7038,6376,6780,6800,7066,6812,7124, 7167,7388,6363,6810,6837,7123,6938,7197,7217,7461,6978,7259,7295,7491,7317,7523,7563,775 3,5615,6273,6349,6776,6399,6804,6836,7116,6461,6849,6907,7189,6948,7232,7268,7489,6737,69 44,6977,7235,7032,7292,7316,7520,7092,7321,7380,7554,7431,7606,7631,7788,6803,7008,7067,7 304,7122,7344,7382,7596,7180,7425,7453,7611,7486,7661,7679,7819,7253,7484,7493,7672,7521, 7694,7665,7835,7584,7750,7764,7871,7771,7921,7938,8002,5668,6397,6405,6937,6661,6951,698 2,7258,6777,7000,7033,7297,7077,7323,7379,7598,6801,7075,7121,7328,7158,7383,7437,7619,72 05,7455,7473,7649,7519,7675,7720,7841,6940,7125,7166,7436,7216,7468,7511,7666,7296,7512,7 529,7718,7585,7689,7759,7885,7339,7548,7604,7751,7620,7770,7790,7908,7662,7795,7794,7934, 7836,7945,7965,8039,7003,7203,7262,7513,7322,7530,7562,7733,7381,7597,7608,7765,7643,777 5,7793,7919,7438,7623,7667,7789,7680,7798,7837,7952,7732,7845,7858,7968,7896,7986,7998,80 69,7490,7673,7716,7840,7758,7842,7892,7973,7762,7889,7910,7994,7930,8009,8026,8090,7776,7 924,7942,8015,7960,8029,8021,8096,7980,8047,8057,8114,8075,8122,8131,8152,4589,5149,5236, 5866,5312,5973,6088,6503,5397,6094,6152,6526,6227,6618,6622,7034,5399,6226,6272,6617,635 0,6805,6815,7100,6462,6816,6936,7181,6950,7220,7263,7517,5405,6299,6398,6811,6476,6917,69 45,7212,6522,6958,6994,7270,7036,7309,7337,7532,6576,7009,7061,7320,7117,7378,7407,7590,7 131,7389,7456,7622,7459,7648,7674,7865,5915,6463,6500,6949,6542,6995,7035,7299,6683,7063, 7093,7357,7137,7427,7454,7602,6767,7099,7161,7391,7207,7458,7465,7640,7234,7466,7472,767 8,7543,7695,7746,7888,6802,7206,7230,7471,7287,7510,7516,7686,7311,7542,7565,7731,7610,77 56,7766,7911,7356,7594,7621,7767,7663,7783,7821,7931,7715,7824,7846,7953,7859,7971,7990,8 067,5932,6525,6619,7060,6749,7098,7157,7430,6789,7168,7213,7467,7254,7482,7487,7681,6848, 7231,7286,7488,7310,7537,7561,7722,7347,7588,7609,7761,7641,7777,7806,7916,6946,7298,733 6,7564,7424,7605,7603,7778,7439,7626,7645,7800,7687,7822,7832,7955,7475,7664,7697,7829,77 23,7853,7862,7974,7749,7884,7900,7995,7933,8011,8027,8091,6979,7359,7426,7630,7464,7660,7 688,7825,7535,7714,7736,7856,7741,7864,7894,7985,7549,7737,7748,7891,7779,7899,7927,8008, 7816,7932,7941,8016,7964,8040,8050,8099,7589,7791,7802,7917,7833,7935,7944,8023,7847,796 2,7975,8046,7991,8058,8073,8117,7904,7977,7996,8061,8013,8077,8082,8129,8024,8087,8095,81 34,8106,8142,8151,8171,6039,6686,6781,7169,6846,7221,7271,7522,6906,7293,7319,7539,7358,7 577,7618,7807,6970,7338,7429,7599,7457,7659,7642,7818,7469,7670,7690,7844,7734,7854,7869, 7981,7120,7452,7470,7658,7534,7683,7717,7857,7538,7735,7743,7870,7757,7895,7907,8004,755 2,7752,7774,7906,7815,7926,7939,8017,7830,7957,7963,8041,7976,8051,8064,8110,7136,7533,75 36,7730,7553,7740,7760,7898,7591,7782,7801,7920,7823,7936,7961,8031,7696,7814,7834,7940,7 848,7969,7978,8048,7897,7979,7997,8062,8014,8076,8081,8128,7742,7852,7890,7970,7905,7993, 8006,8066,7929,8010,8019,8080,8030,8088,8098,8137,7943,8025,8043,8094,8056,8101,8109,814 4,8068,8115,8121,8149,8126,8157,8159,8179,7160,7555,7576,7803,7682,7820,7831,7956,7719,78 43,7855,7972,7893,7984,8003,8065,7747,7868,7901,7987,7918,8007,8020,8079,7937,8028,8018,8 085,8049,8097,8105,8140,7817,7909,7925,8012,7954,8022,8042,8092,7967,8044,8055,8102,8063, 8107,8118,8148,7992,8059,8072,8111,8083,8123,8127,8155,8089,8133,8136,8161,8143,8164,8166, 8176,7849,7928,7966,8045,7983,8054,8060,8108,7999,8074,8078,8120,8086,8124,8135,8158,800 5,8084,8093,8132,8104,8138,8139,8165,8116,8145,8147,8167,8153,8172,8174,8184,8038,8100,81 03,8141,8119,8146,8150,8169,8125,8154,8156,8173,8162,8175,8180,8186,8130,8160,8163,8177,8 168,8178,8181,8187,8170,8182,8183,8188,8185,8189,8190,8191]
›APPENDIX · 7 of 21
Sequence Group 2: Q2_2048
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,41,144,28,6 9,42,516,49,74,272,1024,1025,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,137,82,56,27,97,39,259,84,138,145,261,29,1026,1028,43,98,515,88,140,30,146,71,262,265, 161,576,45,100,640,51,148,46,75,266,273,517,104,162,1032,1040,53,193,152,77,164,768,268,274, 518,54,83,57,521,112,135,78,289,194,85,276,522,58,1056,1027,168,139,99,86,60,280,89,290,529, 524,196,141,101,147,1029,1088,176,142,530,321,31,200,90,545,292,322,532,263,149,102,105,304, 296,163,92,47,267,385,1033,1030,546,324,208,386,150,153,165,106,55,328,536,577,548,113,154, 79,1041,1034,269,108,578,224,166,519,552,195,270,641,523,275,580,291,1042,1152,59,169,560,1 14,277,156,87,197,116,170,61,531,525,642,1036,1057,281,278,526,177,293,388,91,584,1089,1044, 769,198,172,120,201,336,62,282,1280,1058,143,103,178,294,93,644,202,592,323,392,1048,1060, 297,770,107,180,151,209,284,648,1031,1153,94,204,298,400,608,352,325,533,155,210,305,547,30 0,109,1090,1536,184,534,537,115,167,225,326,306,1035,1064,772,157,656,329,110,117,212,171,1 092,1154,776,330,226,549,538,387,308,216,1043,1037,416,271,279,158,1072,1038,337,550,672,1 18,332,579,540,389,173,121,553,199,784,179,228,338,312,704,1096,1281,390,174,554,581,1045,1 156,393,283,122,448,353,561,1059,1282,203,63,340,394,527,582,556,181,295,285,232,124,205,18 2,643,562,286,585,1050,1537,299,354,1104,1061,211,401,185,396,1049,1046,344,586,645,593,53 5,240,206,95,327,564,800,402,1160,1284,356,307,301,417,1288,1062,213,568,832,588,186,646,40 4,227,896,594,418,302,1538,1120,649,771,360,539,1091,1065,1168,1052,111,331,214,309,188,449, 217,408,609,596,551,650,1093,1066,229,159,420,310,1540,1073,541,773,1098,1296,610,657,333, 119,600,339,218,368,652,230,391,313,450,542,1184,1544,334,233,555,774,175,123,658,612,1312, 1552,341,777,220,314,1216,1568,424,395,673,583,1094,1068,355,287,183,234,1155,1105,125,557, 660,616,1074,1097,1039,1344,342,316,241,778,563,345,452,397,1157,1076,1047,1158,403,207,6 74,558,785,432,357,187,236,664,624,587,1408,1100,780,705,126,242,565,398,1161,1106,346,456, 358,405,1080,1051,1121,1063,303,569,244,595,189,566,676,361,706,589,215,786,647,348,419,40 6,464,680,801,362,1283,1108,590,409,1162,1169,1285,1053,570,788,597,572,219,311,1067,1122,1 539,1112,708,598,601,651,421,792,802,611,1164,1054,602,410,1170,1095,231,688,653,248,369,19 0,364,654,659,335,1286,1289,480,315,221,370,1185,1600,1069,1124,613,422,425,451,1664,1075, 614,543,235,412,343,372,1172,1070,775,317,222,426,1099,1290,453,237,559,833,804,712,1297,1 541,1128,1186,834,661,808,779,1077,1217,617,604,1176,1101,433,720,816,836,347,897,1188,179 2,1292,1298,243,662,454,318,675,618,1542,1078,898,781,376,428,1107,1081,665,736,567,840,62 5,238,1545,1136,1159,1102,359,457,1313,1218,399,787,591,678,1109,1300,434,677,349,245,458,6 66,620,363,127,191,782,407,1546,1082,1192,1163,436,626,571,465,1123,1110,681,246,707,350,10 84,1304,599,668,790,460,1113,1314,249,682,573,411,803,789,709,365,1553,1548,1220,1165,440,6 28,689,374,423,466,793,250,1125,1171,1200,1166,1554,1345,1055,1224,371,481,574,413,1114,15 69,1316,1346,603,366,468,655,900,805,615,684,1556,1287,710,429,1173,1126,794,252,1129,1328, 373,605,848,690,713,632,1320,1187,482,806,1116,1071,427,904,1291,1409,414,223,663,692,1570, 1348,835,619,1232,1410,472,455,796,809,1174,1177,1189,1130,714,721,837,716,864,810,606,912, 1079,1352,722,696,377,435,817,319,1560,1601,621,812,1572,1137,484,430,1178,1103,1293,1132, 838,667,488,239,378,459,1602,1248,1190,1543,1576,1219,622,627,437,380,1294,1665,1547,1299, 818,461,496,669,679,724,841,629,351,467,1604,1315,1083,1193,438,737,1584,1138,251,462,442, 441,469,247,1301,1180,683,842,1111,1221,1140,1194,738,899,670,783,1085,1555,1549,1666,849, 820,1305,1302,728,928,1550,1201,791,367,901,630,1317,1412,685,844,633,711,1115,1608,1793,1 222,1196,1144,1225,1360,253,691,1086,1306,824,902,686,740,850,375,444,470,483,415,1167,112 7,1202,1318,1117,1668,1226,1616,485,905,1347,1416,795,473,1321,1794,634,744,852,960,1131,1 204,865,693,1175,1233,797,906,1308,1672,715,807,1118,1228,474,636,1322,1424,1632,1376,694, 254,717,575,913,798,1349,1557,1179,1234,1329,1571,1324,1133,811,379,1208,1558,697,431,607, 489,1561,1139,866,723,486,908,718,813,476,856,1191,1249,1350,1330,839,725,1796,1181,1680,1 353,698,914,752,868,1134,1141,819,814,1236,1195,1800,1354,1250,1573,1562,1411,1332,1240,43 9,929,490,623,671,739,916,463,843,381,1440,1295,1303,1182,1361,1574,497,930,1696,1142,821, 726,961,872,1356,1603,492,631,1564,1413,1197,1145,729,700,443,741,1577,1223,1808,1203,125 2,1362,845,920,1336,1728,382,822,1414,1198,851,730,1578,1605,1417,1307,498,880,1146,1472,7 42,445,471,635,932,687,1377,1585,903,825,1227,1087,1364,1418,500,846,745,826,1551,1606,158 0,1205,1319,1309,732,446,1256,1148,1229,1206,1667,1586,962,936,475,853,867,637,1310,1609,1 323,1378,1235,1425,907,487,695,746,828,753,1209,1420,1368,1610,854,857,1669,1617,1559,126 4,1230,1119,504,799,255,964,1351,1588,1824,1426,1380,1331,909,719,477,915,1325,1441,638,74 8,944,869,1237,1592,491,699,1856,1612,754,858,1210,1670,1428,1251,478,968,1920,1618,1442,1 326,1673,1795,383,910,1384,1563,1135,1355,815,976,870,917,727,493,1238,1333,873,701,1212,1 473,1241,1432,931,756,1633,1620,1575,1674,860,499,1253,1183,1444,1334,1565,1797,731,823,9 22,874,1634,1681,918,502,1357,1143,1624,1363,933,743,1242,1392,760,881,1676,1254,1415,133 7,1474,1566,1358,1257,494,702,1579,1798,921,501,1199,1147,1682,1636,1365,1801,876,847,992, 447,1244,1338,733,827,1448,1419,934,882,1697,1607,937,963,1379,1311,1207,1258,1149,1581,7 47,505,855,924,1684,1640,1366,1340,1265,1802,734,829,1587,1369,1476,1421,965,938,1427,123 1,1698,1582,1809,1456,884,506,1381,1211,749,945,1260,1688,1648,1611,966,755,859,940,1804,1 729,1150,1266,1589,1422,1370,1480,830,911,871,639,1382,1429,1327,1593,1268,1619,888,479,1 213,1590,1700,1385,1730,1613,946,750,1239,1810,1671,1372,1443,1430,1488,1704,969,508,861, 757,1825,1386,970,919,1614,1433,875,862,1594,1812,1621,1596,758,948,1243,1335,1732,1622,1 625,1675,1445,1816,977,923,1826,1635,972,761,1626,1434,1255,1712,877,952,1677,1272,495,70 3,1393,1214,1388,1678,935,978,1683,1359,1504,1339,1245,1394,1637,1446,1449,1475,1638,1567, 1259,1436,883,762,1367,1396,503,925,1799,1341,1246,1450,878,735,1477,1261,993,885,1583,18 57,1828,1736,939,994,1858,1685,1832,1803,1641,1628,1457,1744,1840,1860,980,926,764,941,13 71,1921,1267,1686,1478,1342,967,886,1699,1642,831,947,1922,1805,1400,1452,1689,1760,507,8 89,1591,1864,1649,1262,984,751,1383,1481,942,996,1423,1811,1615,1702,1458,1701,1373,1269, 1482,1690,1644,1387,971,890,1151,1215,1806,1431,1460,1650,509,949,973,1000,1595,1489,1705, 1270,1731,1374,892,950,1623,1692,1814,1484,1273,1706,863,759,1008,510,1597,1435,1827,181 3,1733,1389,1464,1652,1713,1398,1447,1490,979,953,1817,1274,1395,1505,1598,1437,763,974,1 627,1390,1492,1679,954,879,1924,1829,981,982,1639,1708,1734,1453,1818,1276,927,995,1397,1 629,1872,1714,1737,1656,1506,1830,1451,1928,1438,1247,1687,1716,1859,1643,1496,1479,1820, 1833,765,956,1738,1745,1861,1740,1888,1834,887,985,1630,1936,1746,1720,1401,1459,997,986, 1841,1343,1645,1836,1508,1454,1862,1691,943,891,1512,1263,1402,1483,1646,1651,1461,1404,1 842,1485,998,766,1520,1693,511,988,1703,1748,1865,1653,1375,1491,1462,1761,1275,1486,1466, 1465,1001,951,1493,1271,1707,1866,1762,1923,1694,1807,1873,1844,1752,1952,1815,1391,1002, 893,1925,1654,1709,1868,1657,1735,1277,1715,975,894,1848,1926,1710,1764,1874,1399,1468,1 494,1507,1439,1509,1929,1009,955,1819,1497,1658,1768,1876,1984,1889,1717,1821,1930,1739,1 831,1004,1010,1498,1660,957,983,1718,1278,1741,1599,1937,1822,958,987,1835,1403,1721,1455, 1631,1513,1890,1747,1012,999,1510,1932,1742,1837,1500,1880,1863,1749,1016,767,1722,1938, 1776,1892,1843,1838,1463,1953,1514,1647,1695,1763,1940,1487,1867,1405,989,1003,1521,1954, 1845,1750,1985,1896,1516,1655,1753,1724,1467,1765,990,1005,1869,1944,1406,1846,1875,1754, 1522,1904,1766,1469,1495,1659,959,1011,1956,1711,1927,1849,1524,1870,1769,1850,1756,1470, 1986,1960,1499,1877,1891,1661,1931,1511,1013,895,1719,1770,1852,1777,1878,1881,1528,1823, 1279,1988,1933,1743,1501,1939,1662,1772,1006,1014,1968,1893,1515,1723,1778,1882,1502,199 2,1407,1934,1839,2000,1894,1941,1017,1018,1751,1517,1897,1725,1955,1780,1884,1523,1755,18 47,1946,1898,1942,1526,1957,1767,991,1020,1784,1905,1518,1726,1945,1525,1900,1871,2016,14 71,1757,1851,1958,1906,1961,1987,1771,1529,1879,1948,1758,1853,1989,1962,1908,1530,1773,1 969,1990,1779,1883,1964,1854,1935,1895,1663,1912,1503,1970,1774,1993,1532,1885,1781,1994, 1943,1899,1886,1782,1972,2001,1947,1996,1785,1901,1976,1519,1727,1959,2002,1007,1015,190 7,1786,1527,1949,1902,1759,2017,1909,1963,2018,2004,1950,1788,1965,1991,1910,1855,1971,15 31,1913,2008,1775,1966,2020,1995,1914,1533,1973,1997,2024,1916,1974,1887,1783,2032,1534,2 003,1977,1019,1021,1787,1998,1978,1903,2005,2006,1951,2019,1789,1980,1911,2009,2021,2010, 1967,1915,2022,1790,1535,2012,2025,1975,1022,1023,2026,1917,1999,1918,2033,1979,2028,203 4,1981,2007,1982,2011,2036,2023,2040,1791,2013,2027,2014,2029,1983,2035,2037,1919,2030,20 38,2041,2042,2015,2044,2031,2039,2043,2045,2046,2047]
›APPENDIX · 8 of 21
Sequence Group 2: Z2_2048
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,89,57,97,105, 170,6,17,21,40,23,45,51,91,29,55,59,100,73,112,117,185,34,61,76,115,81,126,135,198,88,137,147, 224,154,234,256,369,9,18,26,54,30,58,72,107,36,77,62,118,85,129,141,205,44,75,87,136,93,144,1 53,230,103,156,172,246,184,264,282,405,53,90,101,152,113,162,179,261,122,180,197,274,209,29 5,312,440,139,203,227,301,232,313,337,467,253,343,362,485,379,508,544,722,15,25,31,74,39,80, 83,140,48,86,94,151,104,161,167,260,56,95,106,163,116,178,194,276,128,195,204,290,229,309,33 1,455,66,110,123,183,130,196,212,302,150,225,233,315,252,342,355,484,166,243,262,347,275,37 5,381,504,298,394,422,535,444,562,615,723,70,127,143,215,160,231,251,345,171,254,266,368,28 3,380,404,529,192,277,291,392,314,418,442,568,325,446,470,590,492,624,646,819,211,303,320,4 25,348,454,473,610,378,481,505,638,536,651,699,867,403,518,545,680,560,717,737,907,613,748, 767,902,799,950,1005,1188,20,37,41,92,49,96,108,177,50,109,119,186,132,208,216,329,63,120,13 3,219,145,228,241,330,155,240,257,361,278,377,384,503,68,142,157,221,174,244,263,376,182,27 2,284,388,294,414,429,558,181,292,305,413,324,443,457,591,350,475,493,623,517,645,683,851,7 9,169,175,268,191,288,304,406,199,311,319,441,338,466,480,619,255,334,349,469,370,490,516,6 40,398,521,550,674,571,716,739,892,287,364,389,502,412,534,552,704,434,565,577,721,616,755, 785,933,471,614,625,776,641,802,763,959,690,848,868,1019,879,1073,1110,1226,84,187,193,323, 245,341,354,474,269,360,371,497,395,523,547,708,285,393,409,528,424,553,573,725,447,581,607, 751,639,779,818,963,328,415,428,572,456,600,631,764,496,632,647,814,691,795,859,1023,533,6 70,714,849,730,878,898,1064,760,905,904,1098,960,1125,1149,1301,363,445,476,633,522,650,68 2,829,551,705,718,869,745,885,903,1071,574,733,765,893,786,906,961,1126,828,977,998,1158,10 34,1198,1218,1377,622,777,810,962,858,972,1030,1169,866,1025,1066,1208,1090,1237,1286,143 4,886,1080,1120,1253,1138,1291,1267,1460,1186,1321,1345,1510,1395,1542,1563,1666,27,43,52, 102,60,121,134,213,67,138,146,218,159,236,242,372,69,158,168,235,176,289,299,402,200,300,32 2,435,340,460,477,637,71,173,190,293,202,321,335,450,214,344,356,482,374,509,531,652,226,36 5,383,520,407,546,563,696,419,559,586,732,589,750,778,1007,111,201,210,339,220,357,373,499, 247,385,399,539,421,567,580,710,267,401,427,561,449,588,597,742,468,598,606,784,667,803,842, 1024,286,448,464,603,487,630,636,790,511,666,685,825,720,854,876,1067,538,698,731,877,761, 891,935,1091,807,940,980,1127,999,1161,1202,1369,114,217,237,382,265,400,423,570,279,432,45 1,599,472,612,617,787,310,465,486,618,510,661,681,820,537,694,719,865,743,887,918,1068,336, 498,530,684,564,715,711,888,575,736,749,910,791,938,956,1129,611,762,805,951,821,987,1004,1 170,847,1022,1046,1209,1097,1241,1287,1435,351,543,566,738,596,754,794,941,655,806,836,994, 839,1006,1032,1197,671,837,846,1029,889,1041,1085,1236,928,1096,1115,1260,1148,1304,1330, 1467,695,899,916,1069,957,1099,1124,1273,981,1140,1171,1320,1203,1348,1385,1517,1048,1173, 1212,1355,1247,1397,1410,1561,1276,1425,1457,1584,1490,1624,1663,1767,131,250,273,433,308, 461,483,644,318,491,519,663,542,689,724,919,346,532,569,709,587,753,744,932,601,766,798,97 6,830,990,1009,1187,408,576,602,752,654,789,811,995,662,831,841,1018,855,1033,1053,1232,67 2,850,884,1052,925,1084,1111,1261,954,1133,1141,1305,1172,1331,1366,1502,420,653,660,824,6 73,838,864,1040,697,890,911,1072,939,1106,1139,1299,804,924,958,1114,982,1159,1178,1322,10 35,1179,1213,1356,1252,1396,1405,1560,840,986,1028,1160,1049,1205,1234,1368,1087,1240,126 3,1404,1298,1430,1466,1591,1121,1277,1309,1456,1344,1471,1499,1632,1376,1511,1535,1651,15 52,1697,1707,1833,426,675,688,917,788,934,955,1132,815,973,991,1168,1031,1196,1227,1367,84 3,1008,1047,1199,1070,1235,1266,1401,1107,1290,1262,1421,1323,1461,1489,1602,929,1065,108 1,1246,1128,1272,1308,1440,1157,1312,1337,1476,1357,1491,1520,1650,1204,1349,1384,1503,14 11,1543,1553,1681,1431,1577,1590,1721,1625,1738,1746,1812,983,1086,1156,1313,1189,1336,13 54,1498,1219,1394,1400,1534,1424,1544,1585,1706,1233,1420,1441,1576,1488,1594,1595,1739,1 516,1633,1641,1747,1667,1784,1798,1884,1300,1470,1477,1603,1521,1640,1662,1757,1545,1680, 1696,1785,1734,1799,1850,1946,1562,1720,1735,1813,1756,1832,1851,1947,1766,1866,1867,198 6,1885,1987,2010,2011,64,65,98,149,99,164,189,280,124,188,207,306,238,327,333,514,125,206,2 22,326,249,358,397,526,270,396,386,555,439,585,605,774,148,239,259,366,271,391,417,557,307, 437,453,592,501,628,643,813,332,459,512,635,525,664,687,844,554,693,727,896,740,920,952,113 5,165,248,296,436,316,452,500,609,352,513,462,648,541,669,703,861,390,507,549,692,579,712,7 35,912,595,746,780,942,812,968,996,1185,431,556,593,734,629,768,797,965,658,800,835,984,863, 1017,1050,1230,701,857,901,1027,914,1051,1083,1269,947,1095,1122,1293,1151,1318,1360,153 6,223,281,317,506,359,524,527,702,410,548,582,729,604,759,771,964,438,583,608,769,642,796,8 32,988,668,833,860,1012,909,1043,1077,1255,478,626,659,809,676,834,872,1036,728,897,915,10 55,946,1094,1113,1292,770,931,966,1103,985,1145,1153,1316,1020,1174,1214,1347,1242,1378,14 37,1537,494,665,707,875,758,913,945,1101,775,948,970,1134,997,1152,1184,1339,826,989,1013,1 166,1054,1206,1238,1386,1063,1244,1274,1412,1302,1446,1464,1615,871,1037,1058,1217,1104,1 254,1279,1428,1150,1285,1317,1454,1350,1469,1515,1653,1183,1328,1361,1494,1374,1529,1549, 1683,1433,1558,1579,1676,1601,1704,1741,1842,258,353,367,578,411,584,620,793,416,621,649,8 16,678,862,880,1075,463,656,679,883,713,908,927,1076,741,926,953,1119,992,1147,1162,1315,48 8,706,747,895,782,936,967,1146,808,978,1000,1164,1016,1200,1223,1372,801,1014,1039,1195,10 62,1239,1257,1413,1108,1281,1303,1445,1327,1463,1497,1643,515,773,783,974,823,1010,1038,1 190,845,1045,1057,1231,1088,1268,1284,1443,949,1078,1105,1271,1136,1296,1326,1458,1176,13 33,1364,1492,1389,1528,1551,1672,1003,1130,1165,1314,1194,1346,1370,1518,1228,1381,1399,1 533,1438,1569,1587,1695,1275,1436,1447,1580,1459,1604,1573,1713,1506,1638,1654,1749,1659, 1783,1802,1860,540,817,827,1061,937,1093,1112,1280,975,1118,1137,1307,1175,1335,1363,1522, 1001,1167,1193,1338,1216,1371,1391,1539,1245,1403,1427,1565,1455,1583,1614,1717,1074,120 1,1222,1390,1256,1418,1449,1574,1306,1450,1465,1612,1507,1599,1647,1751,1343,1484,1526,16 39,1540,1658,1674,1774,1570,1679,1678,1796,1714,1809,1823,1895,1123,1243,1282,1451,1334,1 468,1496,1621,1365,1519,1530,1655,1557,1661,1677,1781,1392,1547,1575,1673,1588,1682,1715, 1810,1620,1723,1736,1826,1762,1846,1858,1923,1444,1581,1610,1716,1646,1718,1758,1831,165 2,1753,1776,1854,1792,1869,1888,1942,1664,1786,1806,1875,1818,1891,1881,1950,1840,1903,19 11,1966,1927,1974,1983,2006,297,387,430,594,458,657,686,873,479,700,726,882,757,922,930,11 42,489,756,772,921,792,1011,1021,1182,852,1026,1060,1229,1092,1258,1283,1453,495,781,822,1 015,856,1059,1079,1250,874,1100,1116,1288,1144,1319,1341,1472,900,1131,1155,1332,1191,136 2,1379,1512,1207,1373,1406,1546,1409,1564,1582,1743,627,853,870,1089,894,1117,1143,1311,94 3,1163,1177,1353,1211,1383,1402,1524,971,1181,1221,1375,1249,1408,1415,1554,1270,1416,142 6,1586,1483,1605,1634,1752,1002,1248,1264,1423,1295,1448,1452,1596,1325,1482,1501,1619,15 32,1644,1656,1777,1352,1514,1541,1657,1571,1671,1699,1793,1609,1702,1724,1811,1737,1829,1 848,1921,634,881,923,1154,969,1180,1215,1388,993,1224,1251,1417,1278,1432,1439,1589,1044, 1265,1294,1442,1324,1479,1495,1616,1351,1508,1531,1649,1555,1665,1688,1778,1082,1310,134 0,1500,1380,1527,1525,1668,1393,1548,1559,1684,1597,1700,1710,1815,1429,1572,1607,1705,16 17,1729,1740,1834,1637,1750,1768,1855,1795,1871,1889,1943,1109,1359,1382,1550,1414,1568,1 598,1703,1475,1608,1626,1732,1629,1742,1760,1845,1485,1627,1636,1755,1669,1765,1789,1868, 1692,1794,1805,1876,1822,1896,1906,1953,1509,1675,1686,1779,1711,1797,1808,1883,1725,182 0,1835,1902,1849,1912,1925,1969,1770,1837,1856,1915,1873,1929,1934,1981,1886,1939,1949,19 88,1960,1996,2005,2027,677,944,979,1225,1042,1259,1289,1462,1056,1297,1329,1481,1358,1505, 1538,1689,1102,1342,1387,1523,1407,1567,1556,1694,1419,1578,1600,1722,1622,1730,1745,184 1,1192,1398,1422,1566,1474,1593,1611,1733,1480,1623,1631,1748,1645,1761,1773,1862,1486,16 42,1660,1772,1691,1788,1803,1877,1708,1817,1821,1897,1836,1907,1918,1964,1210,1473,1478,1 618,1487,1628,1648,1764,1513,1670,1685,1782,1701,1800,1819,1893,1606,1690,1712,1804,1726, 1827,1838,1904,1763,1839,1857,1916,1874,1928,1933,1980,1630,1728,1754,1828,1771,1853,186 4,1920,1791,1870,1879,1932,1892,1940,1952,1991,1807,1887,1899,1948,1910,1955,1963,1998,19 22,1967,1973,2003,1978,2013,2015,203 5,1220,1493,1504,1687,1592,1698,1709,1816,1613,1719,1 731,1830,1759,1844,1861,1919,1635,1744,1769,1847,1780,1865,1880,1931,1801,1890,1878,1937, 1905,1951,1959,1994,1693,1775,1787,1872,1814,1882,1898,1944,1825,1900,1909,1956,1917,196 1,1970,2002,1852,1913,1924,1965,193 5,1975,1979,2009,1941,1985,1990,2017,1997,2020,2022,20 32,1727,1790,1824,1901,1843,1908,1914,1962,1859,1926,1930,1972,1938,1976,1989,2014,1863,1 936,1945,1984,1958,1992,1993,2021,1968,1999,2001,2023,2007,2028,2030,2040,1894,1954,1957, 1995,1971,2000,2004,2025,1977,2008,2012,2029,2018,2031,2036,2042,1982,2016,2019,2033,202 4,2034,2037,2043,2026,2038,2039,2044,2041,2045,2046,2047]
›APPENDIX · 9 of 21
Sequence Group 2: Q2_4096
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,41,144,28,6 9,42,516,49,74,272,1024,1025,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,137,82,56,27,97,39,259,84,138,145,261,29,1026,1028,43,98,515,88,140,30,146,71,262,265, 161,576,45,100,640,51,148,46,75,266,273,517,104,162,1032,1040,53,193,2048,2049,2050,2052,15 2,77,164,768,268,274,518,54,83,57,521,112,135,78,289,194,85,276,522,58,1056,1027,168,139,99, 86,60,280,89,290,529,524,196,141,101,147,1029,1088,176,142,530,321,31,200,90,545,292,322,53 2,263,149,102,105,304,296,163,92,47,267,385,1033,1030,546,324,2056,2064,2080,2051,208,386,1 50,153,165,106,55,328,536,577,548,113,154,79,1041,1034,269,108,578,224,166,519,552,195,270, 641,523,275,580,291,1042,1152,59,169,560,114,277,156,87,197,116,170,61,531,525,642,1036,105 7,2053,2112,2057,2054,281,278,526,177,293,388,91,584,1089,1044,769,198,172,120,201,336,62,2 82,1280,1058,143,103,178,294,93,644,202,592,323,392,1048,1060,297,770,107,180,151,209,284,6 48,1031,1153,94,204,2065,2058,2066,2176,298,400,608,352,325,533,155,210,305,547,300,109,10 90,1536,184,534,537,115,167,225,326,306,1035,1064,772,157,656,329,2060,2081,2113,2068,110,1 17,212,171,1092,1154,776,330,226,549,538,387,308,216,1043,1037,416,271,279,158,1072,1038,3 37,550,672,118,332,579,540,389,173,121,553,199,784,179,228,338,312,704,1096,1281,390,174,23 04,2082,2072,2084,554,581,1045,1156,393,283,122,448,353,561,1059,1282,203,63,340,394,527,5 82,556,181,295,285,232,124,205,182,643,562,286,585,1050,1537,2055,2177,2114,2560,299,354,1 104,1061,211,401,185,396,1049,1046,344,586,645,593,535,240,206,95,327,564,800,402,1160,128 4,356,307,301,417,2059,2088,2116,2178,1288,1062,213,568,832,588,186,646,404,227,896,594,41 8,302,1538,1120,649,771,360,539,1091,1065,1168,1052,111,331,214,309,2067,2061,2096,2062,18 8,449,217,408,609,596,551,650,1093,1066,229,159,420,310,1540,1073,2120,2305,2069,2180,541, 773,1098,1296,610,657,333,119,600,339,218,368,652,230,391,313,2083,2306,2074,2561,450,542, 1184,1544,334,233,555,774,175,123,658,612,1312,1552,341,777,220,314,1216,1568,2128,2085,20 73,2070,424,395,673,583,1094,1068,355,287,183,234,1155,1105,125,557,660,616,2184,2308,2312, 2086,1074,1097,1039,1344,342,316,241,778,563,345,452,397,1157,1076,1047,1158,403,207,674, 558,785,432,357,187,236,664,624,587,2562,2144,2115,2089,1408,1100,780,705,126,242,565,398, 1161,1106,346,456,358,405,1080,1051,2192,2076,2117,2090,1121,1063,303,569,244,595,189,566, 676,361,706,589,215,786,647,348,2564,2097,2122,2320,419,406,464,680,801,362,1283,1108,590, 409,1162,1169,1285,1053,570,788,3072,3073,2208,2568,597,572,219,311,1067,1122,1539,1112,23 36,2576,2240,2592,708,598,601,651,421,792,802,611,1164,1054,602,410,1170,1095,231,688,653,2 48,369,190,364,654,659,335,1286,1289,480,315,221,370,1185,1600,1069,1124,613,422,2118,2092, 2179,2129,425,451,1664,1075,614,543,235,412,2098,2121,2063,2368,343,372,1172,1070,775,317, 222,426,1099,1290,453,237,2181,2100,2071,2182,559,833,804,712,1297,1541,1128,1186,834,661, 808,779,1077,1217,617,604,1176,1101,433,720,816,836,347,897,1188,1792,1292,1298,243,662,45 4,318,675,618,1542,1078,2432,2124,2185,2130,898,781,376,428,2104,2075,2145,2087,1107,1081, 665,736,567,840,625,238,2307,2132,2186,2193,1545,1136,1159,1102,359,457,1313,1218,399,787, 591,678,1109,1300,434,677,349,245,458,666,620,363,127,191,2309,2077,3074,3076,782,407,1546, 1082,1192,1163,436,626,2091,2146,2563,2136,571,465,1123,1110,681,246,707,350,1084,1304,59 9,668,790,460,1113,1314,249,682,573,411,803,789,709,365,2188,2078,2194,2119,1553,1548,1220, 1165,440,628,689,374,2310,2313,2209,2624,2093,2148,2688,2099,423,466,793,250,1125,1171,120 0,1166,1554,1345,1055,1224,371,481,574,413,1114,1569,1316,1346,603,366,468,655,2196,2094,2 123,2314,900,805,615,684,1556,1287,710,429,2321,2565,2152,2210,1173,1126,794,252,3080,308 8,2101,2241,1129,1328,373,605,848,690,713,632,1320,1187,482,806,1116,1071,427,904,1291,140 9,414,223,663,692,1570,1348,835,619,1232,1410,2200,2125,2212,2816,472,455,796,809,1174,117 7,1189,1130,714,721,837,716,864,810,606,912,2316,2322,2566,2102,1079,1352,722,696,377,435, 817,319,2131,2105,2569,2160,1560,1601,621,812,1572,1137,484,430,2183,2126,2337,2242,1178, 1103,1293,1132,838,667,488,239,2133,2324,2570,2106,378,459,1602,1248,1190,1543,1576,1219,3 104,3075,2216,2187,2147,2134,2108,2328,622,627,437,380,1294,1665,1547,1299,818,461,496,66 9,679,724,841,629,2137,2338,2577,2572,2244,2189,2149,2195,351,467,1604,1315,1083,1193,438, 737,1584,1138,251,462,442,441,469,247,1301,1180,683,842,1111,1221,1140,1194,3077,3136,2224, 2190,738,899,670,783,1085,1555,1549,1666,849,820,1305,1302,2578,2369,2079,2248,728,928,15 50,1201,791,367,901,630,2138,2593,2340,2370,2580,2311,2197,2150,1317,1412,685,844,633,711, 1115,1608,1793,1222,1196,1144,1225,1360,253,691,1086,1306,824,902,686,740,850,375,444,470, 483,415,1167,1127,1202,1318,1117,1668,1226,1616,485,905,1347,1416,2153,2352,2344,2211,795, 473,1321,1794,2140,2095,2315,2433,3081,3078,2594,2372,634,744,852,960,1131,1204,865,693,1 175,1233,797,906,2256,2434,2198,2201,2213,2154,2103,2376,1308,1672,715,807,1118,1228,474, 636,1322,1424,1632,1376,694,254,717,575,2584,2625,2596,2161,913,798,1349,1557,2202,2127,3 089,3082,1179,1234,1329,1571,1324,1133,811,379,1208,1558,697,431,607,489,1561,1139,866,723, 486,908,2317,2156,2626,2272,718,813,476,856,1191,1249,1350,1330,2214,2567,2600,2243,2318, 2689,2571,2323,839,725,1796,1181,1680,1353,698,914,2628,2339,3090,3200,752,868,1134,1141,8 19,814,1236,1195,1800,1354,1250,1573,2107,2217,2608,2162,1562,1411,1332,1240,439,929,490, 623,2325,2204,2135,2245,671,739,916,463,843,381,1440,1295,1303,1182,1361,1574,2164,2218,2 109,2579,2573,2690,3084,3105,497,930,1696,1142,821,726,961,872,2329,2326,2574,2225,1356,1 603,492,631,2341,2436,2139,2632,1564,1413,1197,1145,729,700,443,741,1577,1223,1808,1203,3 137,3092,2817,2246,2220,2168,2249,2384,1252,1362,845,920,1336,1728,382,822,1414,1198,851, 730,2110,2330,3328,3106,1578,1605,1417,1307,498,880,1146,1472,2191,2151,2226,2342,742,445, 471,635,932,687,1377,1585,903,825,1227,1087,2141,2692,2250,2640,2371,2440,3096,3108,1364, 1418,500,846,2345,2818,2155,2228,745,826,1551,1606,1580,1205,1319,1309,2199,2257,2332,269 6,732,446,1256,1148,1229,1206,1667,1586,962,936,475,853,867,637,1310,1609,1323,1378,1235,1 425,907,487,695,746,3079,3201,2142,2252,2346,2448,2656,2400,828,753,1209,1420,1368,1610,8 54,857,2373,2581,2203,2258,1669,1617,1559,1264,1230,1119,504,799,2353,2595,2348,2157,255, 964,1351,1588,1824,1426,1380,1331,3138,3584,2232,2582,909,719,477,915,1325,1441,638,748,9 44,869,1237,1592,491,699,1856,1612,2585,2163,2215,2273,2374,2354,3083,3112,754,858,1210,1 670,1428,1251,478,968,1920,1618,1442,1326,1673,1795,383,910,2820,2205,2704,2377,2158,2165, 2260,2219,3140,3202,2824,2378,2274,2597,2586,2435,1384,1563,1135,1355,815,976,870,917,23 56,2264,3091,3085,2464,2319,2327,2206,727,493,1238,1333,873,701,1212,1473,1241,1432,931,7 56,1633,1620,1575,1674,3120,3086,2385,2598,860,499,1253,1183,2720,2166,2380,2627,1444,133 4,1565,1797,2588,2437,2221,2169,731,823,922,874,1634,1681,918,502,1357,1143,1624,1363,260 1,2247,2832,2227,933,743,1242,1392,2276,2386,2360,2752,760,881,1676,1254,3144,3329,2438,2 222,1415,1337,1474,1566,1358,1257,494,702,2602,2629,3093,3204,1579,1798,921,501,2441,2331, 2170,2496,1199,1147,1682,1636,1365,1801,876,847,2401,2609,3107,3330,2251,2111,2388,2442,9 92,447,1244,1338,733,827,1448,1419,934,882,1697,1607,937,963,1379,1311,2575,2630,2604,222 9,1207,1258,1149,1581,747,505,855,924,1684,1640,1366,1340,2343,2333,2280,2172,1265,1802,7 34,829,2253,2230,2691,2610,1587,1369,1476,1421,2334,2633,3098,3585,2347,2402,3152,3109,96 5,938,1427,1231,1698,1582,1809,1456,884,506,1381,1211,2259,2449,2233,2444,3097,3094,2392, 2634,2693,2641,2583,2288,749,945,1260,1688,1648,1611,966,755,2254,2143,2375,2612,2848,245 0,3208,3332,859,940,1804,1729,1150,1266,1589,1422,1370,1480,830,911,871,639,1382,1429,132 7,1593,1268,1619,2404,2355,2349,2465,3336,3110,2261,2616,888,479,1213,1590,2880,2636,2234, 2694,1700,1385,1730,1613,946,750,1239,1810,1671,1372,1443,1430,2452,2275,2944,2642,1488, 1704,969,508,2466,2350,3586,3168,2697,2819,2408,2587,861,757,1825,1386,970,919,1614,1433, 3139,3113,3216,3100,2159,2379,2262,2357,875,862,1594,1812,2236,2497,2265,2456,1621,1596,7 58,948,2657,2644,2599,2698,1243,1335,1732,1622,1625,1675,1445,1816,3141,3114,2277,2207,97 7,923,1826,1635,972,761,1626,1434,2468,2358,3588,3121,2589,2821,3146,3344,2658,2705,2381, 2167,2648,2387,2266,2416,1255,1712,877,952,2700,2278,2439,2361,1677,1272,495,703,1393,121 4,1388,1678,935,978,1683,1359,1504,1339,1245,1394,1637,1446,1449,1475,2498,2590,3232,3592, 2382,2281,2603,2822,2223,2171,2706,2660,3360,3600,2389,2825,1638,1567,1259,1436,2268,236 2,3264,3616,883,762,1367,1396,2472,2443,2721,2631,503,925,1799,1341,1246,1450,878,735,314 2,3116,2403,2335,1477,1261,993,885,2231,2282,3203,3153,1583,1857,1828,1736,2173,2605,2708, 2664,939,994,1858,1685,3122,3145,3087,3392,1832,1803,1641,1628,2390,2364,2289,2826,2611, 2393,2500,2445,1457,1744,1840,1860,980,926,764,941,1371,1921,1267,1686,3205,3124,3095,320 6,2451,2255,2722,2606,2833,2480,2405,2235,2284,2712,2672,2635,1478,1342,967,886,3456,3148, 2828,2753,1699,1642,831,947,1922,1805,1400,1452,2174,2290,2613,2446,1689,1760,507,889,15 91,1864,1649,1262,984,751,1383,1481,942,996,1423,1811,3209,3154,2394,2504,2406,2453,3128, 3099,1615,1702,1458,1701,3169,3111,2351,2617,2292,2643,2237,2614,1373,1269,1482,1690,164 4,1387,971,890,2724,2409,2754,2637,1151,1215,1806,1431,2263,2834,2695,2396,2467,2454,2512, 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8,1834,887,985,1630,1936,1746,1720,1401,1459,2723,2666,3590,3126,2946,2829,2424,2476,3155, 3129,2713,2784,997,986,1841,1343,1645,1836,1508,1454,1862,1691,943,891,2615,2888,2673,22 86,3593,3184,3207,3150,1512,1263,1402,1483,2407,2505,3361,3266,2447,2835,2639,2726,3157,3 348,2482,2725,1646,1651,1461,1404,1842,1485,998,766,2397,2293,2506,2714,2668,2411,2175,22 39,2830,2455,3594,3130,1520,1693,511,988,1703,1748,1865,1653,3240,3211,2484,2674,1375,149 1,1462,1761,1275,1486,1466,1465,2619,2513,3171,3158,1001,951,1493,1271,2729,2294,2755,239 8,1707,1866,1762,1923,3132,3352,2647,2716,2838,2508,3161,3362,1694,1807,1873,1844,2297,27 30,2621,2459,2851,2837,2757,2413,3601,3596,3268,3213,1752,1952,1815,1391,2488,2676,2737,2 422,2471,2514,2841,2298,1002,893,1925,1654,1709,1868,1657,1735,1277,1715,975,894,3173,321 9,3248,3214,1848,1926,1710,1764,3602,3393,3103,3272,2419,2529,2622,2461,1874,1399,1468,14 94,3162,3617,3364,3394,2651,2414,2516,2703,1507,1439,1509,1929,2948,2853,2663,2732,3604,3 335,2758,2477,3221,3174,2842,2300,1009,955,1819,1497,1658,1768,1876,1984,3177,3376,2421,2 653,1889,1717,1821,1930,2896,2738,2761,2680,3368,3235,2530,2854,1739,1831,1004,1010,3164, 3119,2475,2952,1498,1660,957,983,3339,3457,2462,2271,2711,2740,3618,3396,2883,2667,3280,3 458,2520,2503,2844,2857,1718,1278,1741,1599,3222,3225,3237,3178,1937,1822,958,987,2762,27 69,2885,2764,2912,2858,2654,2960,3127,3400,2770,2744,1835,1403,1721,1455,1631,1513,1890,1 747,2425,2483,2865,2367,1012,999,1510,1932,3608,3649,2669,2860,1742,1837,1500,1880,3620,3 185,2532,2478,1863,1749,1016,767,3226,3151,3341,3180,2886,2715,2536,2287,2426,2507,3650,3 296,1722,1938,1776,1892,1843,1838,1463,1953,3238,3591,3624,3267,2670,2675,2485,2428,3342, 3713,3595,3347,1514,1647,1695,1763,2866,2509,2544,2717,2727,2772,2889,2677,1940,1487,186 7,1405,2399,2515,3652,3363,3131,3241,2486,2785,3632,3186,2299,2510,989,1003,1521,1954,249 0,2489,2517,2295,1845,1750,1985,1896,3349,3228,2731,2890,3159,3269,3188,3242,1516,1655,17 53,1724,1467,1765,990,1005,2786,2947,2718,2831,3133,3603,3597,3714,2897,2868,3353,3350,27 76,2976,3598,3249,1869,1944,1406,1846,1875,1754,1522,1904,2839,2415,2949,2678,3365,3460,2 733,2892,2681,2759,3163,3656,1766,1469,1495,1659,3841,3270,3244,3192,3273,3408,2301,2739, 3134,3354,2872,2950,959,1011,1956,1711,2734,2788,2898,2423,2492,2518,2531,2463,3215,3175, 3250,3366,3165,3716,3274,3664,1927,1849,1524,1870,1769,1850,1756,1470,2533,2953,3395,346 4,1986,1960,1499,1877,2843,2521,3369,3842,1891,1661,1931,1511,2682,2792,2900,3008,3179,32 52,2913,2741,1013,895,1719,1770,3223,3281,2845,2954,3356,3720,2763,2855,3166,3276,2522,26 84,3370,3472,3680,3424,1852,1777,1878,1881,2742,2302,2765,2623,1528,1823,1279,1988,2961,2 846,3397,3605,3227,3282,3377,3619,1933,1743,1501,1939,3372,3181,2859,2427,1662,1772,1006, 1014,3256,3606,2745,2479,2655,2537,3609,3187,1968,1893,1515,1723,2914,2771,2534,2956,276 6,2861,2524,2904,3239,3297,3398,3378,2887,2773,3844,3229,3728,3401,2746,2962,2800,2916,31 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986,3475,3279,1788,1965,1991,1910,3746,3630,3857,3504,2932,2554,3429,3259,2797,2993,3308, 3736,3696,3659,3014,2803,2907,2988,3852,3777,1855,1971,1531,1913,3198,3314,3637,3470,200 8,1775,1966,2020,3418,3528,2878,2959,2919,2687,3430,3477,3375,3641,3316,3667,2936,2527,32 61,3638,3748,3433,3778,3661,2994,2798,3287,3858,1995,1914,1533,1973,3719,3420,3491,3478,3 536,3752,3017,2556,2909,2805,3873,3434,3018,2967,3662,3481,2923,2910,3642,3860,3669,3644, 2806,2996,3291,3383,3780,3670,1997,2024,1916,1974,3673,3723,3493,3864,3025,2971,3874,368 3,3020,2809,3674,3482,3303,3760,2925,3000,1887,1783,2032,1534,3725,3320,2543,2751,3441,32 62,3436,3726,2983,3026,3731,3407,3552,3387,3293,3442,3685,3494,3497,3523,3686,3615,3307,3 484,2003,1977,1019,1021,2931,2810,3415,3444,2551,2973,3847,3389,3294,3498,2926,2783,3525, 3309,3041,2933,3631,3905,3876,3784,2987,3042,3906,3733,1787,1998,1978,1903,3880,3851,368 9,3676,2005,2006,1951,2019,3505,3792,3888,3908,3028,2974,2812,2989,3419,3969,3315,3734,17 89,1980,1911,2009,3526,3390,3015,2934,3747,3690,2879,2995,3970,3853,3448,3500,3737,3808,2 555,2937,2021,2010,1967,1915,3639,3912,3697,3310,3032,2799,3431,3529,2990,3044,3471,3859, 3663,3750,3506,3749,2022,1790,1535,2012,3421,3317,3530,3738,3692,3435,3019,2938,3199,326 3,3854,3479,3508,3698,2557,2997,3021,3048,3643,3537,3753,3318,3779,3422,2940,2998,3671,37 40,3862,3532,3321,3754,2025,1975,1022,1023,2911,2807,3056,2558,3645,3483,3875,3861,3781,3 437,3512,3700,3761,3446,3495,3538,3027,3001,3865,3322,3443,3553,3646,3485,2026,1917,1999, 1918,2811,3022,3675,3438,3540,3727,3002,2927,3972,3877,3029,3030,3687,3756,3782,3501,386 6,3324,2975,3043,3445,3677,3920,3762,2033,1979,2028,2034,3785,3704,3554,3878,3499,3976,34 86,3295,3735,3764,3907,3691,3544,3527,3868,3881,2813,3004,3786,3793,3909,3788,3936,3882,2 935,3033,3678,3984,3794,3768,3449,3507,3045,3034,3889,3391,1981,2007,1982,2011,3693,3884, 3556,3502,3910,3739,2991,2939,3560,3311,3450,3531,3694,3699,3509,3452,3890,3533,3046,281 4,3568,3741,2559,3036,3751,3796,3913,3701,3423,3539,3510,3809,2036,2023,2040,1791,3323,35 34,3514,3513,3049,2999,3541,3319,3755,3914,3810,3971,3742,3855,3921,3892,3800,4000,3863,3 439,3050,2941,3973,3702,3757,3916,3705,3783,2013,2027,2014,2029,3325,3763,3023,2942,3896, 3974,3758,3812,3922,3447,3516,3542,3555,3487,3557,3977,3057,3003,3867,3545,3706,3816,392 4,4032,3937,3765,3869,3978,3787,3879,3052,3058,1983,2035,2037,1919,3546,3708,3005,3031,37 66,3326,3789,3647,3985,3870,3006,3035,3883,3451,3769,3503,3679,3561,3938,3795,3060,3047,3 558,3980,3790,3885,3548,3928,3911,3797,3064,2815,3770,3986,3824,3940,3891,3886,3511,4001, 3562,3695,3743,3811,3988,3535,3915,3453,3037,3051,3569,4002,3893,3798,4033,3944,3564,370 3,3801,3772,3515,3813,3038,3053,3917,3992,3454,3894,3923,3802,3570,3952,3814,3517,3543,37 07,3007,3059,4004,3759,3975,3897,3572,3918,3817,3898,3804,3518,4034,4008,3547,3925,3939,3 709,3979,3559,3061,2943,3767,3818,3900,3825,3926,3929,3576,3871,3327,4036,3981,3791,3549, 3987,3710,3820,3054,3062,4016,3941,3563,3771,2030,2038,2041,2042,3826,3930,3550,4040,345 5,3982,3887,4048,3942,3989,3065,3066,3799,3565,3945,3773,4003,3828,3932,3571,3803,3895,39 94,3946,3990,3574,4005,3815,3039,3068,3832,3953,3566,3774,3993,3573,3948,3919,4064,3519,3 805,3899,4006,3954,4009,4035,3819,3577,3927,3996,3806,3901,4037,4010,3956,3578,3821,4017, 4038,3827,3931,4012,3902,3983,3943,3711,3960,3551,4018,3822,4041,3580,3933,3829,4042,399 1,2015,2044,2031,2039,3947,3934,3830,4020,4049,3995,4044,3833,3949,4024,3567,3775,4007,40 50,3055,3063,3955,3834,3575,3997,3950,3807,4065,3957,4011,4066,4052,3998,3836,4013,4039,3 958,3903,4019,3579,3961,4056,3823,4014,4068,4043,3962,3581,4021,2043,2045,2046,2047,4045, 4072,3964,4022,3935,3831,4080,3582,4051,4025,3067,3069,3835,4046,4026,3951,4053,4054,399 9,4067,3837,4028,3959,4057,4069,4058,4015,3963,4070,3838,3583,4060,4073,4023,3070,3071,40 74,3965,4047,3966,4081,4027,4076,4082,4029,4055,4030,4059,4084,4071,4088,3839,4061,4075,4 062,4077,4031,4083,4085,3967,4078,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095]
›APPENDIX · 10 of 21
Sequence Group 2: Z2_4096
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,89,57,97,105, 174,6,17,21,40,23,45,51,91,29,55,59,100,73,112,117,189,34,61,76,115,81,126,139,206,88,141,151, 232,158,242,268,393,9,18,26,54,30,58,72,107,36,77,62,118,85,133,145,213,44,75,87,140,93,148,1 57,238,103,160,176,258,188,276,294,433,53,90,101,156,113,166,183,273,122,184,205,286,217,31 1,332,472,143,211,235,317,240,333,357,507,265,363,386,529,403,556,600,818,15,25,31,74,39,80, 83,144,48,86,94,155,104,165,171,272,56,95,106,167,116,182,202,288,132,203,212,306,237,325,35 1,491,66,110,123,187,134,204,220,318,154,233,241,335,264,362,375,528,170,255,274,367,287,39 9,405,552,314,422,454,587,480,622,687,819,70,127,147,223,164,239,263,365,175,266,278,392,29 5,404,432,581,200,289,307,420,334,450,474,628,345,482,510,658,536,696,726,947,219,319,340,4 57,368,490,513,682,402,525,553,714,588,731,791,1011,431,570,601,764,620,813,841,1071,685,85 2,883,1066,923,1130,1205,1484,20,37,41,92,49,96,108,181,50,109,119,190,136,216,224,349,63,12 0,137,227,149,236,253,350,159,252,269,385,290,401,408,551,68,146,161,229,178,256,275,400,18 6,284,300,416,310,442,461,618,185,308,321,441,344,475,493,659,370,515,537,695,569,725,767,9 87,79,173,179,280,195,304,320,434,207,327,339,473,358,506,524,691,267,354,369,509,394,534,5 68,720,426,573,606,758,631,812,843,1056,303,388,417,550,440,586,608,800,466,625,641,817,688, 859,901,1105,511,686,697,892,721,930,871,1139,778,984,1016,1227,1035,1305,1366,1534,84,191, 201,343,257,361,374,514,281,384,395,545,423,575,603,804,301,421,437,580,456,609,637,825,48 3,645,679,855,715,895,946,1143,348,443,460,636,492,672,703,880,544,708,727,942,779,915,999, 1231,585,754,810,985,830,1034,1062,1292,868,1069,1068,1346,1140,1389,1429,1673,387,481,52 0,709,574,730,766,961,607,801,814,1017,849,1041,1067,1303,638,837,881,1057,902,1070,1141,1 390,960,1161,1198,1438,1246,1498,1526,1797,694,893,938,1142,998,1152,1238,1449,1010,1233,1 294,1508,1334,1569,1642,1910,1042,1320,1380,1589,1410,1651,1611,1960,1478,1697,1737,2058, 1823,2130,2163,2394,27,43,52,102,60,121,138,221,67,142,150,226,163,244,254,396,69,162,172,2 43,180,305,315,430,208,316,342,467,360,500,521,713,71,177,194,309,210,341,355,486,222,364,3 80,526,398,557,583,736,234,389,407,572,435,602,623,788,451,619,650,836,657,854,894,1207,111, 209,218,359,228,381,397,547,259,409,427,591,453,627,644,806,279,429,459,621,485,656,669,84 6,508,670,678,900,751,931,974,1232,302,484,504,675,531,702,712,910,559,750,769,953,816,994, 1032,1295,590,790,831,1033,869,1047,1107,1335,935,1120,1172,1391,1199,1441,1502,1781,114,2 25,245,406,277,428,455,630,291,464,487,671,512,684,689,903,326,505,530,690,558,745,765,948, 589,786,815,1009,847,1043,1086,1300,356,546,582,768,624,811,807,1044,639,840,853,1074,911, 1118,1136,1393,683,870,933,1131,949,1179,1204,1450,983,1230,1266,1509,1345,1573,1643,1911, 371,599,626,842,668,858,914,1121,739,934,968,1194,971,1206,1244,1497,755,969,982,1237,1045, 1261,1325,1568,1100,1344,1371,1604,1428,1676,1710,1967,787,1063,1084,1301,1137,1347,1388, 1621,1173,1416,1451,1696,1503,1752,1809,2065,1272,1461,1520,1759,1579,1833,1858,2161,162 8,1881,1953,2212,2014,2296,2379,2627,135,262,285,465,324,501,527,724,338,535,571,747,598,7 77,824,1087,366,584,629,805,651,857,848,1104,673,882,922,1160,962,1182,1213,1479,436,640,67 4,856,738,909,939,1195,746,963,973,1226,995,1245,1277,1556,756,986,1040,1276,1093,1324,136 7,1605,1134,1397,1417,1677,1460,1711,1778,2046,452,737,744,952,757,970,1008,1260,789,1046, 1075,1304,1119,1362,1411,1663,932,1092,1138,1370,1174,1439,1466,1698,1247,1467,1521,1768, 1588,1832,1849,2160,972,1178,1236,1440,1273,1505,1558,1780,1327,1572,1607,1848,1662,1902, 1966,2223,1381,1629,1681,1952,1736,1975,2039,2316,1796,2059,2099,2347,2140,2465,2475,282 1,458,759,776,1085,908,1106,1135,1396,943,1153,1183,1448,1239,1496,1535,1779,975,1212,1267, 1499,1302,1559,1610,1837,1363,1650,1606,1877,1699,1961,2013,2250,1101,1293,1321,1578,139 2,1620,1680,1916,1437,1684,1729,1988,1769,2015,2068,2346,1504,1753,1808,2047,1859,2131,21 41,2417,1903,2193,2222,2521,2297,2554,2582,2768,1175,1326,1436,1685,1485,1728,1758,2038,1 527,1822,1836,2098,1880,2132,2213,2474,1557,1876,1917,2192,2012,2230,2231,2555,2064,2317, 2337,2583,2395,2688,2714,2996,1672,1974,1989,2251,2069,2336,2378,2609,2133,2416,2464,268 9,2546,2715,2870,3206,2162,2520,2547,2769,2608,2820,2871,3207,2626,2934,2935,3442,2997,34 43,3570,3571,64,65,98,153,99,168,193,292,124,192,215,322,246,347,353,566,125,214,230,346,26 1,382,425,578,282,424,410,611,471,649,677,890,152,247,271,390,283,419,449,617,323,469,489,6 60,549,700,723,941,352,495,564,711,577,748,771,980,610,785,827,1060,844,1088,1132,1399,169, 260,312,468,336,488,548,681,372,565,502,728,597,753,799,1005,418,555,605,784,643,808,839,10 76,663,850,896,1122,940,1148,1196,1477,463,616,661,838,701,884,921,1145,742,928,967,1176,10 07,1225,1274,1554,797,997,1065,1235,1078,1275,1323,1613,1127,1343,1382,1657,1431,1694,177 2,2104,231,293,337,554,383,576,579,798,438,604,646,829,676,867,887,1144,470,647,680,885,722, 920,964,1180,752,965,1004,1220,1073,1263,1309,1591,522,698,743,937,760,966,1020,1248,828, 1061,1079,1279,1126,1342,1369,1656,886,1103,1146,1351,1177,1421,1433,1692,1228,1462,1522, 1739,1574,1798,1913,2105,538,749,803,1023,866,1077,1125,1349,891,1128,1150,1398,1197,1432, 1476,1731,954,1181,1221,1446,1278,1506,1570,1810,1291,1576,1622,1864,1674,1922,1964,2267, 1019,1249,1282,1525,1360,1590,1631,1900,1430,1641,1693,1946,1754,1973,2063,2357,1475,170 8,1773,2018,1786,2093,2137,2419,1909,2146,2195,2408,2249,2472,2573,2850,270,373,391,642,4 39,648,692,913,448,693,729,944,762,1006,1036,1307,503,740,763,1039,809,1072,1095,1308,845, 1094,1133,1379,1192,1423,1442,1687,532,802,851,1059,898,1116,1147,1422,936,1162,1200,1444, 1224,1500,1531,1784,929,1222,1251,1491,1290,1571,1597,1865,1364,1637,1675,1921,1703,1963, 2037,2339,567,889,899,1154,951,1214,1250,1486,981,1265,1281,1555,1332,1612,1640,1919,1129, 1310,1361,1615,1408,1660,1702,1954,1464,1717,1776,2016,1813,2092,2139,2404,1203,1394,144 5,1686,1490,1738,1782,2066,1552,1805,1835,2097,1914,2173,2215,2455,1623,1912,1923,2196,19 55,2252,2181,2493,2050,2322,2358,2597,2375,2675,2734,2920,596,945,955,1289,1117,1341,1368, 1636,1155,1378,1409,1679,1463,1719,1775,2070,1201,1447,1489,1730,1524,1783,1815,2107,157 7,1839,1883,2169,1947,2199,2266,2505,1306,1501,1530,1814,1596,1870,1925,2182,1678,1926,19 65,2264,2051,2243,2343,2599,1735,2008,2082,2323,2128,2374,2406,2646,2174,2411,2410,2712,2 494,2753,2795,3023,1383,1575,1638,1927,1718,1972,2036,2281,1777,2067,2094,2359,2145,2377, 2409,2673,1820,2135,2183,2405,2220,2418,2495,2754,2280,2523,2552,2802,2618,2862,2914,312 3,1920,2197,2258,2504,2342,2506,2610,2811,2356,2601,2660,2882,2708,2941,3004,3190,2392,26 90,2738,2955,2790,3007,2981,3250,2848,3043,3087,3326,3127,3362,3415,3534,313,411,462,662, 494,741,770,1021,523,796,826,1038,865,1090,1102,1418,533,864,888,1089,912,1215,1229,1474,9 92,1234,1288,1553,1340,1598,1639,1945,539,897,950,1223,996,1283,1311,1582,1022,1348,1376, 1648,1420,1695,1733,1980,1064,1395,1435,1716,1487,1774,1799,2060,1507,1785,1850,2134,185 7,2168,2198,2575,699,993,1018,1333,1058,1377,1419,1683,1123,1443,1465,1757,1511,1807,1838, 2080,1151,1473,1529,1787,1581,1856,1867,2142,1614,1868,1882,2214,1999,2253,2318,2600,120 2,1580,1608,1879,1659,1924,1944,2240,1701,1998,2045,2279,2096,2340,2372,2661,1756,2062,21 29,2373,2175,2399,2467,2709,2257,2470,2524,2755,2553,2809,2868,3121,710,1037,1091,1434,11 49,1472,1523,1812,1193,1532,1583,1869,1630,1908,1915,2221,1264,1609,1658,1918,1700,1991,2 019,2276,1755,2056,2095,2345,2143,2393,2436,2662,1322,1682,1732,2044,1804,2083,2081,2396, 1821,2136,2147,2424,2241,2468,2482,2771,1901,2180,2255,2473,2277,2533,2572,2822,2321,259 8,2640,2883,2711,2943,3005,3191,1365,1771,1806,2138,1866,2172,2242,2471,1983,2256,2298,25 44,2313,2574,2616,2861,2009,2299,2320,2603,2397,2625,2697,2940,2452,2710,2737,2976,2794,3 032,3070,3265,2057,2407,2426,2663,2483,2713,2752,2983,2525,2792,2823,3042,2869,3088,3125, 3333,2642,2841,2912,3091,2953,3153,3170,3413,2998,3183,3249,3468,3300,3492,3533,3703,761, 1124,1163,1533,1262,1599,1649,1962,1280,1661,1709,1997,1770,2049,2106,2437,1350,1734,1811, 2071,1851,2171,2144,2454,1871,2194,2248,2522,2282,2534,2581,2849,1488,1834,1878,2170,198 2,2229,2259,2545,1996,2283,2315,2596,2341,2617,2645,2922,2010,2338,2376,2644,2439,2696,27 35,2977,2480,2789,2793,3033,2840,3071,3106,3324,1510,1981,1990,2278,2011,2312,2344,2624,2 061,2398,2425,2674,2469,2732,2791,3021,2254,2438,2492,2736,2526,2803,2842,3068,2619,2843, 2913,3104,2954,3152,3169,3412,2314,2532,2602,2808,2643,2881,2932,3120,2699,2942,2979,316 8,3020,3188,3264,3471,2739,2999,3035,3248,3086,3267,3303,3494,3122,3327,3361,3515,3394,35 97,3599,3771,1528,2017,2048,2427,2228,2466,2481,2788,2265,2507,2535,2810,2611,2860,2921,3 107,2319,2580,2641,2863,2672,2933,2980,3155,2733,3006,2978,3181,3069,3251,3283,3478,2453, 2647,2691,2952,2770,2982,3034,3204,2801,3040,3085,3280,3105,3301,3334,3514,2880,3089,312 4,3325,3171,3363,3395,3569,3189,3441,3470,3625,3493,3664,3666,3768,2527,2698,2800,3041,28 51,3084,3090,3302,2915,3126,3154,3360,3182,3392,3469,3598,2923,3180,3205,3440,3282,3476,3 477,3665,3332,3495,3513,3667,3535,3732,3734,3972,3022,3266,3281,3479,3335,3512,3532,3701, 3393,3568,3596,3733,3626,3735,3892,3974,3414,3624,3627,3769,3700,3770,3893,3975,3702,389 4,3895,4020,3973,4021,4022,4023,128,129,130,199,131,248,251,412,196,250,297,444,328,477,47 9,718,197,296,298,476,331,498,543,734,378,542,518,781,613,821,861,1098,198,329,377,516,379, 541,563,783,445,595,615,832,705,876,905,1165,478,633,716,879,733,926,979,1190,780,989,1015, 1284,1030,1314,1372,1669,249,330,414,594,446,614,704,863,496,717,634,906,773,957,1001,1217, 540,707,775,988,793,1012,1029,1298,835,1048,1108,1338,1164,1400,1454,1761,593,782,833,102 8,877,1054,1115,1385,918,1156,1189,1414,1241,1483,1540,1844,991,1211,1287,1513,1312,1541,1 593,1895,1357,1603,1654,1937,1707,1984,2052,2386,299,413,447,706,499,732,735,1000,560,774, 794,1027,860,1053,1083,1384,612,795,862,1055,904,1114,1186,1424,956,1187,1216,1470,1297,15 37,1567,1875,654,874,919,1159,958,1188,1252,1514,1026,1285,1313,1543,1356,1602,1635,1936, 1082,1331,1386,1619,1415,1691,1713,1976,1494,1742,1802,2031,1852,2090,2191,2387,666,927,1 003,1255,1052,1299,1355,1617,1099,1358,1402,1668,1455,1712,1760,2025,1184,1425,1471,1740, 1542,1794,1846,2108,1561,1854,1898,2150,1948,2208,2246,2559,1243,1515,1548,1817,1624,187 4,1905,2186,1706,1933,1977,2234,2032,2263,2351,2635,1751,2002,2053,2308,2088,2381,2421,26 95,2189,2440,2463,2686,2519,2762,2845,3108,376,497,517,792,561,820,872,1113,562,873,907,11 66,976,1240,1256,1565,635,916,977,1259,1013,1296,1329,1566,1031,1328,1373,1653,1426,1705, 1720,1971,664,1002,1049,1269,1110,1336,1387,1704,1158,1412,1456,1724,1482,1790,1825,2086, 1157,1480,1517,1789,1560,1847,1885,2151,1626,1907,1949,2207,2001,2245,2311,2607,719,1097, 1111,1404,1171,1468,1516,1762,1191,1539,1547,1845,1594,1894,1932,2203,1359,1586,1625,1897, 1670,1942,2000,2236,1746,2005,2074,2302,2111,2380,2423,2676,1459,1664,1725,1970,1788,203 0,2076,2360,1830,2101,2117,2385,2200,2447,2501,2741,1899,2190,2209,2488,2237,2530,2459,27 75,2330,2604,2636,2867,2655,2945,2994,3158,772,1167,1185,1551,1337,1601,1634,1906,1405,16 52,1671,1957,1743,2007,2055,2364,1457,1741,1765,2024,1816,2077,2113,2389,1855,2121,2179,2 443,2235,2491,2558,2779,1564,1791,1824,2112,1884,2164,2219,2460,1956,2224,2247,2550,2331, 2515,2623,2875,2029,2294,2370,2605,2402,2654,2682,2928,2456,2693,2692,2974,2776,3017,305 3,3253,1655,1853,1928,2225,2006,2262,2310,2569,2075,2361,2382,2637,2433,2665,2687,2939,21 14,2413,2461,2677,2502,2694,2777,3018,2568,2805,2834,3062,2890,3118,3146,3349,2206,2489,2 542,2778,2622,2796,2886,3077,2634,2877,2930,3136,2966,3173,3234,3418,2666,2956,3012,3197, 3038,3239,3215,3448,3102,3277,3309,3510,3371,3550,3575,3690,415,519,592,834,632,917,978,1 253,655,990,1014,1258,1051,1316,1330,1688,665,1050,1096,1315,1112,1469,1495,1750,1208,151 2,1550,1831,1600,1888,1929,2233,667,1109,1170,1481,1210,1549,1587,1862,1254,1616,1644,193 4,1690,1985,2027,2268,1286,1665,1715,2004,1763,2054,2091,2348,1795,2087,2126,2412,2149,24 42,2490,2847,875,1209,1242,1595,1268,1645,1689,1959,1339,1721,1747,2035,1801,2103,2120,23 66,1403,1749,1819,2089,1861,2148,2157,2430,1896,2158,2178,2500,2291,2531,2590,2876,1458,1 860,1892,2167,1939,2218,2232,2510,1987,2290,2325,2565,2384,2614,2652,2931,2034,2350,2403, 2653,2457,2671,2743,2967,2539,2748,2812,3019,2835,3065,3130,3341,878,1257,1317,1714,1401, 1748,1803,2110,1427,1828,1863,2159,1904,2188,2201,2503,1538,1893,1938,2202,1986,2285,230 9,2560,2033,2334,2383,2633,2431,2667,2718,2936,1592,1958,2026,2324,2100,2371,2367,2668,21 15,2420,2441,2702,2511,2746,2772,3025,2187,2458,2537,2763,2561,2819,2844,3078,2595,2874,2 902,3137,2973,3177,3235,3419,1627,2043,2102,2422,2156,2446,2514,2749,2271,2538,2584,2830, 2587,2846,2888,3117,2295,2585,2594,2885,2669,2897,2961,3172,2728,2972,3003,3208,3052,325 6,3290,3455,2335,2683,2716,2937,2773,2975,3016,3221,2813,3044,3079,3276,3131,3312,3357,35 21,2904,3081,3140,3319,3187,3373,3386,3573,3224,3405,3445,3600,3486,3644,3687,3803,959,13 54,1413,1829,1536,1889,1935,2244,1546,1943,2003,2287,2042,2329,2388,2719,1618,2028,2109,2 365,2127,2445,2432,2740,2165,2462,2518,2804,2570,2826,2853,3103,1764,2116,2166,2444,2270, 2509,2543,2831,2286,2571,2589,2866,2615,2889,2909,3164,2300,2606,2664,2908,2725,2960,299 5,3209,2766,3029,3045,3257,3080,3291,3338,3502,1800,2269,2284,2564,2301,2586,2632,2896,23 49,2670,2703,2944,2747,2990,3039,3247,2536,2724,2774,3002,2814,3063,3094,3278,2891,3095,3 141,3320,3196,3372,3381,3572,2588,2818,2884,3064,2905,3133,3166,3340,2963,3176,3211,3380, 3246,3410,3454,3607,3013,3225,3261,3444,3308,3459,3499,3652,3348,3511,3543,3675,3560,372 5,3739,3869,1818,2303,2328,2717,2508,2742,2767,3028,2551,2797,2827,3076,2887,3116,3159,33 39,2591,2852,2903,3119,2938,3167,3214,3377,2991,3238,3210,3401,3279,3449,3485,3618,2729,2 929,2957,3186,3024,3220,3260,3424,3061,3268,3297,3464,3321,3487,3524,3674,3132,3313,3356, 3503,3387,3551,3561,3709,3411,3589,3606,3753,3645,3774,3782,3848,2815,2962,3060,3269,310 9,3296,3318,3498,3147,3370,3376,3542,3404,3552,3601,3738,3165,3400,3425,3588,3484,3610,36 11,3775,3520,3653,3661,3783,3691,3820,3834,3924,3252,3458,3465,3619,3525,3660,3686,3793,3 553,3708,3724,3821,3766,3835,3886,3990,3574,3752,3767,3849,3792,3868,3887,3991,3802,3906, 3907,4034,3925,4035,4058,4059,652,653,822,1025,823,1080,1169,1452,924,1168,1219,1518,1318, 1563,1585,1994,925,1218,1270,1562,1353,1646,1745,2022,1406,1744,1722,2079,1843,2125,2177, 2486,1024,1319,1375,1666,1407,1727,1793,2085,1519,1841,1873,2152,1969,2216,2239,2549,158 4,1887,1992,2227,2021,2288,2327,2592,2078,2333,2391,2680,2428,2720,2764,3031,1081,1352,14 92,1840,1544,1872,1968,2185,1632,1993,1890,2260,2041,2293,2355,2629,1726,1979,2073,2332,2 119,2368,2415,2704,2155,2434,2496,2750,2548,2784,2832,3101,1827,2084,2153,2414,2217,2476, 2517,2781,2274,2528,2579,2816,2631,2865,2906,3162,2353,2621,2685,2879,2706,2907,2959,321 7,2759,2971,3014,3241,3055,3274,3328,3544,1271,1453,1545,1978,1647,2020,2023,2354,1766,20 72,2122,2401,2176,2451,2479,2780,1842,2123,2184,2477,2238,2516,2576,2824,2292,2577,2628,2 856,2701,2899,2949,3199,1930,2210,2275,2541,2304,2578,2648,2892,2400,2681,2707,2911,2758, 2970,3001,3240,2478,2731,2782,2987,2817,3049,3057,3272,2872,3082,3142,3311,3178,3350,342 1,3545,1950,2289,2363,2651,2450,2705,2757,2985,2487,2760,2786,3030,2833,3056,3100,3299,25 66,2825,2857,3074,2910,3134,3174,3358,2927,3184,3222,3388,3254,3430,3452,3635,2639,2893,2 918,3145,2988,3198,3227,3408,3054,3233,3273,3438,3314,3457,3519,3677,3099,3288,3329,3490, 3346,3537,3557,3711,3417,3566,3591,3704,3617,3736,3777,3878,1374,1633,1667,2118,1767,212 4,2204,2513,1792,2205,2261,2556,2306,2630,2656,2947,1891,2272,2307,2659,2369,2700,2727,29 48,2429,2726,2765,3011,2828,3051,3066,3271,1940,2362,2435,2679,2498,2744,2783,3050,2540,2 806,2836,3072,2864,3128,3151,3344,2529,2858,2895,3115,2926,3175,3201,3389,2992,3229,3255, 3429,3287,3451,3497,3663,1995,2485,2499,2798,2563,2854,2894,3110,2593,2901,2917,3163,296 4,3216,3232,3427,2761,2950,2989,3219,3036,3244,3286,3446,3092,3293,3336,3488,3365,3536,35 59,3696,2839,3026,3073,3270,3114,3310,3342,3522,3160,3353,3375,3541,3422,3581,3603,3723,3 223,3420,3431,3592,3447,3620,3585,3745,3506,3658,3678,3785,3683,3819,3838,3900,2040,2557, 2567,2925,2745,2969,3000,3228,2799,3010,3037,3259,3083,3295,3331,3526,2837,3075,3113,329 8,3144,3343,3367,3547,3185,3379,3407,3577,3439,3595,3634,3749,2946,3129,3150,3366,3200,33 98,3433,3586,3258,3434,3453,3632,3507,3615,3671,3787,3307,3480,3530,3659,3548,3682,3698,3 810,3582,3707,3706,3832,3746,3845,3859,3935,3015,3179,3230,3435,3294,3456,3496,3641,3337, 3523,3538,3679,3565,3685,3705,3817,3368,3555,3587,3697,3604,3710,3747,3846,3640,3755,377 2,3862,3798,3882,3898,3963,3428,3593,3630,3748,3670,3750,3794,3867,3676,3789,3812,3890,38 28,3909,3928,3986,3688,3822,3842,3915,3854,3931,3921,3994,3876,3943,3951,4010,3967,4018,4 031,4054,1493,1723,1826,2154,1886,2273,2326,2649,1931,2352,2390,2658,2449,2722,2730,3046, 1941,2448,2484,2721,2512,2855,2873,3098,2612,2878,2924,3161,2968,3202,3231,3437,1951,249 7,2562,2859,2620,2919,2951,3194,2650,2984,3008,3236,3048,3275,3305,3460,2684,3027,3059,32 92,3111,3330,3351,3516,3135,3345,3382,3554,3385,3576,3594,3779,2211,2613,2638,2965,2678,3 009,3047,3263,2751,3067,3093,3317,3139,3355,3378,3528,2787,3097,3149,3347,3193,3384,3391, 3562,3218,3396,3406,3602,3475,3621,3654,3788,2838,3192,3212,3403,3243,3432,3436,3612,328 5,3474,3501,3639,3540,3668,3680,3813,3316,3518,3549,3681,3583,3695,3727,3829,3629,3730,37 56,3847,3773,3865,3884,3961,2226,2657,2723,3058,2785,3096,3143,3364,2829,3156,3195,3397,3 226,3416,3423,3605,2900,3213,3242,3426,3284,3467,3491,3636,3315,3508,3539,3673,3563,3689, 3716,3814,2958,3262,3304,3500,3352,3531,3529,3692,3369,3556,3567,3712,3613,3728,3742,385 1,3409,3584,3623,3737,3637,3761,3776,3870,3657,3786,3804,3891,3831,3911,3929,3987,2993,33 23,3354,3558,3390,3580,3614,3731,3463,3628,3646,3764,3649,3778,3796,3881,3481,3647,3656,3 791,3693,3801,3825,3908,3720,3830,3841,3916,3858,3936,3946,3997,3509,3699,3714,3815,3743, 3833,3844,3923,3757,3856,3871,3942,3885,3952,3965,4013,3806,3873,3896,3955,3913,3969,397 8,4029,3926,3983,3993,4036,4004,4044,4053,4075,2305,2756,2807,3157,2898,3203,3237,3450,29 16,3245,3289,3473,3322,3505,3546,3717,2986,3306,3359,3527,3383,3579,3564,3722,3399,3590,3 616,3754,3642,3762,3781,3877,3112,3374,3402,3578,3462,3609,3631,3765,3472,3643,3651,3784, 3669,3797,3809,3902,3482,3662,3684,3808,3719,3824,3839,3917,3740,3853,3857,3937,3872,394 7,3958,4008,3138,3461,3466,3638,3483,3648,3672,3800,3517,3694,3713,3818,3729,3836,3855,39 33,3622,3718,3744,3840,3758,3863,3874,3944,3799,3875,3897,3956,3914,3968,3977,4028,3650,3 760,3790,3864,3807,3889,3904,3960,3827,3910,3919,3976,3932,3984,3996,4039,3843,3927,3939, 3992,3950,3999,4007,4046,3962,4011,4017,4051,4026,4061,4063,4083,3148,3489,3504,3715,360 8,3726,3741,3852,3633,3751,3763,3866,3795,3880,3901,3959,3655,3780,3805,3883,3816,3905,39 20,3971,3837,3930,3918,3981,3945,3995,4003,4042,3721,3811,3823,3912,3850,3922,3938,3988,3 861,3940,3949,4000,3957,4005,4014,4050,3888,3953,3964,4009,3979,4019,4027,4057,3985,4033, 4038,4065,4045,4068,4070,4080,3759,3826,3860,3941,3879,3948,3954,4006,3899,3966,3970,401 6,3982,4024,4037,4062,3903,3980,3989,4032,4002,4040,4041,4069,4012,4047,4049,4071,4055,40 76,4078,4088,3934,3998,4001,4043,4015,4048,4052,4073,4025,4056,4060,4077,4066,4079,4084,4 090,4030,4064,4067,4081,4072,4082,4085,4091,4074,4086,4087,4092,4089,4093,4094,4095]
›APPENDIX · 11 of 21
Sequence Group 2: Q2_8192
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,41,144,28,6 9,42,516,49,74,272,1024,1025,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134, 384,76,137,82,56,27,97,39,259,84,138,145,261,29,1026,1028,43,98,515,88,140,30,146,71,262,265, 161,576,45,100,640,51,148,46,75,266,273,517,104,162,1032,1040,53,193,2048,2049,2050,2052,15 2,77,164,768,268,274,518,54,83,57,521,112,135,78,289,194,85,276,522,58,1056,1027,168,139,99, 86,60,280,89,290,529,524,196,141,101,147,1029,1088,176,142,530,321,31,200,90,545,292,322,53 2,263,149,102,105,304,296,163,92,47,267,385,1033,1030,546,324,2056,2064,2080,2051,208,386,1 50,153,165,106,55,328,536,577,548,113,154,79,1041,1034,269,108,578,224,166,519,552,195,270, 641,523,275,580,291,1042,1152,59,169,560,114,277,156,87,197,116,170,61,531,525,642,1036,105 7,2053,2112,2057,2054,281,278,526,177,4096,4097,4098,4100,4104,4112,4128,4099,293,388,91,5 84,1089,1044,769,198,172,120,201,336,62,282,1280,1058,143,103,178,294,93,644,202,592,323,39 2,1048,1060,297,770,107,180,151,209,284,648,1031,1153,94,204,2065,2058,2066,2176,298,400,6 08,352,325,533,155,210,305,547,300,109,1090,1536,184,534,537,115,167,225,326,306,1035,1064, 772,157,656,329,2060,2081,2113,2068,110,117,212,171,1092,1154,776,330,226,549,538,387,308,2 16,1043,1037,416,271,279,158,1072,1038,337,550,672,118,332,579,540,389,173,121,553,199,784, 179,228,338,312,704,1096,1281,390,174,2304,2082,2072,2084,554,581,1045,1156,4101,4160,410 5,4102,4113,4106,4114,4224,393,283,122,448,353,561,1059,1282,203,63,340,394,527,582,556,18 1,295,285,232,124,205,182,643,562,286,585,1050,1537,2055,2177,2114,2560,299,354,1104,1061, 211,401,185,396,1049,1046,344,586,645,593,535,240,206,95,327,564,800,402,1160,1284,356,307, 301,417,2059,2088,2116,2178,1288,1062,213,568,832,588,186,646,404,227,896,594,418,302,1538, 1120,649,771,360,539,1091,1065,1168,1052,111,331,214,309,2067,2061,2096,2062,4108,4129,41 61,4116,4352,4130,4120,4132,188,449,217,408,609,596,551,650,1093,1066,229,159,420,310,1540, 1073,2120,2305,2069,2180,541,773,1098,1296,610,657,333,119,600,339,218,368,652,230,391,31 3,2083,2306,2074,2561,450,542,1184,1544,334,233,555,774,175,123,658,612,1312,1552,341,777, 220,314,1216,1568,2128,2085,2073,2070,424,395,673,583,1094,1068,355,287,183,234,1155,1105, 125,557,660,616,2184,2308,2312,2086,1074,1097,1039,1344,4103,4225,4162,4608,4107,4136,416 4,4226,342,316,241,778,563,345,452,397,1157,1076,1047,1158,403,207,674,558,785,432,357,187, 236,664,624,587,2562,2144,2115,2089,1408,1100,780,705,126,242,565,398,1161,1106,346,456,35 8,405,1080,1051,2192,2076,2117,2090,1121,1063,303,569,244,595,189,566,4115,4109,4144,4110, 4168,4353,4117,4228,676,361,706,589,215,786,647,348,2564,2097,2122,2320,419,406,464,680,80 1,362,1283,1108,590,409,1162,1169,1285,1053,570,788,3072,3073,2208,2568,597,572,219,311,10 67,1122,1539,1112,2336,2576,2240,2592,708,598,601,651,421,792,802,611,1164,1054,602,410,11 70,1095,231,688,653,248,369,190,364,654,659,335,1286,1289,480,315,221,370,1185,1600,1069,1 124,613,422,2118,2092,2179,2129,425,451,1664,1075,4131,4354,4122,4609,4176,4133,4121,4118, 614,543,235,412,2098,2121,2063,2368,343,372,1172,1070,775,317,222,426,1099,1290,453,237,2 181,2100,2071,2182,559,833,804,712,1297,1541,1128,1186,834,661,808,779,1077,1217,617,604,1 176,1101,433,720,816,836,347,897,1188,1792,1292,1298,243,662,454,318,675,618,1542,1078,243 2,2124,2185,2130,4232,4356,4360,4134,4610,4192,4163,4137,898,781,376,428,2104,2075,2145,2 087,1107,1081,665,736,567,840,625,238,2307,2132,2186,2193,1545,1136,1159,1102,359,457,1313, 1218,399,787,591,678,1109,1300,434,677,349,245,458,666,620,363,127,191,2309,2077,3074,307 6,782,407,1546,1082,1192,1163,436,626,4240,4124,4165,4138,4612,4145,4170,4368,2091,2146,2 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5172,5143,5254,4499,4303,4770,4654,2407,2505,3361,3266,2447,2835,2639,2726,3157,3348,248 2,2725,1646,1651,1461,1404,4881,4528,4453,4283,4332,4760,4720,4683,1842,1485,998,766,2397, 2293,2506,2714,2668,2411,2175,2239,2830,2455,3594,3130,6658,6240,6211,6185,5504,5196,487 6,4801,1520,1693,511,988,1703,1748,1865,1653,3240,3211,2484,2674,1375,1491,1462,1761,1275, 1486,1466,1465,2619,2513,3171,3158,1001,951,1493,1271,2729,2294,2755,2398,4222,4338,4661, 4494,5257,5202,4442,4552,4454,4501,5176,5147,6288,6172,6213,6186,1707,1866,1762,1923,313 2,3352,2647,2716,2838,2508,3161,3362,1694,1807,1873,1844,2297,2730,2621,2459,2851,2837,27 57,2413,3601,3596,3268,3213,1752,1952,1815,1391,5217,5159,4399,4665,4340,4691,4285,4662,4 772,4457,4802,4685,4311,4882,4743,4444,6660,6193,6218,6416,4515,4502,4560,4776,4897,4458, 5379,5204,4686,4505,5258,5265,2488,2676,2737,2422,2471,2514,2841,2298,1002,893,1925,1654, 1709,1868,1657,1735,5381,5149,4666,4884,7168,7169,6304,6664,4693,4668,4315,4407,5163,521 8,5635,5208,1277,1715,975,894,3173,3219,3248,3214,1848,1926,1710,1764,3602,3393,3103,3272, 2419,2529,2622,2461,1874,1399,1468,1494,3162,3617,3364,3394,2651,2414,2516,2703,6432,667 2,6336,6688,4804,4694,4697,4747,1507,1439,1509,1929,2948,2853,2663,2732,4517,4888,4898,47 07,5260,5150,4698,4506,3604,3335,2758,2477,3221,3174,2842,2300,5266,5191,4327,4784,4749,4 344,4465,4286,1009,955,1819,1497,1658,1768,1876,1984,3177,3376,2421,2653,1889,1717,1821,1 930,2896,2738,2761,2680,3368,3235,2530,2854,4460,4750,4755,4431,5382,5385,4576,4411,1739, 1831,1004,1010,3164,3119,2475,2952,4317,4466,5281,5696,5165,5220,4709,4518,1498,1660,957, 983,3339,3457,2462,2271,6214,6188,6275,6225,4521,4547,5760,5171,2711,2740,3618,3396,2883, 2667,3280,3458,2520,2503,2844,2857,1718,1278,1741,1599,4710,4639,4331,4508,6194,6217,615 9,6464,3222,3225,3237,3178,1937,1822,958,987,4439,4468,5268,5166,4871,4413,4318,4522,2762, 2769,2885,2764,2912,2858,2654,2960,3127,3400,2770,2744,1835,1403,1721,1455,5195,5386,454 9,4333,6277,6196,6167,6278,4655,4929,4900,4808,5393,5637,5224,5282,1631,1513,1890,1747,24 25,2483,2865,2367,1012,999,1510,1932,3608,3649,2669,2860,1742,1837,1500,1880,3620,3185,25 32,2478,1863,1749,1016,767,3226,3151,3341,3180,4930,4757,4904,4875,5173,5313,4713,4700,28 86,2715,2536,2287,2426,2507,3650,3296,1722,1938,1776,1892,1843,1838,1463,1953,3238,3591,3 624,3267,2670,2675,2485,2428,5272,5197,4529,4816,4912,4932,4443,4993,3342,3713,3595,3347, 1514,1647,1695,1763,5284,5888,5388,5394,4339,4758,4550,4414,2866,2509,2544,2717,2727,277 2,2889,2677,4771,4714,5638,5174,6528,6220,6281,6226,4994,4877,4472,4524,6200,6171,6241,61 83,1940,1487,1867,1405,2399,2515,3652,3363,3131,3241,2486,2785,3632,3186,2299,2510,989,10 03,1521,1954,2490,2489,2517,2295,5203,5177,4761,4832,4663,4936,4721,4334,6403,6228,6282,6 289,5641,5232,5255,5198,4455,4553,5409,5314,4495,4883,4687,4774,1845,1750,1985,1896,3349, 3228,2731,2890,3159,3269,3188,3242,1516,1655,1753,1724,5205,5396,4530,4773,4445,4341,455 4,4762,4716,4459,4223,4287,6405,6173,7170,7172,1467,1765,990,1005,2786,2947,2718,2831,313 3,3603,3597,3714,2897,2868,3353,3350,2776,2976,3598,3249,1869,1944,1406,1846,1875,1754,15 22,1904,2839,2415,2949,2678,3365,3460,2733,2892,2681,2759,3163,3656,4878,4503,5642,5178,5 288,5259,4532,4722,6187,6242,6659,6232,4667,4561,5219,5206,1766,1469,1495,1659,3841,3270, 3244,3192,4777,4342,4803,4446,5180,5400,4695,4764,3273,3408,2301,2739,3134,3354,2872,295 0,959,1011,1956,1711,2734,2788,2898,2423,2492,2518,2531,2463,3215,3175,3250,3366,4886,455 6,5209,5410,4345,4778,4669,4507,3165,3716,3274,3664,1927,1849,1524,1870,4899,4885,4805,44 61,6284,6174,6290,6215,5649,5644,5316,5261,4536,4724,4785,4470,1769,1850,1756,1470,2533,2 953,3395,3464,1986,1960,1499,1877,2843,2521,3369,3842,6406,6409,6305,6720,6189,6244,6784, 6195,4519,4562,4889,4346,5221,5267,5296,5262,1891,1661,1931,1511,2682,2792,2900,3008,565 0,5441,5151,5320,4467,4577,4670,4509,3179,3252,2913,2741,1013,895,1719,1770,5210,5665,541 2,5442,4699,4462,4564,4751,3223,3281,2845,2954,3356,3720,2763,2855,3166,3276,2522,2684,33 70,3472,3680,3424,6292,6190,6219,6410,4996,4901,4711,4780,1852,1777,1878,1881,2742,2302,2 765,2623,1528,1823,1279,1988,2961,2846,3397,3605,5652,5383,4806,4525,6417,6661,6248,6306, 5269,5222,4890,4348,7176,7184,6197,6337,5225,5424,4469,4701,4944,4786,4809,4728,5416,528 3,4578,4902,5212,5167,4523,5000,3227,3282,3377,3619,1933,1743,1501,1939,5387,5505,4510,43 19,4759,4788,5666,5444,3372,3181,2859,2427,1662,1772,1006,1014,3256,3606,2745,2479,2655,2 537,3609,3187,1968,1893,1515,1723,2914,2771,2534,2956,2766,2861,2524,2904,3239,3297,3398, 3378,2887,2773,3844,3229,3728,3401,2746,2962,4931,4715,5328,5506,6296,6221,6308,6912,456 8,4551,4892,4905,5270,5273,5285,5226,4810,4817,4933,4812,4960,4906,4702,5008,6412,6418,66 62,6198,5175,5448,4818,4792,2800,2916,3182,3189,2867,2862,3284,3243,4473,4531,4913,4415,6 227,6201,6665,6256,1778,1882,1502,1992,3848,3402,3298,3621,5656,5697,4717,4908,5668,5233, 4580,4526,1407,1934,1839,2000,3610,3459,3380,3288,2487,2977,2538,2671,1894,1941,1017,101 8,6279,6222,6433,6338,5274,5199,5389,5228,2719,2787,2964,2511,1751,1517,1897,1725,4934,47 63,4584,4335,6229,6420,6666,6202,2891,2429,3488,3343,3351,3230,3409,3622,4474,4555,5698,5 344,5286,5639,5672,5315,1955,1780,1884,1523,2545,2978,3744,3190,7200,7171,6312,6283,6243, 6230,6204,6424,2869,2774,3009,2920,3404,3651,2540,2679,4718,4723,4533,4476,5390,5761,564 3,5395,4914,4557,4592,4765,4775,4820,4937,4725,3612,3461,3245,3193,2777,2748,2491,2789,17 55,1847,1946,1898,1942,1526,1957,1767,3625,3271,3856,3251,3300,3410,2893,2968,6233,6434,6 673,6668,6340,6285,6245,6291,4447,4563,5700,5411,5179,5289,4534,4833,5680,5234,4347,4558, 4538,4537,4565,4343,5397,5276,4779,4938,5207,5317,5236,5290,3384,3776,2430,2870,991,1020, 1784,1905,7173,7232,6320,6286,4834,4995,4766,4879,3462,3246,2899,2778,1518,1726,1945,152 5,3626,3653,3465,3355,2546,2928,3194,3520,5181,5651,5645,5762,4945,4916,5401,5398,2790,24 93,2519,2683,1900,1871,2016,1471,2980,2735,3425,3633,2951,2873,3275,3135,1757,1851,1958,1 906,3412,3466,2548,2894,1961,1987,1771,1529,2793,2874,3599,3654,6674,6465,6175,6344,4824, 5024,5646,5297,4887,4463,4997,4726,6234,6689,6436,6466,3628,3253,3367,3357,2780,2494,330 4,3196,6676,6407,6293,6246,5413,5508,4781,4940,4729,4807,5211,5704,5889,5318,5292,5240,32 77,3254,3715,3634,3010,2984,2523,2901,2915,2685,3358,3657,1879,1948,1758,1853,5321,5456,4 349,4787,5182,5402,4920,4998,3371,3426,3283,3473,2955,2535,2743,2794,4782,4836,4946,4471, 4540,4566,4579,4511,5263,5223,5298,5414,5213,5764,5322,5712,4581,5001,5443,5512,6249,644 8,6440,6307,4891,4569,5417,5890,6236,6191,6411,6529,7177,7174,6690,6468,4730,4840,4948,50 56,2876,2801,3257,3468,1989,1962,1908,1530,1773,1969,1990,1779,3416,3658,2902,2905,3717,3 665,3607,3312,3278,3167,2552,2847,1883,1964,1854,1935,2303,3012,3399,3636,3872,3474,3428, 3379,2957,2767,2525,2963,5227,5300,4961,4789,5271,5329,4893,5002,6352,6530,6294,6297,630 9,6250,6199,6472,5404,5768,4811,4903,5214,5324,4570,4732,1895,1663,1912,1503,1970,1774,19 93,1532,5418,5520,5728,5472,4790,4350,4813,4671,3373,3489,2686,2796,2992,2917,3285,3640,2 539,2747,3904,3660,2802,2906,3258,3718,6680,6721,6692,6257,5009,4894,5445,5653,3476,3299, 2526,3016,3968,3666,3490,3374,6298,6223,7185,7178,5275,5330,5425,5667,5420,5229,4907,447 5,5304,5654,4793,4527,1885,1781,1994,1943,3721,3843,2431,2958,3432,3611,3183,3403,2863,30 24,2918,2965,4703,4585,5657,5235,4962,4819,4582,5004,6413,6252,6722,6368,4814,4909,4572,4 952,5287,5345,5446,5426,6310,6663,6696,6339,1899,1886,1782,1972,2775,2541,3286,3381,6414, 6785,6667,6419,4935,4821,5892,5277,2921,2749,3260,3521,2001,1947,1996,1785,5776,5449,479 4,5010,6724,6435,7186,7296,3289,3480,2979,2804,1901,1976,1519,1727,4848,4964,5230,5237,49 15,4910,5332,5291,5896,5450,5346,5669,6203,6313,6704,6258,3681,3668,3623,3722,2908,2547,3 301,3231,5658,5507,5428,5336,4535,5025,4586,4719,3492,3382,3613,3845,1959,2002,1007,1015, 2779,2871,2970,2922,3682,3729,2966,2550,3405,3191,3672,3411,2981,2791,3290,3440,6421,630 0,6231,6341,4767,4835,5012,4559,2808,2929,3724,3302,3463,3385,3522,3614,4939,4477,5536,53 91,5399,5278,5457,5670,6260,6314,6205,6675,6669,6786,7180,7201,3406,3305,2542,2750,3627,3 846,2969,2549,3247,3195,3730,3684,3413,3849,2924,2895,4593,5026,5792,5238,4917,4822,5057, 4968,6425,6422,6670,6321,5452,5699,4588,4727,6437,6532,6235,6728,5660,5509,5293,5241,190 7,1786,1527,1949,3040,2495,3292,3386,4825,4796,4539,4837,5673,5319,5904,5299,7233,7188,69 13,6342,6316,6264,6345,6480,5348,5458,4941,5016,5432,5824,4478,4918,2781,2875,3496,3467,2 982,2930,3745,3655,1902,1759,2017,1909,2985,3011,3427,3359,3255,3306,3197,3629,2795,2553, 2903,2972,5510,5294,4947,4826,6206,6426,7424,7202,5674,5701,5513,5403,4594,4976,5242,556 8,6287,6247,6322,6438,4838,4541,4567,4731,1963,2018,2004,1950,3732,3688,3414,3388,3313,38 50,2782,2877,3635,3417,3524,3469,3013,2986,3475,3279,1788,1965,1991,1910,5028,4783,5473,5 681,4999,4921,5323,5183,6237,6788,6346,6736,6467,6536,7192,7204,3746,3630,3857,3504,2932, 2554,3429,3259,5460,5514,4596,4942,6441,6914,6251,6324,4841,4922,5647,5702,5676,5301,541 5,5405,6295,6353,6428,6792,4828,4542,5352,5244,2797,2993,3308,3736,3696,3659,3014,2803,29 07,2988,3852,3777,1855,1971,1531,1913,5325,5302,5763,5682,5058,5032,4571,4949,4963,4733,5 406,5705,5419,5474,5331,5521,5003,4583,4791,4842,7175,7297,6238,6348,3198,3314,3637,3470, 2008,1775,1966,2020,3418,3528,2878,2959,2919,2687,3430,3477,6442,6544,6752,6496,4924,484 9,5305,5516,3375,3641,3316,3667,2936,2527,3261,3638,3748,3433,3778,3661,2994,2798,3287,38 58,5464,5706,4950,4953,6469,6677,6299,6354,1995,1914,1533,1973,3719,3420,3491,3478,5765,5 713,5655,5360,5326,5215,4600,4895,3536,3752,3017,2556,2909,2805,3873,3434,6449,6691,6444, 6253,4351,5060,5447,5684,5920,5522,5476,5427,7234,7680,6328,6678,3018,2967,3662,3481,292 3,2910,3642,3860,5005,4815,4573,5011,5421,5537,4734,4844,5040,4965,5333,5688,4587,4795,59 52,5708,6681,6259,6311,6369,6470,6450,7179,7208,3669,3644,2806,2996,3291,3383,3780,3670,4 850,4954,5306,5766,5524,5347,4574,5064,6016,5714,5538,5422,5769,5891,4479,5006,1997,2024, 1916,1974,3673,3723,3493,3864,3025,2971,3874,3683,3020,2809,3674,3482,3303,3760,2925,300 0,1887,1783,2032,1534,6916,6301,6800,6473,6254,6261,6356,6315,3725,3320,2543,2751,3441,32 62,3436,3726,7236,7298,6920,6474,6370,6693,6682,6531,5480,5659,5231,5451,4911,5072,4966,5 013,2983,3026,3731,3407,3552,3387,3293,3442,6452,6360,7187,7181,6560,6415,6423,6302,4823, 4589,5334,5429,4969,4797,5308,5569,3685,3494,3497,3523,3686,3615,3307,3484,5337,5528,502 7,4852,5729,5716,5671,5770,7216,7182,6481,6694,4956,4595,5349,5279,6816,6262,6476,6723,55 40,5430,5661,5893,2003,1977,1019,1021,2931,2810,3415,3444,2551,2973,3847,3389,3294,3498,2 926,2783,6684,6533,6317,6265,4827,4919,5018,4970,3525,3309,3041,2933,3631,3905,3876,3784, 5730,5777,5014,4598,5453,5239,5720,5459,6697,6343,6928,6323,5029,4839,5338,5488,2987,304 2,3906,3733,1787,1998,1978,1903,6372,6482,6456,6848,4856,4977,5772,5350,3880,3851,3689,36 76,2005,2006,1951,2019,7240,7425,6534,6318,5511,5433,5570,5662,5454,5353,4590,4798,6698,6 725,7189,7300,5675,5894,5017,4597,6537,6427,6266,6592,5295,5243,5778,5732,5461,5897,4972, 4943,3505,3792,3888,3908,3028,2974,2812,2989,6497,6705,7203,7426,6347,6207,6484,6538,341 9,3969,3315,3734,1789,1980,1911,2009,5088,4543,5340,5434,4829,4923,5544,5515,5030,4978,57 93,5703,5033,5059,5475,5407,6671,6726,6700,6325,5303,5354,5245,5677,3526,3390,3015,2934,3 747,3690,2879,2995,3970,3853,3448,3500,3737,3808,2555,2937,4843,4601,4951,5020,5780,5736, 5462,5436,2021,2010,1967,1915,3639,3912,3697,3310,6439,6429,6376,6268,5361,5898,4830,492 5,3032,2799,3431,3529,2990,3044,3471,3859,6349,6326,6787,6706,5683,5465,5572,5517,3663,37 50,3506,3749,2022,1790,1535,2012,6430,6729,7194,7681,6443,6498,7248,7205,5061,5034,5523,5 327,5794,5678,5905,5552,4980,4602,5477,5307,6355,6545,6329,6540,3421,3317,3530,3738,3692, 3435,3019,2938,3199,3263,3854,3479,3508,3698,2557,2997,7193,7190,6488,6730,6789,6737,667 9,6384,4845,5041,5356,5784,5744,5707,5062,4851,6350,6239,6471,6708,6944,6546,7304,7428,30 21,3048,3643,3537,3753,3318,3779,3422,4955,5036,5900,5825,5246,5362,5685,5518,5466,5576,4 926,5007,4967,4735,5478,5525,2940,2998,3671,3740,3862,3532,3321,3754,5423,5689,5364,5715, 6500,6451,6445,6561,7432,7206,6357,6712,4984,4575,5309,5686,6976,6732,6330,6790,5796,548 1,5826,5709,2025,1975,1022,1023,2911,2807,3056,2558,5042,4846,5335,5906,5767,5468,5539,55 26,3645,3483,3875,3861,3781,3437,3512,3700,6548,6371,7040,6738,5584,5800,5065,4604,6562,6 446,7682,7264,6793,6915,6504,6683,3761,3446,3495,3538,3027,3001,3865,3322,3443,3553,3646, 3485,2026,1917,1999,1918,4957,4853,5921,5482,5066,5015,5710,5529,7235,7209,7312,7196,625 5,6475,6358,6453,4971,4958,5690,5908,6332,6593,6361,6552,5717,5692,4854,5044,6753,6740,66 95,6794,2811,3022,3675,3438,3540,3727,3002,2927,3972,3877,3029,3030,3687,3756,3782,3501,5 339,5431,5828,5718,5721,5771,5541,5912,7237,7210,6373,6303,5073,5019,5922,5731,5068,4857, 5722,5530,6564,6454,7684,7217,3866,3324,2975,3043,3445,3677,3920,3762,6685,6917,7242,744 0,6754,6801,6477,6263,6744,6483,6362,6512,5351,5808,4973,5048,6796,6374,6535,6457,5773,53 68,4591,4799,2033,1979,2028,2034,3785,3704,3554,3878,5489,5310,5484,5774,5031,5074,5779,5 455,5600,5435,5341,5490,5733,5542,5545,5571,6594,6686,7328,7688,6478,6377,6699,6918,6319, 6267,6802,6756,7456,7696,6485,6921,3499,3976,3486,3295,3735,3764,3907,3691,3544,3527,386 8,3881,2813,3004,3786,3793,5734,5663,5355,5532,6364,6458,7360,7712,3909,3788,3936,3882,29 35,3033,3678,3984,4979,4858,5463,5492,6568,6539,6817,6727,3794,3768,3449,3507,3045,3034,3 889,3391,4599,5021,5895,5437,5342,5546,4974,4831,7238,7212,6499,6431,5573,5357,5089,4981, 1981,2007,1982,2011,3693,3884,3556,3502,6327,6378,7299,7249,5679,5953,5924,5832,6269,670 1,6804,6760,5035,5090,5954,5781,7218,7241,7183,7488,5928,5899,5737,5724,6486,6460,6385,69 22,6707,6489,6596,6541,3910,3739,2991,2939,3560,3311,3450,3531,5553,5840,5936,5956,5076,5 022,4860,5037,3694,3699,3509,3452,3890,3533,3046,2814,5467,6017,5363,5782,7301,7220,7191, 7302,6547,6351,6818,6702,6929,6576,6501,6331,3568,3741,2559,3036,3751,3796,3913,3701,638 0,6808,6768,6731,5574,5438,5063,4982,3423,3539,3510,3809,2036,2023,2040,1791,7552,7244,69 24,6849,5795,5738,4927,5043,6018,5901,5496,5548,6270,6386,6709,6542,3323,3534,3514,3513,3 049,2999,3541,3319,5785,5856,4603,4985,5687,5960,5745,5358,5080,4847,5479,5577,5038,5092, 5519,5907,7305,7250,6490,6600,6502,6549,7224,7195,5711,5798,5554,5797,7265,7207,6447,671 3,6388,6739,6333,6710,5469,5365,5578,5786,5740,5483,5067,4986,6820,6505,6850,6733,5247,53 11,5902,5527,6359,6930,6791,6492,3755,3914,3810,3971,3742,3855,3921,3892,6563,6550,6608,6 824,6945,6506,7427,7252,3800,4000,3863,3439,3050,2941,3973,3702,6734,6553,7306,7313,7429, 7197,6714,6932,5556,5746,4605,5045,5069,5096,5691,5585,3757,3916,3705,3783,2013,2027,201 4,2029,5801,5366,5827,5470,4988,5046,5719,5788,3325,3763,3023,2942,3896,3974,3758,3812,59 10,5580,5369,5802,6741,6716,6363,6455,7211,7266,7683,7256,6852,6742,6745,6795,3922,3447,3 516,3542,3555,3487,3557,3977,4959,4855,5104,4606,6565,6936,6946,6755,5693,5531,5923,5909, 5829,5485,5560,5748,7308,7198,6746,6554,5809,5494,5543,5586,7314,7239,6375,6832,6797,639 2,6513,6334,5075,5049,5913,5370,5491,5601,5694,5533,3057,3003,3867,3545,3706,3816,3924,40 32,3937,3765,3869,3978,3787,3879,3052,3058,6508,6798,6803,6479,7430,7433,6624,6459,6365,6 514,7329,7744,4859,5070,5723,5486,7213,7268,6757,6566,5588,5775,5050,4975,1983,2035,2037, 1919,3546,3708,3005,3031,6569,6595,7808,7219,6020,5925,5077,5078,3766,3326,3789,3647,398 5,3870,3006,3035,6758,6687,6379,6556,6487,6516,7316,7214,5735,5804,5830,5549,6919,6461,63 66,6570,5914,5372,5023,5091,5493,5725,5968,5810,3883,3451,3769,3503,3679,3561,3938,3795,5 833,5752,5602,5926,7243,7434,6597,6381,5547,6024,5534,5343,6703,6977,6948,6856,3060,3047, 3558,3980,3790,3885,3548,3928,7441,7685,7272,7330,5783,5812,5955,5739,3911,3797,3064,281 5,3770,3986,3824,3940,5592,5575,5916,5929,6978,6805,6952,6923,7221,7361,6761,6748,7320,72 45,6577,6864,4861,5052,5834,5841,6960,6980,6491,7041,7332,7936,7436,7442,6387,6806,6598,6 462,5957,5836,5984,5930,4983,5081,5726,6032,5842,5816,5497,5555,6819,6762,7686,7222,3891, 3886,3511,4001,3562,3695,3743,3811,7042,6925,6520,6572,7251,7225,6809,6880,5093,5082,593 7,5439,5741,5932,5604,5550,5958,5787,5039,4987,6711,6984,6769,6382,3988,3535,3915,3453,30 37,3051,3569,4002,3893,3798,4033,3944,3564,3703,3801,3772,7689,7280,7303,7246,5608,5359,5 498,5579,6503,6601,7457,7362,6543,6931,6735,6822,7253,7444,6578,6821,5742,5747,5557,5500, 3515,3813,3038,3053,3917,3992,3454,3894,5938,5581,5094,4862,6493,6389,6602,6810,6764,650 7,6271,6335,6926,6551,7690,7226,5616,5789,4607,5084,5799,5844,5961,5749,3923,3802,3570,39 52,3814,3517,3543,3707,3007,3059,4004,3759,3975,3897,3572,3918,7336,7307,6580,6770,5471,5 587,5558,5857,5371,5582,5562,5561,6715,6609,7267,7254,5097,5047,5589,5367,6825,6390,6851, 6494,5803,5962,5858,6019,7228,7448,6743,6812,6934,6604,7257,7458,5790,5903,5969,5940,639 3,6826,6717,6555,6947,6933,6853,6509,3817,3898,3804,3518,4034,4008,3547,3925,7697,7692,73 64,7309,5848,6048,5911,5487,6584,6772,6833,6518,6567,6610,6937,6394,5098,4989,6021,5750,5 805,5964,5753,5831,3939,3709,3979,3559,3061,2943,3767,3818,5373,5811,5071,4990,7269,7315, 7344,7310,5944,6022,5806,5860,7698,7489,7199,7368,3900,3825,3926,3929,3576,3871,3327,403 6,6515,6625,6718,6557,5970,5495,5564,5590,3981,3791,3549,3987,3710,3820,3054,3062,7258,77 13,7460,7490,6747,6510,6612,6799,5603,5535,5605,6025,7044,6949,6759,6828,7700,7431,6854,6 573,7317,7270,6938,6396,4016,3941,3563,3771,2030,2038,2041,2042,5105,5051,5915,5593,5754, 5864,5972,6080,7273,7472,6517,6749,5985,5813,5917,6026,6992,6834,6857,6776,7464,7331,662 6,6950,5835,5927,5100,5106,7260,7215,6571,7048,5594,5756,5053,5079,7435,7553,6558,6367,68 07,6836,7714,7492,6979,6763,7376,7554,6616,6599,6940,6953,5814,5374,5837,5695,7318,7321,7 333,7274,6033,5918,5054,5083,6858,6865,6981,6860,7008,6954,6750,7056,7223,7496,6866,6840, 5931,5499,5817,5551,3826,3930,3550,4040,3455,3982,3887,4048,5727,5609,5986,5843,6521,657 9,6961,6463,5108,5095,5606,6028,7704,7745,6765,6956,5838,5933,5596,5976,7716,7281,6628,65 74,3942,3989,3065,3066,3799,3565,3945,3773,5959,5845,5112,4863,7322,7247,7437,7276,6982,6 811,6632,6383,6522,6603,7746,7392,5818,6034,5872,5988,5939,5934,5559,6049,4003,3828,3932, 3571,3803,3895,3994,3946,7334,7687,7720,7363,6766,6771,6581,6524,7438,7809,7691,7443,561 0,5743,5791,5859,6962,6605,6640,6813,6823,6868,6985,6773,6036,5583,5963,5501,6495,6611,77 48,7459,3990,3574,4005,3815,3039,3068,3832,3953,7227,7337,6582,6881,7728,7282,6395,6606,5 085,5099,5617,6050,6586,6585,6613,6391,5941,5846,6081,5992,7445,7324,6827,6986,7255,7365, 7284,7338,5612,5751,5849,5820,5563,5861,5086,5101,6882,7043,6814,6927,3566,3774,3993,357 3,3948,3919,4064,3519,7229,7699,7693,7810,6993,6964,7449,7446,3805,3899,4006,3954,4009,40 35,3819,3577,6872,7072,7694,7345,5965,6040,5502,5942,5971,5850,5618,6000,6935,6511,7045,6 774,7461,7556,6829,6988,6777,6855,7259,7752,5862,5565,5591,5755,7937,7366,7340,7288,7369, 7504,6397,6835,7230,7450,6968,7046,5055,5107,6052,5807,6830,6884,6994,6519,3927,3996,380 6,3901,4037,4010,3956,3578,6588,6614,6627,6559,7311,7271,7346,7462,7261,7812,7370,7760,60 23,5945,5620,5966,5865,5946,5852,5566,6629,7049,7491,7560,6082,6056,5595,5973,6939,6617,7 465,7938,5987,5757,6027,5607,6778,6888,6996,7104,7275,7348,7009,6837,5109,4991,5815,5866, 7319,7377,6941,7050,7452,7816,6859,6951,3821,4017,4038,3827,3931,4012,3902,3983,7262,737 2,6618,6780,7466,7568,7776,7520,5948,5873,5974,5977,6838,6398,6861,6719,5624,5919,5375,60 84,7057,6942,7493,7701,7323,7378,7473,7715,6029,5839,5597,6035,3943,3711,3960,3551,4018,3 822,4041,3580,7468,7277,6955,6523,5758,5868,5102,5110,7352,7702,6841,6575,6751,6633,7705, 7283,6064,5989,5611,5819,7010,6867,6630,7052,6862,6957,6620,7000,7335,7393,7494,7474,698 3,6869,7940,7325,7824,7497,6842,7058,6896,7012,7278,7285,6963,6958,7380,7339,3933,3829,40 42,3991,2015,2044,2031,2039,5874,5978,5598,6088,7944,7498,7394,7717,5503,6030,5935,6096,7 706,7555,7476,7384,6583,7073,6634,6767,5990,6037,5113,5114,6815,6883,7060,6607,5847,5613, 5993,5821,6987,6525,7584,7439,7447,7326,7505,7718,6051,5876,5980,5619,6641,7074,7840,728 6,3947,3934,3830,4020,4049,3995,4044,3833,6965,6870,7105,7016,7500,7747,6636,6775,3949,40 24,3567,3775,4007,4050,3055,3063,7708,7557,7341,7289,6873,6844,6587,6885,5851,5943,6042,5 994,6038,5622,6053,5863,7721,7367,7952,7347,7396,7506,6989,7064,3955,3834,3575,3997,3950, 3807,4065,3957,7480,7872,6526,6966,5087,5116,5880,6001,7558,7342,6995,6874,5614,5822,604 1,5621,7722,7749,7561,7451,6642,7024,7290,7616,6886,6589,6615,6779,5996,5967,6112,5567,40 11,4066,4052,3998,3836,4013,4039,3958,7076,6831,7521,7729,7047,6969,7371,7231,5853,5947,6 054,6002,7508,7562,6644,6990,6057,6083,5867,5625,6889,6970,7695,7750,7724,7349,7463,7453, 6876,6590,7400,7292,3903,4019,3579,3961,4056,3823,4014,4068,7373,7350,7811,7730,7106,708 0,6619,6997,7011,6781,7454,7753,5975,6044,5854,5949,7467,7522,7379,7569,7051,6631,6839,68 90,6972,6897,7353,7564,6085,6058,6004,5626,5869,6065,6086,5875,7512,7754,6998,7001,7813,7 761,7703,7408,7374,7263,6648,6943,5979,6060,5950,6031,6399,7108,7495,7732,7968,7570,7524, 7475,7053,6863,6621,7059,4043,3962,3581,4021,2043,2045,2046,2047,5991,5759,6008,5599,606 6,5870,6089,5628,7469,7585,6782,6892,7088,7013,7381,7736,6635,6843,8000,7756,6898,7002,73 54,7814,7572,7395,6622,7112,8064,7762,7586,7470,5981,5877,6090,6039,7817,7939,6527,7054,7 528,7707,7279,7499,6959,7120,7014,7061,4045,4072,3964,4022,3935,3831,4080,3582,5995,5982, 5878,6068,6871,6637,7382,7477,7017,6845,7356,7617,6097,6043,6092,5881,7385,7576,7075,690 0,5997,6072,5615,5823,7777,7764,7719,7818,7004,6643,7397,7327,7588,7478,7709,7941,6055,60 98,5103,5111,6875,6967,7066,7018,7778,7825,7062,6646,4051,4025,3067,3069,3835,4046,4026,3 951,7501,7287,7768,7507,7077,6887,7386,7536,6904,7025,7820,7398,7559,7481,7618,7710,7502, 7401,6638,6846,7723,7942,7065,6645,7343,7291,7826,7780,7509,7945,7020,6991,6003,5882,562 3,6045,7136,6591,7388,7482,6877,6971,7592,7563,7078,7026,7841,7751,5998,5855,6113,6005,70 81,7107,7523,7455,7351,7402,7293,7725,6891,6649,6999,7068,6059,6114,6100,6046,7828,7784,7 510,7484,4053,4054,3999,4067,3837,4028,3959,4057,7409,7946,6878,6973,7731,7513,7620,7565, 7109,7082,7571,7375,5884,6061,6087,6006,7842,7726,7953,7600,7028,6650,7525,7355,6893,708 9,7404,7832,7792,7755,7110,6899,7003,7084,7948,7873,5951,6067,5627,6009,7294,7410,7733,75 66,6104,5871,6062,6116,7514,7624,6974,7055,7015,6783,7526,7573,7471,7737,7412,7763,7032,6 623,7357,7734,4069,4058,4015,3963,4070,3838,3583,4060,7844,7529,7874,7757,7090,6894,7383, 7954,6091,6010,5629,6069,7815,7516,7587,7574,7632,7848,7113,6652,7005,6901,7969,7530,711 4,7063,7758,7577,7019,7006,7738,7956,7765,7740,6902,7092,7387,7479,7876,7766,6093,6120,60 12,6070,7769,7819,7589,7960,7121,7067,7970,7779,7116,6905,7770,7578,4073,4023,3070,3071,4 074,3965,4047,3966,7399,7856,7021,7096,5983,5879,6128,5630,7821,7416,6639,6847,7537,7358, 7532,7822,7079,7122,7827,7503,7648,7483,7389,7538,7781,7590,7593,7619,7782,7711,7403,758 0,6099,6073,5115,5117,7027,6906,7511,7540,6647,7069,7943,7485,7390,7594,7022,6879,7621,74 05,7137,7029,7727,8001,7972,7880,7083,7138,8002,7829,5883,6094,6074,5999,4081,4027,4076,4 082,4029,4055,4030,4059,7976,7947,7785,7772,6101,6102,6047,6115,7601,7888,7984,8004,7124, 7070,6908,7085,7515,8065,7411,7830,5885,6076,6007,6105,7622,7486,7111,7030,7843,7786,6975, 7091,8066,7949,7544,7596,7833,7904,6651,7033,6117,6106,6063,6011,7735,8008,7793,7406,712 8,6895,7527,7625,7086,7140,7567,7955,7759,7846,7602,7845,6118,5886,5631,6108,7517,7413,76 26,7834,7788,7531,7115,7034,7295,7359,7950,7575,7604,7794,6653,7093,7117,7144,7739,7633,7 849,7414,7875,7518,7036,7094,7767,7836,7958,7628,7417,7850,6121,6071,5118,5119,7007,6903, 7152,6654,7741,7579,7971,7957,7877,7533,7608,7796,7857,7542,7591,7634,7123,7097,7961,741 8,7539,7649,7742,7581,6122,6013,6095,6014,6907,7118,7771,7534,7636,7823,7098,7023,8068,79 73,7125,7126,7783,7852,7878,7597,7962,7420,7071,7139,7541,7773,8016,7858,6129,6075,6124,6 130,7881,7800,7650,7974,7595,8072,7582,7391,7831,7860,8003,7787,7640,7623,7964,7977,6909, 7100,7882,7889,8005,7884,8032,7978,7031,7129,7774,8080,7890,7864,7545,7603,7141,7130,798 5,7487,6077,6103,6078,6107,7789,7980,7652,7598,8006,7835,7087,7035,7656,7407,7546,7627,77 90,7795,7605,7548,7986,7629,7142,6910,7664,7837,6655,7132,7847,7892,8009,7797,7519,7635,7 606,7905,6132,6119,6136,5887,7419,7630,7610,7609,7145,7095,7637,7415,4084,4071,4088,3839, 4061,4075,4062,4077,7851,8010,7906,8067,7838,7951,8017,7988,7896,8096,7959,7535,7146,703 7,8069,7798,7853,8012,7801,7879,6109,6123,6110,6125,7421,7859,7119,7038,7992,8070,7854,79 08,8018,7543,7612,7638,7651,7583,7653,8073,7153,7099,7963,7641,7802,7912,8020,8128,8033,7 861,7965,8074,7883,7975,7148,7154,6079,6131,6133,6015,7642,7804,7101,7127,7862,7422,7885, 7743,8081,7966,7102,7131,7979,7547,7865,7599,7775,7657,8034,7891,7156,7143,7654,8076,788 6,7981,7644,8024,8007,7893,7160,6911,7866,8082,7920,8036,7987,7982,7607,8097,7658,7791,78 39,7907,8084,7631,8011,7549,7133,7147,7665,8098,7989,7894,8129,8040,7660,7799,7897,7868,7 611,7909,7134,7149,8013,8088,7550,7990,8019,7898,7666,8048,7910,7613,7639,7803,7103,7155, 8100,7855,8071,7993,7668,8014,7913,7994,7900,7614,8130,8104,7643,8021,4031,4083,4085,396 7,4078,4086,4089,4090,8035,7805,8075,7655,7157,7039,7863,7914,7996,7921,8022,8025,7672,79 67,7423,8132,8077,7887,7645,8083,7806,7916,7150,7158,8112,8037,7659,7867,6126,6134,6137,6 138,7922,8026,7646,8136,7551,8078,7983,8144,8038,8085,7161,7162,7895,7661,8041,7869,8099, 7924,8028,7667,7899,7991,8090,8042,8086,7670,8101,7911,7135,7164,7928,8049,7662,7870,808 9,7669,8044,8015,8160,7615,7901,7995,8102,8050,8105,8131,7915,7673,8023,8092,7902,7997,81 33,8106,8052,7674,4063,4092,4079,4087,4091,4093,4094,4095,7917,8113,8134,7923,8027,8108,7 998,8079,8039,7807,8056,7647,8114,7918,8137,7676,8029,7925,8138,8087,6111,6140,6127,6135, 8043,8030,7926,8116,8145,8091,8140,7929,8045,8120,7663,7871,8103,8146,7151,7159,8051,793 0,7671,8093,8046,7903,8161,8053,8107,8162,8148,8094,7932,8109,8135,8054,7999,8115,7675,80 57,8152,7919,8110,8164,8139,8058,7677,8117,6139,6141,6142,6143,8141,8168,8060,8118,8031,7 927,8176,7678,8147,8121,7163,7165,7931,8142,8122,8047,8149,8150,8095,8163,7933,8124,8055, 8153,8165,8154,8111,8059,8166,7934,7679,8156,8169,8119,7166,7167,8170,8061,8143,8062,8177, 8123,8172,8178,8125,8151,8126,8155,8180,8167,8184,7935,8157,8171,8158,8173,8127,8179,818 1,8063,8174,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191]
›APPENDIX · 12 of 21
Sequence Group 2: Z2_8192
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,78,5,12,14,32,19,38,47,82,22,46,42,89,57,97,105, 174,6,17,21,40,23,45,51,91,29,55,59,100,73,112,117,189,34,61,76,115,81,126,139,206,88,141,151, 232,158,242,276,409,9,18,26,54,30,58,72,107,36,77,62,118,85,133,145,213,44,75,87,140,93,148,1 57,238,103,160,176,266,188,284,302,449,53,90,101,156,113,166,183,281,122,184,205,294,217,31 9,340,488,143,211,235,325,240,341,365,531,273,371,402,553,419,580,632,874,15,25,31,74,39,80, 83,144,48,86,94,155,104,165,171,280,56,95,106,167,116,182,202,296,132,203,212,314,237,333,35 9,515,66,110,123,187,134,204,220,326,154,233,241,343,272,370,383,552,170,255,282,375,295,41 5,421,576,322,438,470,619,504,654,727,875,70,127,147,223,164,239,271,373,175,274,286,408,30 3,420,448,613,200,297,315,436,342,466,490,668,353,506,534,698,560,736,774,1027,219,327,348, 473,376,514,537,722,418,549,577,762,620,779,847,1107,447,602,633,812,652,869,905,1175,725,9 16,947,1170,1003,1250,1349,1692,20,37,41,92,49,96,108,181,50,109,119,190,136,216,224,357,63, 120,137,227,149,236,253,358,159,252,277,401,298,417,424,575,68,146,161,229,178,264,283,416, 186,292,308,432,318,458,477,650,185,316,329,457,352,491,517,699,378,539,561,735,601,773,815, 1075,79,173,179,288,195,312,328,450,207,335,347,489,366,530,548,731,275,362,377,533,410,55 8,600,768,442,605,638,806,671,868,907,1160,311,404,433,574,456,618,640,856,482,665,681,873, 728,923,973,1217,535,726,737,964,769,1010,935,1259,834,1072,1112,1371,1139,1473,1534,1766, 84,191,201,351,265,369,382,538,289,400,411,569,439,607,635,860,309,437,453,612,472,641,677, 881,507,685,719,919,763,967,1026,1263,356,459,476,676,516,712,743,944,568,748,775,1022,835, 987,1095,1375,617,802,866,1073,886,1138,1166,1452,932,1173,1172,1514,1260,1573,1621,1937,4 03,505,544,749,606,778,814,1049,639,857,870,1113,913,1145,1171,1463,678,901,945,1161,974,11 74,1261,1574,1048,1289,1342,1630,1390,1706,1742,2125,734,965,1018,1262,1094,1280,1382,164 9,1106,1377,1454,1716,1502,1801,1898,2270,1146,1488,1556,1829,1602,1907,1867,2344,1686,19 69,2033,2474,2151,2586,2643,2994,27,43,52,102,60,121,138,221,67,142,150,226,163,244,254,412, 69,162,172,243,180,313,323,446,208,324,350,483,368,524,545,761,71,177,194,317,210,349,363,5 10,222,372,388,550,414,581,615,784,234,405,423,604,451,634,655,844,467,651,690,900,697,918, 966,1351,111,209,218,367,228,389,413,571,267,425,443,623,469,667,684,862,287,445,475,653,50 9,696,709,910,532,710,718,972,799,1011,1062,1376,310,508,528,715,555,742,760,982,583,798,81 7,1041,872,1090,1136,1455,622,846,887,1137,933,1151,1219,1503,1015,1240,1300,1575,1343,163 3,1710,2093,114,225,245,422,285,444,471,670,299,480,511,711,536,724,729,975,334,529,554,730, 582,793,813,1028,621,842,871,1105,911,1147,1198,1460,364,570,614,816,664,867,863,1148,679,9 04,917,1178,983,1238,1256,1577,723,934,1013,1251,1029,1315,1348,1650,1071,1374,1418,1717, 1513,1805,1899,2271,379,631,666,906,708,922,986,1241,787,1014,1056,1338,1059,1350,1388,17 05,803,1057,1070,1381,1149,1405,1493,1800,1212,1512,1539,1860,1620,1940,1990,2351,843,116 7,1196,1461,1257,1515,1572,1877,1301,1608,1651,1968,1711,2064,2137,2489,1424,1661,1736,20 71,1819,2169,2202,2641,1884,2241,2321,2724,2414,2856,2971,3371,135,270,293,481,332,525,55 1,772,346,559,603,795,630,833,880,1199,374,616,669,861,691,921,912,1216,713,946,1002,1288,1 050,1318,1357,1687,452,680,714,920,786,981,1019,1339,794,1051,1061,1370,1091,1389,1429,17 88,804,1074,1144,1428,1205,1492,1535,1861,1254,1581,1609,1941,1660,1991,2090,2462,468,785, 792,1040,805,1058,1104,1404,845,1150,1179,1472,1239,1530,1603,1927,1012,1204,1258,1538,13 02,1631,1674,1970,1391,1675,1737,2080,1828,2168,2185,2640,1060,1314,1380,1632,1425,1713,1 790,2092,1495,1804,1863,2184,1926,2262,2350,2735,1557,1885,1945,2320,2032,2359,2455,2876, 2124,2475,2547,2923,2604,3113,3139,3717,474,807,832,1197,980,1218,1255,1580,1023,1281,131 9,1648,1383,1704,1767,2091,1063,1356,1419,1707,1462,1791,1866,2173,1531,1906,1862,2237,19 71,2345,2413,2778,1213,1453,1489,1818,1576,1876,1944,2276,1629,1948,2017,2388,2081,2415,2 492,2922,1712,2065,2136,2463,2203,2587,2605,3017,2263,2689,2734,3209,2857,3258,3302,3616, 1303,1494,1628,1949,1693,2016,2070,2454,1743,2150,2172,2546,2240,2588,2725,3138,1789,223 6,2277,2688,2412,2742,2743,3259,2488,2877,2897,3303,2995,3472,3538,4076,1936,2358,2389,27 79,2493,2896,2970,3353,2589,3016,3112,3473,3242,3539,3822,4502,2642,3208,3243,3617,3352,3 716,3823,4503,3370,3934,3935,5042,4077,5043,5378,5379,64,65,98,153,99,168,193,300,124,192, 215,330,246,355,361,590,125,214,230,354,269,390,441,610,290,440,426,643,487,689,717,962,152, 247,279,406,291,435,465,649,331,485,513,700,573,740,771,1021,360,519,588,751,609,796,819,1 068,642,841,883,1164,908,1200,1252,1583,169,268,320,484,344,512,572,721,380,589,526,776,62 9,801,855,1101,434,579,637,840,683,864,903,1180,703,914,968,1242,1020,1276,1340,1685,479,6 48,701,902,741,948,1001,1273,790,1008,1055,1312,1103,1369,1426,1786,853,1093,1169,1379,118 2,1427,1491,1869,1247,1511,1558,1921,1623,1966,2084,2552,231,301,345,578,391,608,611,854,4 54,636,686,885,716,931,951,1272,486,687,720,949,770,1000,1052,1316,800,1053,1100,1364,1177, 1407,1477,1831,546,738,791,1017,808,1054,1116,1392,884,1165,1183,1431,1246,1510,1537,1920, 950,1215,1274,1519,1313,1613,1625,1964,1372,1662,1738,2035,1806,2126,2273,2553,562,797,8 59,1119,930,1181,1245,1517,963,1248,1278,1582,1341,1624,1684,2019,1042,1317,1365,1638,143 0,1714,1802,2138,1451,1816,1878,2208,1938,2282,2348,2795,1115,1393,1442,1741,1528,1830,18 87,2260,1622,1897,1965,2306,2066,2357,2479,2933,1683,1988,2085,2426,2114,2533,2601,3019,2 269,2610,2691,3008,2777,3136,3285,3762,278,381,407,682,455,688,732,985,464,733,777,1024,81 0,1102,1140,1475,527,788,811,1143,865,1176,1207,1476,909,1206,1253,1555,1336,1615,1634,195 1,556,858,915,1163,970,1236,1275,1614,1016,1290,1344,1636,1368,1708,1763,2112,1009,1366,1 395,1699,1450,1803,1845,2209,1532,1893,1939,2281,1975,2347,2453,2899,591,961,971,1282,103 1,1358,1394,1694,1069,1417,1441,1787,1500,1868,1896,2279,1249,1478,1529,1871,1600,1924,19 74,2322,1672,1997,2088,2424,2141,2532,2603,3004,1347,1578,1637,1950,1698,2034,2094,2490,1 784,2133,2171,2545,2274,2653,2727,3071,1879,2272,2283,2692,2323,2780,2669,3157,2466,2882, 2934,3325,2959,3459,3558,3920,628,1025,1043,1449,1237,1509,1536,1892,1283,1554,1601,1943, 1663,1999,2087,2494,1345,1639,1697,2018,1740,2095,2143,2555,1817,2175,2243,2649,2307,269 5,2794,3177,1474,1709,1762,2142,1844,2214,2285,2670,1942,2286,2349,2792,2467,2763,2903,33 27,2023,2408,2522,2883,2584,2958,3006,3398,2654,3011,3010,3536,3158,3593,3667,4119,1559,1 807,1894,2287,1998,2356,2452,2833,2089,2491,2534,2935,2609,2969,3009,3457,2148,2591,2671, 3005,2732,3018,3159,3594,2832,3211,3256,3674,3362,3806,3906,4323,2280,2693,2786,3176,290 2,3178,3354,3699,2932,3345,3420,3834,3516,3949,4092,4462,2992,3474,3562,3979,3646,4095,40 29,4594,3760,4139,4263,4758,4327,4834,4951,5254,321,427,478,702,518,789,818,1117,547,852,8 82,1142,929,1202,1214,1610,557,928,960,1201,984,1359,1373,1682,1088,1378,1448,1785,1508,1 846,1895,2305,563,969,1030,1367,1092,1443,1479,1822,1118,1516,1552,1904,1612,1967,2021,23 64,1168,1579,1627,1996,1695,2086,2127,2476,1715,2113,2186,2590,2201,2648,2694,3287,739,10 89,1114,1501,1162,1553,1611,1947,1243,1635,1673,2069,1719,2135,2174,2520,1279,1681,1761,2 115,1821,2200,2211,2606,1870,2212,2242,2726,2399,2781,2878,3344,1346,1820,1864,2239,1923, 2284,2304,2760,1973,2398,2461,2823,2544,2900,2956,3421,2068,2478,2585,2957,2655,2999,311 5,3517,2785,3118,3212,3595,3257,3697,3820,4321,750,1141,1203,1626,1277,1680,1739,2140,133 7,1764,1823,2213,1886,2268,2275,2733,1416,1865,1922,2278,1972,2391,2427,2820,2067,2472,25 35,2921,2607,2993,3052,3422,1490,1946,2020,2460,2132,2523,2521,2996,2149,2600,2611,3040,2 761,3116,3146,3619,2261,2668,2783,3137,2821,3221,3284,3718,2881,3326,3392,3835,3519,3951, 4093,4463,1533,2083,2134,2602,2210,2652,2762,3119,2367,2784,2858,3240,2873,3286,3360,380 5,2409,2859,2880,3347,2997,3369,3505,3948,3068,3518,3561,4024,3666,4128,4198,4633,2473,30 07,3042,3423,3147,3537,3592,4031,3213,3664,3719,4138,3821,4264,4325,4789,3394,3753,3904,4 267,3977,4385,4426,4949,4078,4447,4593,5092,4692,5164,5253,5743,809,1244,1291,1765,1406,1 847,1905,2346,1440,1925,1989,2397,2082,2465,2554,3053,1518,2022,2139,2495,2187,2651,2608, 3070,2215,2690,2776,3210,2834,3222,3301,3761,1696,2170,2238,2650,2366,2741,2787,3241,239 6,2835,2875,3324,2901,3361,3397,3922,2410,2898,2968,3396,3055,3504,3559,4025,3144,3645,36 65,4129,3752,4199,4282,4756,1718,2365,2390,2822,2411,2872,2920,3368,2477,2998,3041,3458,3 117,3556,3647,4117,2782,3054,3156,3560,3214,3675,3754,4196,3363,3755,3905,4280,3978,4384, 4425,4948,2874,3220,3346,3696,3395,3833,3932,4320,3507,3950,4027,4424,4116,4460,4632,509 5,3563,4079,4131,4592,4262,4635,4695,5166,4322,4759,4833,5219,4930,5429,5431,5995,1760,24 25,2464,3043,2740,3114,3145,3644,2793,3179,3223,3698,3355,3804,3921,4283,2879,3300,3393,3 807,3456,3933,4028,4387,3557,4094,4026,4445,4197,4595,4675,5110,3069,3399,3475,3976,3618, 4030,4130,4500,3673,4136,4261,4672,4281,4693,4790,5218,3832,4265,4324,4757,4427,4835,493 1,5377,4461,5041,5094,5537,5165,5640,5642,5992,3215,3506,3672,4137,3763,4260,4266,4694,39 07,4326,4386,4832,4446,4928,5093,5430,3923,4444,4501,5040,4674,5108,5109,5641,4788,5167,5 217,5643,5255,5868,5870,6884,4118,4634,4673,5111,4791,5216,5252,5741,4929,5376,5428,5869, 5538,5871,6412,6886,4950,5536,5539,5993,5740,5994,6413,6887,5742,6414,6415,7140,6885,714 1,7142,7143,128,129,130,199,131,248,251,428,196,250,305,460,336,493,495,766,197,304,306,492, 339,522,567,782,386,566,542,837,645,877,925,1210,198,337,385,540,387,565,587,839,461,627,6 47,896,745,940,977,1293,494,673,764,943,781,1006,1067,1326,836,1077,1111,1444,1134,1482,15 40,1933,249,338,430,626,462,646,744,927,520,765,674,978,821,1045,1097,1361,564,747,823,107 6,849,1108,1133,1458,899,1152,1220,1506,1292,1592,1654,2073,625,838,897,1132,941,1158,1235, 1569,990,1284,1325,1606,1385,1691,1772,2180,1079,1355,1447,1729,1480,1773,1841,2255,1525, 1859,1910,2297,1987,2384,2468,2978,307,429,463,746,523,780,783,1096,584,822,850,1131,924, 1157,1195,1568,644,851,926,1159,976,1234,1322,1616,1044,1323,1360,1678,1457,1769,1799,223 5,694,938,991,1287,1046,1324,1396,1730,1130,1445,1481,1775,1524,1858,1891,2296,1194,1499, 1570,1875,1607,1963,1993,2360,1702,2038,2130,2447,2188,2530,2687,2979,706,1007,1099,1399, 1156,1459,1523,1873,1211,1526,1594,1932,1655,1992,2072,2441,1320,1617,1679,2036,1774,212 2,2182,2556,1793,2190,2258,2614,2308,2720,2766,3263,1387,1731,1780,2145,1880,2234,2265,26 82,1986,2293,2361,2754,2448,2791,2927,3387,2047,2402,2469,2868,2528,2973,3021,3479,2685,3 056,3111,3470,3199,3610,3757,4284,384,521,541,848,585,876,936,1233,586,937,979,1294,1064,1 384,1400,1797,675,988,1065,1403,1109,1456,1497,1798,1135,1496,1541,1909,1618,1985,2008,23 55,704,1098,1153,1421,1222,1504,1571,1984,1286,1604,1656,2012,1690,2118,2153,2526,1285,16 88,1733,2117,1792,2183,2245,2615,1882,2267,2309,2703,2401,2765,2871,3351,767,1209,1223,15 96,1299,1676,1732,2074,1327,1771,1779,2181,1842,2254,2292,2699,1527,1826,1881,2257,1934,2 302,2400,2756,2042,2405,2498,2862,2559,2972,3023,3460,1659,1928,2013,2354,2116,2446,2500, 2944,2158,2549,2565,2977,2696,3063,3165,3565,2259,2686,2721,3152,2757,3218,3107,3623,289 0,3348,3388,3819,3407,3961,4074,4390,820,1295,1321,1783,1505,1857,1890,2266,1597,1908,193 5,2325,2039,2407,2471,2948,1657,2037,2077,2440,2144,2501,2561,2981,2191,2577,2667,3059,27 55,3155,3262,3627,1796,2119,2152,2560,2244,2644,2731,3108,2324,2736,2767,3246,2891,3195,3 367,3827,2445,2846,2954,3349,3002,3406,3466,3928,3104,3477,3476,4022,3624,4113,4165,4597, 1911,2189,2288,2737,2406,2790,2870,3281,2499,2945,2974,3389,3049,3433,3471,3947,2562,301 3,3109,3461,3166,3478,3625,4114,3280,3677,3738,4190,3842,4294,4362,4813,2702,3153,3230,36 26,3366,3668,3838,4213,3386,3829,3930,4344,3998,4429,4554,4962,3434,3980,4100,4485,4134,4 559,4511,5048,4278,4645,4717,5206,4851,5294,5383,5722,431,543,624,898,672,989,1066,1397,6 95,1078,1110,1402,1155,1484,1498,1960,705,1154,1208,1483,1232,1677,1703,2046,1352,1728,17 82,2159,1856,2248,2289,2753,707,1221,1298,1689,1354,1781,1827,2206,1398,1872,1900,2294,19 62,2385,2443,2796,1446,1929,1995,2404,2075,2470,2531,2924,2123,2527,2582,3012,2613,3058,3 154,3759,939,1353,1386,1843,1420,1901,1961,2327,1507,2009,2043,2451,2129,2551,2576,2950,1 595,2045,2147,2529,2205,2612,2621,3046,2256,2622,2666,3164,2843,3219,3318,3828,1658,2204, 2252,2647,2299,2730,2752,3182,2387,2842,2885,3277,2976,3358,3404,3931,2450,2926,3003,340 5,3105,3439,3567,3999,3227,3572,3700,4115,3739,4193,4338,4797,942,1401,1485,1994,1593,204 4,2131,2558,1619,2156,2207,2623,2264,2684,2697,3167,1770,2253,2298,2698,2386,2837,2869,32 72,2449,2894,2975,3385,3047,3435,3542,3944,1840,2326,2442,2884,2548,2955,2951,3436,2563,3 020,3057,3510,3183,3570,3620,4121,2683,3106,3225,3611,3273,3715,3756,4214,3323,3826,3854, 4345,4021,4441,4555,4963,1883,2459,2550,3022,2620,3062,3194,3573,2799,3226,3312,3734,331 5,3758,3840,4293,2847,3313,3322,3837,3437,3849,3993,4428,3552,4020,4091,4504,4164,4624,46 82,5055,2895,3467,3540,3945,3621,4023,4112,4517,3701,4140,4215,4644,4339,4744,4821,5233,3 888,4257,4348,4751,4459,4853,4906,5381,4528,4941,5045,5464,5150,5588,5703,6083,1047,1522, 1605,2157,1768,2249,2295,2764,1778,2303,2403,2839,2458,2889,2980,3543,1874,2444,2557,294 9,2583,3061,3048,3564,2645,3110,3198,3676,3282,3730,3765,4279,2076,2564,2646,3060,2798,31 81,3231,3735,2838,3283,3317,3818,3359,3841,3893,4396,2860,3350,3432,3892,3549,3992,4075,4 505,3614,4125,4141,4625,4256,4683,4794,5198,2128,2797,2836,3276,2861,3314,3384,3848,2925, 3438,3511,3960,3571,4038,4135,4567,3224,3548,3622,4090,3702,4191,4270,4646,3843,4271,434 9,4752,4484,4852,4877,5380,3316,3714,3836,4192,3889,4341,4398,4796,3995,4440,4507,4876,45 66,4946,5054,5471,4101,4529,4629,5044,4716,5067,5195,5604,4812,5207,5287,5683,5344,5845,5 883,6341,2146,2863,2888,3541,3180,3566,3615,4124,3247,3669,3731,4212,3839,4292,4391,4795, 3319,3764,3855,4295,3946,4399,4510,4873,4039,4558,4506,4937,4647,5049,5149,5506,3553,392 9,3981,4458,4120,4516,4628,4984,4189,4636,4689,5088,4753,5151,5236,5682,4340,4745,4820,51 99,4907,5295,5345,5765,4947,5421,5470,5953,5589,5998,6014,6248,3703,3994,4188,4637,4285,4 688,4750,5194,4363,4850,4872,5286,4940,5320,5465,5882,4397,4936,4985,5420,5148,5474,5475, 5999,5232,5605,5621,6015,5723,6172,6210,6604,4596,5066,5089,5507,5237,5620,5702,6065,532 1,5764,5844,6173,5966,6211,6382,6958,5382,5952,5967,6249,6064,6340,6383,6959,6082,6530,65 31,7250,6605,7251,7466,7467,692,693,878,1129,879,1192,1297,1652,1004,1296,1363,1734,1486, 1795,1825,2394,1005,1362,1422,1794,1521,1902,2041,2430,1598,2040,2010,2503,2179,2581,266 5,3150,1128,1487,1543,1930,1599,2015,2121,2525,1735,2177,2233,2616,2353,2728,2759,3245,18 24,2247,2392,2739,2429,2840,2887,3320,2502,2893,2983,3464,3044,3544,3612,4127,1193,1520,1 700,2176,1776,2232,2352,2681,1888,2393,2250,2788,2457,2845,2931,3373,2014,2363,2497,2892, 2567,2952,3015,3512,2619,3050,3160,3574,3244,3640,3736,4277,2155,2524,2617,3014,2729,314 0,3197,3629,2818,3216,3299,3712,3375,3817,3890,4394,2929,3365,3469,3831,3514,3891,3983,45 13,3599,4019,4102,4561,4167,4642,4784,5288,1423,1653,1777,2362,1903,2428,2431,2930,2078,2 496,2578,3001,2664,3067,3143,3628,2178,2579,2680,3141,2758,3196,3296,3728,2844,3297,3372, 3800,3509,3851,3965,4487,2290,2722,2819,3229,2864,3298,3400,3844,3000,3465,3515,3895,359 8,4018,4089,4560,3142,3555,3630,4035,3713,4161,4185,4640,3824,4258,4350,4719,4442,4814,49 65,5289,2310,2841,2947,3403,3066,3513,3597,4033,3151,3608,3642,4126,3737,4184,4276,4691,3 278,3729,3801,4210,3894,4342,4430,4822,3927,4456,4518,4908,4598,4990,5052,5579,3391,3845, 3910,4361,4036,4486,4531,4944,4166,4553,4641,5014,4746,5065,5223,5685,4275,4680,4785,516 2,4810,5281,5325,5767,4961,5350,5423,5760,5505,5880,6009,6366,1542,1889,1931,2566,2079,25 80,2700,3193,2120,2701,2789,3260,2866,3374,3416,3963,2251,2816,2867,3419,2953,3508,3551,3 964,3045,3550,3613,4099,3732,4163,4194,4639,2300,2946,3051,3463,3162,3568,3631,4162,3228, 3678,3740,4208,3816,4336,4367,4808,3217,3802,3847,4291,3926,4431,4497,4909,4072,4533,459 9,4989,4679,5051,5193,5623,2395,3149,3163,3670,3275,3766,3846,4286,3321,3853,3909,4395,39 96,4512,4552,4987,3609,3966,4037,4515,4132,4564,4678,5046,4268,4685,4792,5160,4837,5280,5 327,5736,3743,4122,4209,4638,4290,4718,4798,5234,4392,4817,4855,5285,4966,5397,5467,5843, 4519,4964,4991,5424,5047,5508,5417,5905,5202,5618,5686,6041,5699,6171,6214,6500,2456,326 1,3279,3925,3569,4017,4088,4532,3671,4098,4133,4627,4259,4687,4787,5238,3741,4211,4289,46 90,4360,4799,4839,5291,4457,4875,4943,5393,5015,5427,5578,5909,3962,4337,4366,4838,4496,4 934,5009,5418,4626,5010,5053,5576,5203,5479,5647,6043,4715,5144,5250,5619,5292,5698,5738, 6138,5398,5763,5762,6208,5906,6245,6307,6655,4103,4443,4534,5011,4686,5064,5192,5585,479 3,5235,5282,5687,5349,5701,5761,6169,4848,5323,5419,5737,5468,5766,5907,6246,5584,5955,59 96,6310,6070,6378,6498,6827,4988,5425,5542,5908,5646,5910,6066,6339,5684,6045,6140,6410,6 180,6533,6648,6954,5720,6174,6242,6563,6254,6651,6601,6986,6364,6671,6727,7066,6831,7138, 7199,7406,1701,2011,2154,2618,2246,2817,2886,3401,2291,2928,2982,3418,3065,3546,3554,414 2,2301,3064,3148,3545,3192,3767,3825,4274,3356,3830,3924,4393,4016,4498,4535,5013,2311,31 61,3274,3803,3364,3911,3967,4482,3402,4032,4096,4556,4160,4643,4713,5068,3468,4123,4187,4 684,4287,4786,4815,5220,4343,4809,4878,5322,4905,5392,5426,6011,2723,3357,3390,3997,3462, 4097,4143,4631,3575,4195,4269,4749,4347,4819,4874,5248,3643,4273,4365,4811,4481,4904,491 1,5346,4514,4932,4942,5466,5107,5509,5606,6044,3742,4480,4508,4939,4563,5008,5012,5476,46 77,5106,5197,5583,5284,5644,5696,6141,4748,5222,5293,5697,5399,5727,5847,6181,5541,5866,5 956,6247,5997,6337,6380,6825,2738,3417,3547,4186,3641,4272,4351,4836,3733,4388,4483,4933, 4530,4960,4967,5469,3852,4509,4562,4986,4676,5091,5163,5580,4747,5204,5283,5681,5347,572 1,5828,6142,3982,4630,4712,5196,4816,5251,5249,5724,4849,5324,5351,5824,5477,5864,5886,62 51,4945,5416,5511,5881,5581,5961,6008,6342,5617,6042,6084,6411,6183,6535,6649,6955,4073,4 755,4818,5326,4910,5396,5478,5867,5071,5540,5590,5964,5601,6010,6068,6377,5145,5591,5616, 6047,5725,6081,6177,6532,5840,6182,6241,6564,6306,6664,6722,6989,5205,5739,5826,6143,588 7,6209,6244,6603,5957,6304,6343,6670,6381,6784,6829,7069,6086,6361,6496,6787,6561,6881,69 38,7197,6606,6943,6985,7252,7028,7332,7405,7787,2865,3596,3679,4389,3850,4499,4557,5050,3 908,4565,4681,5105,4754,5201,5290,5829,4034,4714,4823,5239,4879,5395,5348,5842,4935,5422, 5504,5954,5586,5962,6013,6365,4288,4854,4938,5394,5070,5473,5543,5965,5104,5587,5603,604 0,5645,6069,6137,6502,5146,5622,5700,6136,5831,6176,6215,6565,5884,6253,6305,6665,6360,67 23,6790,7064,4346,5069,5090,5582,5147,5600,5680,6080,5221,5726,5825,6170,5865,6212,6255,6 653,5510,5830,5904,6240,5958,6311,6362,6720,6071,6363,6497,6788,6562,6880,6937,7196,5602, 5960,6046,6336,6087,6409,6528,6824,6179,6534,6567,6936,6652,6952,6988,7255,6243,6607,666 7,6984,6726,6991,7031,7334,6826,7067,7137,7403,7194,7469,7471,7947,4364,5161,5200,5827,54 72,5846,5885,6252,5577,5911,5963,6338,6067,6376,6501,6791,5607,6012,6085,6379,6168,6529,6 600,6883,6213,6650,6566,6941,6721,6987,7027,7330,5841,6139,6175,6560,6250,6602,6666,6956, 6309,6668,6725,7024,6789,7029,7070,7402,6408,6785,6828,7065,6939,7139,7195,7465,6953,724 9,7254,7537,7333,7540,7542,7944,5959,6178,6308,6669,6367,6724,6786,7030,6499,6830,6882,71 36,6942,7192,7253,7470,6503,6940,6957,7248,7026,7328,7329,7541,7068,7335,7401,7543,7407,7 788,7790,8040,6654,6990,7025,7331,7071,7400,7404,7785,7193,7464,7468,7789,7538,7791,7948, 8042,7198,7536,7539,7945,7784,7946,7949,8043,7786,7950,7951,8044,8041,8045,8046,8047,256, 257,258,263,259,392,395,592,260,394,397,596,496,657,659,998,261,396,398,656,499,662,759,103 4,502,758,754,1081,889,1121,1185,1550,262,497,501,752,503,757,827,1083,597,831,891,1124,993, 1224,1229,1589,658,893,996,1227,1033,1270,1331,1670,1080,1333,1415,1808,1438,1834,1956,2 377,393,498,594,830,598,890,992,1187,660,997,894,1230,1037,1309,1409,1725,756,995,1039,133 2,1085,1412,1437,1814,1127,1464,1560,1914,1588,1980,2030,2513,829,1082,1125,1436,1225,147 0,1567,1977,1266,1584,1669,2006,1745,2063,2164,2632,1335,1723,1811,2101,1832,2165,2229,27 15,1953,2315,2370,2801,2419,2852,3024,3530,399,593,599,994,663,1032,1035,1408,824,1038,10 86,1435,1184,1469,1547,1976,888,1087,1186,1471,1228,1566,1666,2024,1308,1667,1724,2058,18 13,2109,2223,2675,954,1190,1267,1587,1310,1668,1748,2102,1434,1809,1833,2167,1952,2314,23 35,2800,1546,1855,1978,2319,2007,2383,2421,2848,2098,2486,2574,2963,2656,3078,3207,3531,9 58,1271,1411,1751,1468,1815,1919,2317,1551,1954,1982,2376,2031,2420,2512,2941,1664,2025,2 059,2484,2166,2570,2634,3084,2217,2658,2718,3130,2808,3248,3310,3811,1747,2103,2196,2593, 2328,2674,2745,3202,2418,2773,2849,3290,2964,3331,3487,3955,2511,2914,3025,3428,3076,352 5,3601,4063,3205,3636,3691,4058,3779,4202,4333,4860,500,661,753,1084,825,1120,1188,1565,8 26,1189,1231,1590,1328,1744,1752,2221,895,1264,1329,1755,1413,1812,1853,2222,1439,1852,19 57,2369,2026,2417,2432,2831,956,1410,1465,1757,1562,1912,1979,2416,1586,2004,2052,2480,20 62,2538,2597,3074,1585,2060,2105,2537,2216,2635,2677,3131,2330,2747,2809,3239,2913,3309,3 431,3899,999,1549,1563,2000,1643,2056,2104,2514,1671,2111,2195,2633,2230,2714,2772,3235,1 955,2226,2329,2717,2378,2806,2912,3304,2506,2917,3030,3414,3087,3524,3603,4048,2055,2372, 2481,2830,2536,2962,3032,3496,2626,3081,3097,3529,3232,3651,3725,4153,2719,3206,3249,370 8,3305,3786,3663,4219,3450,3896,3968,4379,4003,4537,4622,4926,1036,1591,1665,2199,1913,23 13,2334,2746,2001,2368,2379,2825,2487,2919,3027,3500,2053,2485,2517,2940,2592,3033,3093,3 577,2659,3101,3191,3639,3291,3711,3810,4223,2220,2539,2596,3092,2676,3184,3255,3688,2824, 3268,3311,3798,3451,3771,3919,4383,2961,3410,3522,3897,3582,4002,4054,4492,3660,4061,406 0,4602,4220,4669,4741,5169,2371,2657,2768,3269,2918,3330,3430,3865,3031,3497,3526,3969,36 33,4009,4059,4527,3094,3589,3689,4049,3726,4062,4221,4670,3864,4241,4318,4766,4414,4882,4 918,5365,3238,3709,3794,4222,3918,4232,4406,4777,3954,4401,4494,4892,4582,5001,5122,5534, 4010,4568,4660,5029,4722,5131,5075,5624,4846,5209,5273,5770,5407,5858,5915,6234,595,755,8 28,1126,892,1265,1330,1749,955,1334,1414,1754,1467,1836,1854,2380,957,1466,1548,1835,1564, 2057,2099,2510,1720,2100,2198,2627,2312,2708,2769,3289,959,1561,1642,2061,1722,2197,2227, 2662,1750,2316,2340,2774,2382,2853,2943,3336,1810,2373,2423,2916,2515,3026,3079,3484,257 1,3075,3122,3588,3129,3638,3710,4335,1191,1721,1746,2231,1756,2341,2381,2827,1915,2433,25 07,2967,2573,3083,3100,3502,1983,2509,2595,3077,2661,3128,3173,3606,2716,3174,3190,3724,3 383,3787,3878,4400,2054,2660,2712,3187,2803,3254,3288,3750,2855,3382,3441,3857,3528,3914, 4000,4495,2966,3486,3583,4001,3661,4015,4155,4583,3791,4176,4252,4671,4319,4769,4886,534 1,1226,1753,1837,2422,1981,2508,2575,3086,2027,2624,2663,3175,2744,3204,3233,3727,2110,27 13,2802,3234,2854,3377,3429,3812,2965,3482,3527,3953,3607,4011,4086,4524,2228,2826,2942,3 440,3080,3523,3503,4012,3095,3600,3637,4066,3751,4174,4216,4697,3203,3662,3789,4203,3813, 4299,4332,4778,3887,4382,4450,4893,4601,5005,5123,5535,2331,2991,3082,3602,3172,3650,377 0,4177,3339,3790,3872,4314,3875,4334,4412,4881,3411,3873,3886,4405,4013,4437,4573,5000,41 48,4600,4651,5060,4740,5172,5230,5631,3483,4055,4084,4525,4217,4603,4668,5085,4253,4728,4 779,5208,4887,5304,5385,5777,4464,4805,4912,5311,5019,5433,5458,5913,5100,5497,5609,5980, 5694,6104,6219,6539,1311,1918,2005,2625,2108,2709,2775,3308,2194,2807,2915,3379,2990,344 9,3576,4087,2318,2960,3085,3501,3123,3649,3632,4152,3185,3690,3778,4240,3866,4302,4357,48 47,2516,3096,3186,3648,3338,3749,3795,4315,3378,3867,3877,4378,3915,4413,4469,4980,3412,3 898,4008,4468,4109,4572,4623,5061,4206,4701,4729,5173,4804,5231,5338,5750,2572,3337,3376, 3856,3413,3874,3952,4436,3485,4014,4067,4536,4175,4618,4723,5143,3788,4108,4218,4650,425 4,4767,4826,5210,4415,4827,4913,5328,5028,5432,5449,5912,3876,4298,4404,4768,4465,4889,49 82,5340,4575,5004,5063,5448,5142,5526,5630,5991,4661,5101,5177,5608,5272,5639,5735,6124,5 364,5771,5811,6163,5876,6329,6347,6773,2594,3415,3448,4085,3748,4154,4207,4700,3799,4233, 4303,4776,4407,4880,4927,5339,3879,4356,4451,4883,4526,4983,5074,5437,4619,5130,5062,549 3,5211,5625,5693,6034,4149,4493,4569,5018,4696,5084,5176,5548,4765,5180,5265,5660,5329,56 95,5780,6162,4888,5305,5384,5751,5459,5859,5877,6273,5527,5945,5990,6417,6105,6450,6478,6 712,4255,4574,4764,5181,4861,5264,5310,5734,4919,5406,5436,5810,5496,5860,5981,6346,4981, 5492,5549,5944,5692,6006,6007,6451,5776,6125,6153,6479,6235,6616,6642,6996,5168,5638,566 1,6035,5781,6152,6218,6513,5861,6272,6328,6617,6442,6643,6838,7238,5914,6416,6443,6713,65 12,6772,6839,7239,6538,6910,6911,7506,6997,7507,7642,7643,952,953,1122,1433,1123,1544,164 1,2028,1268,1640,1727,2106,1838,2219,2225,2910,1269,1726,1758,2218,1917,2342,2505,2938,20 02,2504,2434,3035,2631,3121,3189,3706,1432,1839,1959,2374,2003,2483,2569,3073,2107,2629,2 673,3132,2829,3252,3307,3797,2224,2679,2908,3271,2937,3380,3443,3884,3034,3481,3579,4052, 3604,4104,4204,4703,1545,1916,2096,2628,2192,2672,2828,3201,2332,2909,2710,3328,2989,340 9,3495,3941,2482,2851,3029,3480,3099,3520,3591,4068,3135,3634,3720,4178,3796,4228,4316,48 45,2599,3072,3133,3590,3253,3692,3777,4225,3342,3784,3871,4296,3943,4377,4466,4978,3493,3 917,4057,4403,4070,4467,4571,5077,4183,4591,4662,5137,4743,5190,5332,5816,1759,2029,2193, 2850,2343,2936,2939,3494,2518,3028,3102,3581,3188,3659,3695,4224,2630,3103,3200,3693,330 6,3776,3868,4300,3408,3869,3940,4372,4065,4439,4541,5031,2770,3250,3343,3793,3424,3870,39 72,4416,3580,4053,4071,4471,4182,4590,4649,5136,3694,4151,4226,4607,4297,4733,4761,5188,4 380,4806,4914,5275,5006,5366,5545,5817,2810,3381,3499,3975,3658,4069,4181,4605,3707,4200, 4230,4702,4317,4760,4844,5267,3858,4301,4373,4774,4470,4890,5002,5386,4491,5016,5086,548 0,5170,5554,5628,6059,3971,4417,4474,4917,4616,5030,5103,5524,4742,5121,5189,5594,5306,56 37,5775,6189,4843,5228,5333,5706,5354,5805,5873,6275,5533,5890,5947,6264,6033,6344,6469,6 810,1958,2333,2375,3098,2519,3120,3236,3769,2568,3237,3329,3808,3426,3942,4004,4539,2711, 3340,3427,4007,3521,4064,4111,4540,3605,4110,4205,4659,4312,4735,4770,5183,2804,3498,3635, 4051,3722,4172,4227,4734,3792,4242,4328,4772,4376,4884,4923,5352,3785,4374,4419,4867,449 0,5003,5037,5481,4620,5117,5171,5553,5215,5627,5733,6155,2911,3705,3723,4234,3815,4358,44 18,4862,3885,4449,4473,4979,4580,5076,5120,5551,4201,4542,4617,5079,4720,5140,5214,5610,4 824,5245,5336,5704,5389,5804,5875,6260,4331,4698,4773,5182,4866,5274,5342,5778,4976,5373, 5435,5809,5546,5925,5983,6319,5087,5544,5555,5948,5611,6036,5933,6373,5754,6130,6190,649 3,6207,6595,6678,6896,2988,3809,3859,4489,4173,4589,4648,5116,4235,4658,4721,5175,4807,52 47,5335,5782,4329,4775,4865,5266,4916,5343,5391,5819,5017,5439,5499,5921,5595,5951,6058,6 393,4538,4885,4922,5390,5036,5486,5557,5934,5174,5558,5629,6056,5755,6027,6159,6495,5271, 5688,5794,6131,5856,6206,6262,6558,5926,6267,6266,6640,6374,6697,6747,7023,4663,5007,511 8,5559,5246,5636,5732,6089,5337,5779,5806,6191,5889,6217,6265,6593,5404,5863,5935,6261,59 88,6274,6375,6698,6088,6419,6448,6754,6522,6822,6890,7147,5552,5949,6050,6392,6158,6394,6 514,6763,6188,6505,6580,6850,6636,6917,7004,7222,6232,6618,6682,6931,6742,7007,6973,7290, 6808,7051,7103,7374,7151,7418,7479,7606,2097,2435,2598,3134,2678,3341,3442,3973,2771,349 2,3578,4006,3657,4106,4150,4730,2805,3656,3704,4105,3768,4359,4381,4842,3912,4402,4488,49 77,4588,5038,5119,5593,2811,3721,3814,4375,3916,4475,4543,5022,3974,4604,4656,5128,4732,5 191,5269,5652,4056,4699,4763,5244,4863,5334,5367,5772,4891,5353,5450,5862,5457,5920,5950, 6471,3251,3913,3970,4581,4050,4657,4731,5179,4179,4771,4825,5309,4895,5375,5438,5792,423 1,4841,4921,5355,5021,5456,5483,5878,5078,5484,5498,5982,5671,6037,6126,6504,4330,5020,50 72,5495,5139,5556,5592,6024,5213,5670,5749,6079,5808,6156,6204,6581,5308,5774,5857,6205,5 927,6239,6331,6637,6049,6334,6420,6699,6449,6761,6836,7145,3270,4005,4107,4762,4229,4840, 4915,5388,4313,4924,5023,5485,5102,5532,5547,5989,4448,5073,5138,5550,5212,5663,5707,607 6,5307,5768,5807,6161,5879,6233,6292,6582,4570,5178,5268,5748,5372,5795,5793,6236,5405,58 72,5891,6280,6025,6332,6354,6715,5525,5932,6039,6345,6077,6429,6468,6774,6129,6494,6552,6 851,6639,6919,7005,7223,4621,5331,5374,5874,5482,5924,6026,6335,5655,6048,6106,6440,6121, 6470,6520,6821,5689,6107,6128,6507,6237,6537,6625,6916,6316,6638,6681,6968,6746,7040,708 6,7305,5769,6263,6282,6583,6355,6641,6696,6975,6421,6744,6775,7050,6837,7104,7149,7381,65 54,6801,6888,7107,6929,7177,7202,7477,6998,7215,7289,7532,7348,7564,7605,7775,3425,4180,4 243,4925,4438,5039,5129,5626,4472,5141,5229,5669,5330,5753,5818,6293,4606,5270,5387,5783, 5451,5923,5888,6318,5487,5946,6032,6418,6090,6430,6477,6809,4864,5434,5494,5922,5654,600 5,6051,6441,5668,6091,6123,6492,6157,6521,6557,6898,5690,6154,6216,6556,6295,6624,6679,69 69,6352,6741,6745,7041,6800,7087,7122,7372,4894,5653,5662,6078,5691,6120,6160,6536,5773,6 238,6281,6594,6333,6676,6743,7021,6038,6294,6372,6680,6422,6755,6802,7084,6523,6803,6889, 7120,6930,7176,7201,7476,6122,6428,6506,6760,6555,6849,6908,7144,6627,6918,6971,7200,702 0,7220,7304,7535,6683,6999,7043,7288,7102,7307,7351,7566,7146,7375,7417,7587,7450,7669,76 71,7851,4920,5705,5752,6283,6004,6330,6353,6740,6057,6395,6431,6762,6515,6820,6897,7123,6 127,6476,6553,6823,6592,6909,6972,7179,6677,7006,6970,7213,7085,7291,7323,7550,6317,6559, 6619,6928,6714,6974,7042,7236,6753,7048,7101,7320,7121,7349,7382,7586,6848,7105,7148,737 3,7203,7419,7451,7641,7221,7505,7534,7697,7565,7736,7738,7848,6423,6626,6752,7049,6811,71 00,7106,7350,6891,7150,7178,7416,7214,7448,7533,7670,6899,7212,7237,7504,7322,7548,7549,7 737,7380,7567,7585,7739,7607,7812,7814,8068,7022,7306,7321,7551,7383,7584,7604,7773,7449, 7640,7668,7813,7698,7815,7980,8070,7478,7696,7699,7849,7772,7850,7981,8071,7774,7982,798 3,8116,8069,8117,8118,8119,1304,1305,1306,1647,1307,1848,1851,2436,1644,1850,2049,2540,21 60,2637,2639,3294,1645,2048,2050,2636,2163,2706,2815,3334,2338,2814,2750,3453,3037,3533,3 653,4146,1646,2161,2337,2748,2339,2813,2907,3455,2541,2987,3039,3584,3265,3684,3745,4245, 2638,3089,3292,3687,3333,3782,3883,4310,3452,3901,3959,4476,3990,4546,4652,5157,1849,216 2,2438,2986,2542,3038,3264,3655,2704,3293,3090,3746,3445,3861,3937,4369,2812,3267,3447,39 00,3489,3956,3989,4522,3587,4040,4156,4586,4244,4704,4782,5313,2985,3454,3585,3988,3685,4 046,4171,4665,3774,4236,4309,4726,4409,4859,4956,5444,3903,4355,4479,4897,4544,4957,5033, 5519,4613,5059,5134,5569,5227,5656,5756,6226,2051,2437,2543,3266,2707,3332,3335,3936,290 4,3446,3490,3987,3652,4045,4083,4664,3036,3491,3654,4047,3744,4170,4306,4736,3860,4307,43 68,4830,4521,4953,4999,5491,3126,3682,3775,4239,3862,4308,4420,4898,3986,4477,4545,4959,4 612,5058,5115,5568,4082,4579,4666,5083,4727,5187,5241,5648,4870,5278,5370,5719,5452,5802, 5943,6227,3170,3783,3939,4423,4044,4523,4611,5081,4147,4614,4706,5156,4783,5240,5312,571 3,4304,4737,4831,5276,4958,5362,5446,5820,4993,5454,5522,5894,5596,5976,6030,6455,4411,48 99,4972,5401,5096,5490,5529,5938,5226,5565,5649,6018,5728,6055,6167,6547,5303,5674,5757,6 116,5800,6221,6277,6623,5941,6296,6327,6614,6407,6706,6805,7124,2336,2705,2749,3488,2905, 3532,3680,4169,2906,3681,3747,4246,3880,4408,4432,4997,3091,3772,3881,4435,3957,4520,457 7,4998,3991,4576,4653,5133,4738,5225,5256,5635,3168,3938,4041,4453,4158,4584,4667,5224,42 38,4724,4800,5260,4858,5358,5409,5798,4237,4856,4901,5357,4992,5447,5501,5895,5098,5531,5 597,5975,5673,6029,6119,6511,3295,4145,4159,4708,4251,4828,4900,5314,4311,4955,4971,5445, 5034,5518,5564,5971,4615,5026,5097,5521,5158,5574,5672,6020,5298,5677,5786,6110,5823,622 0,6279,6596,4803,5152,5261,5634,5356,5718,5788,6192,5414,5813,5837,6225,5968,6303,6389,66 85,5523,5942,5977,6368,6021,6426,6323,6719,6146,6508,6548,6835,6575,6921,6994,7182,3444,4 247,4305,4975,4585,5057,5114,5530,4709,5132,5159,5613,5279,5679,5759,6196,4801,5277,5317, 5712,5400,5789,5833,6229,5455,5849,5931,6299,6019,6371,6454,6731,4996,5359,5408,5832,550 0,5916,5987,6324,5612,6000,6031,6446,6147,6403,6527,6843,5717,6102,6202,6509,6258,6574,66 10,6904,6320,6621,6620,6966,6728,7017,7061,7293,5135,5453,5560,6001,5678,6054,6118,6465,5 787,6193,6222,6549,6289,6585,6615,6915,5834,6269,6325,6597,6390,6622,6729,7018,6464,6757, 6794,7078,6858,7134,7170,7397,5974,6369,6438,6730,6526,6748,6854,7093,6546,6845,6906,716 0,6950,7205,7274,7482,6586,6932,7012,7229,7046,7279,7247,7512,7118,7317,7357,7582,7427,76 22,7647,7762,2439,2751,2984,3586,3088,3773,3882,4421,3127,3902,3958,4434,4043,4548,4578,5 184,3169,4042,4144,4547,4168,4829,4871,5302,4352,4896,4974,5415,5056,5512,5561,6017,3171, 4157,4250,4857,4354,4973,5027,5462,4422,5080,5124,5566,5186,5657,5715,6060,4478,5153,524 3,5676,5315,5758,5803,6164,5363,5799,5854,6268,5893,6298,6370,6807,3683,4353,4410,5035,44 52,5125,5185,5615,4587,5257,5299,5731,5369,5815,5848,6198,4707,5301,5403,5801,5461,5892,5 901,6286,5520,5902,5930,6388,6099,6427,6486,6844,4802,5460,5516,5919,5571,5986,6016,6398, 5659,6098,6133,6461,6224,6518,6572,6907,5730,6166,6259,6573,6321,6591,6687,6951,6435,669 2,6764,7019,6795,7081,7154,7389,3686,4433,4549,5242,4705,5300,5371,5822,4739,5412,5463,59 03,5528,5940,5969,6391,4954,5517,5570,5970,5658,6093,6117,6456,5729,6150,6223,6545,6287,6 587,6646,6912,5032,5614,5714,6132,5812,6203,6199,6588,5835,6276,6297,6630,6399,6690,6716, 7033,5939,6322,6433,6707,6457,6771,6804,7094,6491,6842,6870,7161,6965,7209,7275,7483,509 9,5747,5814,6278,5900,6302,6402,6693,6063,6434,6480,6782,6483,6806,6856,7133,6103,6481,64 90,6853,6589,6865,6945,7204,6672,6964,7003,7240,7060,7296,7338,7519,6151,6611,6644,6913,6 717,6967,7016,7261,6765,7052,7095,7316,7155,7360,7413,7593,6872,7097,7164,7367,7219,7429, 7442,7645,7264,7461,7509,7672,7558,7716,7759,7883,3863,4610,4725,5413,4952,5513,5567,602 8,4970,5575,5675,6095,5746,6145,6228,6647,5082,5716,5821,6197,5855,6301,6288,6684,5917,63 26,6406,6756,6466,6778,6813,7119,5316,5836,5918,6300,6062,6397,6439,6783,6094,6467,6485,6 834,6519,6857,6877,7188,6108,6510,6584,6876,6661,6944,6995,7241,6710,7037,7053,7297,7096, 7339,7386,7574,5368,6061,6092,6460,6109,6482,6544,6864,6165,6590,6631,6920,6691,6982,704 7,7287,6432,6660,6718,7002,6766,7079,7110,7318,6859,7111,7165,7368,7228,7428,7437,7644,64 84,6770,6852,7080,6873,7157,7190,7388,6947,7208,7243,7436,7286,7474,7518,7679,7013,7265,7 301,7508,7356,7523,7571,7724,7396,7583,7615,7747,7632,7805,7819,7957,5402,6111,6144,6645, 6396,6686,6711,7036,6447,6749,6779,7092,6855,7132,7183,7387,6487,6812,6871,7135,6914,719 1,7246,7433,6983,7278,7242,7457,7319,7513,7557,7690,6673,6905,6933,7218,7032,7260,7300,74 88,7077,7308,7345,7528,7369,7559,7596,7746,7156,7361,7412,7575,7443,7623,7633,7781,7475,7 661,7678,7833,7717,7854,7862,7928,6767,6946,7076,7309,7125,7344,7366,7570,7171,7426,7432, 7614,7460,7624,7673,7818,7189,7456,7489,7660,7556,7682,7683,7855,7592,7725,7733,7863,776 3,7900,7914,8012,7292,7522,7529,7691,7597,7732,7758,7873,7625,7780,7804,7901,7846,7915,79 74,8086,7646,7832,7847,7929,7872,7956,7975,8087,7882,7994,7995,8130,8013,8131,8154,8155,3 124,3125,3534,3985,3535,4080,4249,4780,3780,4248,4371,4902,4550,4995,5025,5666,3781,4370, 4454,4994,4609,5126,5297,5710,4710,5296,5258,5791,5443,5853,5929,6358,3984,4551,4655,515 4,4711,5263,5361,5797,4903,5441,5489,5896,5633,5984,6023,6445,5024,5503,5664,6003,5709,60 96,6135,6488,5790,6149,6231,6608,6284,6656,6708,7039,4081,4608,4868,5440,4968,5488,5632,5 937,5112,5665,5514,6052,5745,6101,6187,6541,5262,5651,5785,6148,5839,6200,6271,6632,5899, 6290,6384,6694,6444,6736,6792,7117,5411,5796,5897,6270,5985,6348,6405,6733,6074,6424,647 5,6768,6543,6833,6874,7186,6185,6525,6613,6847,6634,6875,6935,7257,6703,6963,7014,7281,70 63,7314,7376,7616,4455,4781,4969,5650,5127,5708,5711,6186,5318,5784,5850,6257,5928,6315,6 351,6732,5442,5851,5936,6349,6022,6404,6472,6776,6100,6473,6540,6816,6629,6867,6925,7231, 5562,5978,6075,6437,6112,6474,6568,6860,6256,6609,6635,6879,6702,6962,7001,7280,6350,667 5,6734,6979,6769,7057,7073,7312,6840,7098,7166,7359,7210,7398,7485,7617,5598,6097,6195,65 71,6314,6633,6701,6977,6359,6704,6738,7038,6793,7072,7116,7347,6462,6777,6817,7090,6878,7 158,7206,7414,6903,7216,7262,7444,7294,7494,7516,7707,6551,6861,6894,7169,6980,7230,7267, 7472,7062,7273,7313,7502,7362,7521,7591,7749,7115,7336,7377,7562,7394,7609,7629,7783,748 1,7638,7663,7776,7689,7816,7857,7966,4654,5113,5155,5838,5319,5852,5972,6401,5360,5973,60 53,6452,6114,6542,6576,6923,5515,6072,6115,6579,6201,6628,6663,6924,6285,6662,6709,7011,6 780,7059,7082,7311,5572,6194,6291,6599,6386,6688,6735,7058,6436,6758,6796,7088,6832,7152, 7175,7392,6425,6818,6863,7131,6902,7207,7233,7445,6992,7269,7295,7493,7327,7515,7569,773 5,5667,6357,6387,6750,6459,6814,6862,7126,6489,6869,6893,7187,6948,7256,7272,7491,6705,69 26,6981,7259,7044,7284,7326,7510,7108,7341,7384,7560,7421,7608,7631,7768,6799,7034,7089,7 310,7130,7358,7390,7594,7184,7409,7431,7613,7486,7653,7675,7803,7263,7484,7495,7664,7511, 7692,7657,7825,7578,7730,7750,7865,7755,7899,7918,7988,5744,6453,6463,6901,6689,6961,700 0,7268,6751,7010,7045,7299,7099,7343,7379,7598,6797,7091,7129,7346,7168,7391,7423,7619,72 17,7435,7463,7649,7503,7667,7706,7829,6922,7153,7174,7422,7232,7454,7497,7658,7298,7498,7 517,7704,7579,7687,7743,7867,7355,7552,7602,7731,7620,7754,7770,7890,7654,7779,7778,7912, 7826,7925,7939,8023,7015,7211,7270,7499,7342,7520,7568,7713,7385,7595,7610,7751,7637,775 7,7777,7897,7424,7627,7659,7769,7676,7782,7827,7926,7712,7835,7852,7942,7878,7970,7986,80 59,7492,7665,7702,7828,7742,7830,7874,7955,7748,7869,7892,7978,7908,7997,8016,8082,7760,7 902,7922,8003,7934,8019,8009,8090,7964,8031,8039,8106,8063,8114,8127,8150,4869,5259,5410, 5898,5502,6073,6134,6569,5563,6184,6230,6578,6313,6658,6674,7054,5573,6312,6356,6657,640 0,6815,6841,7114,6516,6846,6900,7185,6960,7234,7271,7501,5599,6385,6458,6819,6524,6895,69 27,7226,6570,6976,7008,7276,7056,7315,7353,7524,6612,7035,7075,7340,7127,7378,7399,7588,7 159,7393,7438,7626,7441,7648,7666,7859,5979,6517,6550,6949,6598,7009,7055,7303,6695,7083, 7109,7365,7163,7411,7434,7600,6739,7113,7173,7395,7225,7440,7447,7634,7258,7452,7462,767 4,7547,7693,7726,7868,6798,7224,7244,7459,7283,7496,7500,7684,7325,7546,7573,7711,7612,77 40,7752,7893,7364,7590,7621,7753,7655,7767,7807,7909,7701,7810,7836,7927,7853,7953,7972,8 057,6002,6577,6659,7074,6737,7112,7167,7420,6781,7180,7227,7453,7266,7480,7487,7677,6868, 7245,7282,7490,7324,7531,7563,7708,7363,7580,7611,7745,7635,7761,7796,7894,6934,7302,735 2,7572,7408,7603,7601,7764,7425,7628,7639,7792,7685,7808,7822,7931,7473,7656,7695,7817,77 09,7841,7856,7958,7729,7866,7884,7979,7911,7999,8017,8083,6993,7371,7410,7630,7446,7652,7 686,7811,7527,7700,7718,7844,7721,7858,7876,7969,7553,7719,7728,7871,7765,7881,7905,7996, 7800,7910,7921,8004,7938,8024,8034,8093,7581,7771,7794,7895,7823,7913,7924,8011,7837,793 6,7959,8030,7973,8048,8061,8109,7886,7961,7984,8051,8001,8065,8074,8125,8014,8079,8089,81 32,8100,8140,8149,8171,6113,6700,6759,7181,6866,7235,7277,7514,6892,7285,7337,7545,7370,7 577,7618,7797,6978,7354,7415,7599,7439,7651,7636,7802,7455,7662,7688,7834,7714,7842,7861, 7965,7128,7430,7458,7650,7526,7681,7703,7845,7544,7715,7723,7864,7741,7877,7889,7990,755 4,7734,7756,7888,7799,7904,7919,8005,7820,7933,7937,8025,7960,8035,8054,8104,7162,7525,75 30,7710,7555,7720,7744,7880,7589,7766,7793,7898,7809,7916,7935,8021,7694,7798,7824,7920,7 838,7943,7962,8032,7879,7963,7985,8052,8002,8064,8073,8124,7722,7840,7870,7952,7887,7977, 7992,8056,7907,7998,8007,8072,8020,8080,8092,8135,7923,8015,8027,8088,8038,8095,8103,814 2,8058,8107,8113,8147,8122,8157,8159,8179,7172,7561,7576,7795,7680,7806,7821,7932,7705,78 31,7843,7954,7875,7968,7989,8055,7727,7860,7885,7971,7896,7993,8008,8067,7917,8018,8006,8 077,8033,8091,8099,8138,7801,7891,7903,8000,7930,8010,8026,8084,7941,8028,8037,8096,8053, 8101,8110,8146,7976,8049,8060,8105,8075,8115,8123,8153,8081,8129,8134,8161,8141,8164,816 6,8176,7839,7906,7940,8029,7967,8036,8050,8102,7987,8062,8066,8112,8078,8120,8133,8158,79 91,8076,8085,8128,8098,8136,8137,8165,8108,8143,8145,8167,8151,8172,8174,8184,8022,8094,8 097,8139,8111,8144,8148,8169,8121,8152,8156,8173,8162,8175,8180,8186,8126,8160,8163,8177, 8168,8178,8181,8187,8170,8182,8183,8188,8185,8189,8190,8191]
›APPENDIX · 13 of 21
Sequence Group 3: Q3_2048
[0,1,2,4,8,16,32,3,5,64,1024,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11, 40,68,130,19,13,48,14,72,257,1025,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,4 1,144,28,69,42,516,49,1026,74,272,160,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,10 28,23,134,384,76,137,82,56,27,97,39,259,84,138,145,261,1032,29,43,98,515,88,140,30,146,71,262, 265,161,576,45,1040,100,640,51,148,46,75,266,273,517,104,162,53,193,1056,152,77,164,768,268, 274,518,54,83,57,521,1027,112,135,78,289,194,85,276,522,58,168,1029,139,99,86,60,280,89,290, 529,524,196,1088,141,101,147,176,142,530,321,31,200,1033,90,545,292,322,532,263,149,102,105, 1030,304,296,163,92,47,267,385,546,324,1041,208,386,150,153,165,106,55,1034,328,536,577,54 8,113,154,79,269,1042,108,578,224,166,519,552,195,1152,270,641,523,275,580,291,59,1036,169, 560,114,277,156,87,197,1057,116,170,61,531,525,642,281,1089,278,526,177,293,388,91,1044,584, 769,198,172,120,201,336,1280,62,282,143,103,178,294,1058,93,644,202,592,323,1048,392,297,7 70,107,180,151,1060,209,284,648,94,204,298,1031,400,608,352,325,533,1153,155,210,305,547,30 0,1090,109,184,534,537,115,167,1536,225,326,306,772,157,1035,656,329,110,117,212,1064,171,7 76,330,226,549,1092,538,387,308,216,1154,416,271,279,158,337,1043,550,672,118,332,579,1037, 540,389,173,121,1072,553,199,784,179,1038,228,338,312,704,390,1096,174,554,581,393,1281,28 3,122,448,353,1045,561,203,63,340,1156,394,527,582,556,181,1059,295,285,232,124,1282,205,18 2,643,562,1050,286,585,299,1537,354,211,401,185,1104,396,344,586,645,1061,593,535,240,206,1 049,95,327,564,1046,800,402,356,307,1160,301,417,213,568,1284,832,588,186,1288,646,404,227, 896,1062,594,418,302,1538,649,771,360,539,1120,111,331,214,1091,309,188,449,1065,217,408,60 9,596,1168,551,650,229,1052,159,420,310,1093,541,773,610,1066,657,333,119,1540,600,339,218, 1073,368,652,230,1098,391,313,450,1296,542,334,233,1184,555,774,175,1544,123,658,612,1312, 341,777,220,1552,314,424,395,1216,673,583,355,1568,287,183,234,1094,125,557,660,1068,616,3 42,316,1155,241,778,1105,563,345,452,1074,397,403,207,1097,674,558,1039,785,432,357,1344,1 87,236,664,1157,624,587,1076,780,705,126,1047,242,565,1158,398,346,456,1408,358,405,1100,30 3,569,244,1161,595,189,1106,566,676,361,1080,706,589,1051,215,786,647,1121,348,419,1063,406, 464,680,1283,801,362,1108,590,409,1162,570,788,597,1169,572,219,1285,311,708,1053,598,601, 1067,651,421,792,1122,802,611,1539,602,410,1112,231,688,1164,653,248,1054,369,190,364,1170, 654,659,1095,335,480,1286,315,221,1289,370,613,1185,422,425,1600,451,614,1069,543,235,1124, 412,343,372,1664,775,317,1075,222,426,1172,453,237,1070,559,833,1099,804,712,1290,834,661, 1297,808,779,1541,617,1128,604,433,1186,720,816,1077,836,347,1217,897,243,1176,662,454,110 1,318,675,1188,618,898,1792,781,376,1292,428,1298,665,736,1542,567,840,1078,625,238,1107,3 59,457,1081,399,787,1545,591,1136,678,434,1159,677,349,1102,245,458,1313,666,1218,620,363,1 109,127,191,1300,782,1546,407,436,1082,626,571,1192,465,1163,681,246,1123,707,350,1110,599, 1084,668,790,1304,460,249,1113,682,1314,573,411,1553,803,789,1548,709,1220,365,440,1165,62 8,1125,689,374,1171,423,466,1200,793,1166,250,371,1554,481,1345,574,413,1055,603,1224,366,4 68,1114,655,1569,900,805,1316,615,1346,684,710,1556,429,1287,794,252,1173,373,1126,605,848, 1129,690,1328,713,1320,632,482,1187,806,1116,427,904,1071,414,1291,223,663,1409,692,1570,8 35,1348,619,472,1232,455,1410,796,809,1174,714,1177,721,1189,837,716,1130,864,1079,810,135 2,606,912,1560,722,1601,696,1572,377,435,1137,817,1178,319,1103,621,1293,812,484,1132,430,1 602,838,1248,667,488,1190,239,1543,378,1576,459,1219,622,627,1294,437,1665,380,1547,818,12 99,461,496,1604,669,1315,679,1083,724,1193,841,629,1584,351,1138,467,1301,438,1180,737,111 1,251,1221,462,442,1140,441,1194,469,1085,247,1555,683,1549,842,1666,738,899,1305,670,1302, 783,1550,849,1201,820,1317,728,1412,928,1115,791,367,1608,901,1793,630,1222,685,1196,844,1 144,633,1225,711,1360,253,1086,691,1306,824,1167,902,1127,686,740,1202,850,1318,375,1117,4 44,1668,470,1226,483,1616,415,1347,485,1416,905,1321,795,1794,473,1131,634,1204,744,1175,8 52,1233,960,1308,865,1672,693,1118,797,1228,906,1322,715,1424,807,1632,474,1376,636,1349,6 94,1557,254,1179,717,1234,575,1329,913,1571,798,1324,811,1133,379,1208,697,1558,431,607,48 9,1561,866,1139,723,1191,486,1249,908,1350,718,1330,813,1796,476,1181,856,1680,839,1353,72 5,1134,698,1141,914,1236,752,1195,868,1800,819,1354,814,1250,439,1573,929,1562,490,1411,62 3,1332,671,1240,739,1440,916,1295,463,1303,843,1182,381,1361,497,1574,930,1696,821,1142,72 6,1356,1603,961,1564,872,1413,492,1197,631,1145,729,1577,700,1223,443,1808,741,1203,845,12 52,920,1362,382,1336,822,1728,1414,851,1198,730,1578,498,1605,880,1417,742,1307,445,1146,4 71,1472,1377,635,1585,932,1227,687,1087,903,1364,825,1418,500,1551,1606,846,1580,745,1205, 826,1319,732,1309,446,1256,1148,962,1229,936,1206,475,1667,853,1586,867,1310,1609,637,132 3,907,1378,487,1235,695,1425,1209,746,1420,828,1368,753,1610,854,1669,1617,857,1559,504,12 64,799,1230,1119,255,1351,964,1588,909,1824,719,1426,1380,477,1331,915,1325,638,1441,1237, 748,1592,944,1856,869,1612,1210,491,1670,699,1428,1251,754,1920,858,1618,478,1442,1326,96 8,1673,383,1795,910,1384,1563,815,1135,976,1355,1238,870,1333,917,1212,1473,727,1241,493,1 432,873,1633,1620,701,1575,931,1674,1253,756,1183,860,1444,1334,499,1565,731,1797,1634,82 3,1681,922,1357,1143,874,1624,918,1363,1242,502,1392,933,1676,1254,743,1415,1337,760,1474, 881,1566,1358,494,1257,702,1579,1798,921,1199,501,1147,1682,876,1636,1365,847,1801,992,12 44,1338,447,1448,1419,733,1697,827,1607,1379,934,1311,1207,882,1258,937,1149,1581,963,168 4,1640,747,1366,505,1340,1265,855,1802,1587,924,1369,734,1476,1421,829,1427,1231,965,1698, 1582,938,1809,1456,884,1381,506,1211,1260,749,1688,1648,945,1611,1804,966,1729,1150,755,12 66,859,1589,1422,940,1370,1480,830,1382,1429,911,1327,1593,871,1268,1619,639,1213,1590,88 8,1700,1385,479,1730,1613,946,1239,750,1810,1671,969,1372,1443,508,1430,1488,861,1704,182 5,757,1386,1614,970,1433,1594,919,1812,1621,1596,875,1243,1335,862,1732,1622,758,1625,167 5,948,1445,1816,977,1826,1635,923,1626,1434,972,1255,1712,761,1677,1272,877,1393,1214,138 8,952,1678,1683,495,1359,1504,703,1339,1245,935,1394,1637,978,1446,1449,1475,883,1638,156 7,762,1259,1436,503,1367,1396,925,1799,1341,1246,878,1450,1477,735,1261,1583,1857,993,182 8,1736,885,1858,1685,939,1832,1803,1641,994,1628,1457,980,1744,1840,1860,926,1371,1921,76 4,1267,1686,1478,941,1342,1699,967,1642,1922,1805,886,1400,1452,831,1689,1760,1591,947,18 64,1649,507,1262,1383,1481,889,1423,1811,1615,984,1702,1458,751,1701,1373,1269,942,1482,1 690,1644,996,1387,1151,1215,971,1806,1431,890,1460,1650,1595,509,1489,1705,1270,949,1731, 1374,1623,973,1692,1814,1484,1000,1273,1706,1597,892,1435,1827,1813,950,1733,1389,1464,86 3,1652,1713,1398,759,1447,1490,1817,1008,1274,1395,1505,510,1598,1437,1627,979,1390,1492, 1679,953,1924,1829,1639,763,1708,1734,1453,974,1818,1276,1397,1629,954,1872,1714,1737,879, 1656,1506,1830,981,1451,1928,1438,982,1247,1687,1716,1859,927,1643,1496,1479,995,1820,18 33,1738,1745,765,1861,1740,1888,956,1834,1630,1936,1746,887,1720,1401,1459,1841,985,1343, 1645,1836,997,1508,1454,1862,1691,986,1512,1263,1402,1483,943,1646,1651,1461,1404,891,184 2,1485,1520,1693,998,1703,1748,1865,766,1653,1375,1491,1462,511,1761,1275,1486,1466,1465, 988,1493,1271,1707,1866,1001,1762,1923,1694,1807,951,1873,1844,1752,1952,1002,1815,1391,1 925,1654,1709,893,1868,1657,1735,1277,975,1715,1848,1926,1710,894,1764,1874,1399,1468,149 4,1009,1507,1439,1509,1929,1819,955,1497,1658,1768,1876,1984,1004,1889,1717,1821,1930,101 0,1739,1831,1498,1660,1718,957,1278,1741,1599,1937,1822,983,1835,1403,1721,1455,1631,1513, 958,1890,1747,1510,1932,1742,987,1837,1500,1880,1863,1749,1012,1722,1938,1776,1892,1843, 1838,999,1463,1953,1514,1647,1695,1763,1016,1940,1487,1867,1405,1521,767,1954,1845,1750,1 985,1896,1516,1655,989,1753,1724,1467,1765,1869,1944,1003,1406,1846,1875,1754,1522,1904,9 90,1766,1469,1495,1659,1956,1711,1927,1005,1849,1524,1870,1769,1850,1756,1470,959,1986,19 60,1499,1877,1891,1661,1931,1011,1511,1719,1770,1852,1777,1878,1881,1013,1528,1823,1279,1 988,1933,1743,1501,1939,895,1662,1772,1968,1893,1515,1723,1778,1882,1006,1502,1992,1407,1 934,1839,2000,1894,1941,1014,1751,1517,1897,1725,1955,1780,1884,1523,1755,1017,1847,1946, 1898,1942,1526,1957,1767,1784,1905,1018,1518,1726,1945,1525,1900,1871,2016,1471,1757,185 1,991,1958,1906,1961,1987,1771,1529,1879,1948,1758,1853,1020,1989,1962,1908,1530,1773,196 9,1990,1779,1883,1964,1854,1935,1007,1895,1663,1912,1503,1970,1774,1993,1532,1885,1781,19 94,1943,1015,1899,1886,1782,1972,2001,1947,1996,1785,1901,1976,1519,1727,1959,2002,1019,1 907,1786,1527,1949,1902,1759,2017,1909,1963,2018,2004,1950,1788,1965,1991,1021,1910,1855, 1971,1531,1913,2008,1775,1966,2020,1995,1914,1533,1973,1997,2024,1916,1974,1887,1783,102 2,2032,1534,2003,1977,1787,1998,1978,1903,2005,2006,1951,2019,1789,1980,1911,2009,2021,20 10,1967,1915,2022,1790,153 5,1023,2012,2025,1975,2026,1917,1999,1918,2033,1979,2028,2034,1 981,2007,1982,2011,2036,2023,2040,1791,2013,2027,2014,2029,1983,2035,2037,1919,2030,2038, 2041,2042,2015,2044,2031,2039,2043,2045,2046,2047]
›APPENDIX · 14 of 21
Sequence Group 3: Z3_2048
[0,1,2,7,3,8,12,25,4,11,14,29,17,34,36,79,5,13,15,33,20,40,49,84,23,48,44,91,59,100,10 6,170,6,18,22,42,24,47,53,93,30,57,61,101,74,113,119,187,35,63,77,117,82,126,136,199,90,138,14 9,224,155,236,257,366,9,19,27,56,31,60,73,108,37,78,65,120,87,130,143,207,46,76,89,137,95,146, 154,231,104,157,173,247,186,264,280,404,55,92,102,153,115,164,180,260,124,181,198,273,210,2 96,311,436,141,205,228,300,234,312,334,463,253,341,360,485,378,505,540,721,16,26,32,75,41,81, 85,142,50,88,96,152,105,163,167,259,58,97,107,165,118,179,195,275,129,196,206,290,230,307,3 29,453,67,111,125,185,131,197,213,301,150,226,235,315,252,340,354,483,166,244,261,346,274,3 73,381,502,297,392,420,531,441,557,613,722,71,127,145,216,161,232,251,344,171,254,266,365,2 81,380,402,522,193,277,291,390,313,415,438,566,324,444,467,588,491,623,644,818,212,303,318, 424,348,451,471,606,377,479,503,635,532,648,697,870,401,513,542,674,554,713,735,914,610,746, 771,905,797,950,1007,1188,21,38,43,94,51,98,109,178,52,110,121,188,133,208,218,327,66,122,1 34,221,147,229,242,328,156,240,258,359,278,376,385,501,69,144,158,223,175,245,262,375,184,2 71,282,387,294,413,429,552,183,292,305,411,323,440,455,590,350,474,493,622,511,642,679,856, 80,169,176,268,191,287,304,405,201,310,317,437,335,462,478,619,255,330,349,466,367,489,510, 638,395,517,546,671,570,711,738,897,286,362,389,499,410,529,549,699,433,561,578,719,614,758, 781,936,469,612,625,772,639,799,764,963,686,851,872,1019,881,1077,1108,1225,86,189,194,322, 246,339,352,473,270,357,369,495,394,520,545,702,284,391,409,521,423,550,573,726,445,581,60 4,751,637,777,816,971,326,414,428,571,454,597,628,766,494,629,645,813,688,794,863,1023,528, 665,708,852,727,879,901,1059,759,910,908,1100,965,1123,1149,1303,361,442,475,631,518,647,67 7,828,547,700,714,874,745,885,907,1073,574,732,767,899,782,912,967,1125,826,979,1001,1156,1 039,1197,1220,1381,620,774,809,969,861,973,1031,1167,868,1025,1063,1211,1092,1242,1285,143 9,886,1079,1117,1257,1138,1292,1272,1458,1183,1324,1346,1513,1392,1543,1579,1673,28,45,54, 103,62,123,135,214,68,139,148,220,160,238,243,370,70,159,168,237,177,288,298,400,202,299,32 1,434,338,457,477,634,72,174,190,293,204,319,332,449,215,343,355,481,372,506,525,650,227,36 4,383,516,406,543,559,693,416,553,583,730,587,750,776,1011,112,203,211,336,222,356,371,498,2 49,386,396,536,419,564,580,705,267,399,427,556,447,585,593,740,465,594,603,779,664,801,844, 1024,285,446,459,601,487,626,632,789,509,662,682,825,718,858,876,1065,535,696,729,877,761,8 95,940,1094,808,946,981,1128,1003,1163,1201,1375,116,219,239,382,265,397,422,568,279,431,45 0,596,470,609,616,784,309,461,486,617,507,657,676,819,533,690,716,867,742,888,923,1067,333, 497,524,680,560,710,707,890,575,734,748,916,791,942,958,1132,607,763,804,952,821,991,1005,1 169,849,1021,1047,1213,1098,1247,1287,1442,351,539,563,737,591,756,792,948,654,806,833,997, 838,1009,1035,1194,667,835,847,1029,892,1045,1085,1240,931,1096,1115,1259,1147,1306,1332, 1468,691,903,920,1069,959,1102,1121,1277,983,1143,1172,1322,1204,1349,1386,1524,1051,1176, 1216,1358,1252,1398,1414,1571,1280,1429,1455,1591,1492,1626,1668,1784,132,250,272,432,306, 458,482,641,316,490,514,660,538,685,724,925,345,527,567,703,584,754,743,935,598,769,796,97 7,830,993,1015,1185,408,577,600,753,653,787,811,999,659,831,842,1017,860,1037,1057,1230,66 8,854,883,1055,929,1083,1110,1262,954,1136,1145,1308,1174,1335,1366,1506,418,651,656,823,6 70,837,865,1043,694,894,918,1075,944,1104,1141,1298,802,927,961,1113,985,1158,1178,1327,10 41,1181,1218,1360,1254,1395,1411,1567,840,989,1027,1160,1053,1208,1235,1372,1090,1244,126 7,1408,1295,1432,1465,1604,1119,1282,1314,1452,1344,1475,1503,1635,1378,1517,1539,1659,15 59,1700,1710,1847,425,673,683,921,786,938,956,1134,814,975,995,1165,1033,1192,1227,1369,84 5,1013,1049,1199,1071,1237,1269,1404,1106,1290,1264,1423,1330,1461,1489,1617,933,1061,108 1,1249,1130,1274,1311,1445,1154,1316,1341,1478,1363,1496,1528,1654,1206,1352,1384,1510,14 17,1547,1563,1689,1436,1587,1600,1722,1630,1739,1752,1822,987,1088,1152,1319,1190,1338,13 55,1499,1223,1389,1401,1536,1426,1551,1595,1705,1232,1420,1448,1583,1485,1608,1612,1745,1 521,1640,1649,1758,1679,1792,1806,1896,1300,1472,1482,1621,1532,1644,1664,1771,1555,1684, 1694,1799,1728,1814,1856,1920,1575,1716,1733,1830,1764,1838,1865,1933,1778,1875,1885,194 8,1907,1964,1984,2008,10,39,64,140,83,151,182,283,99,172,200,308,225,337,347,526,114,192,20 9,331,248,363,407,541,269,403,384,565,452,592,611,778,128,233,263,374,276,398,426,572,314,4 43,460,595,508,633,649,815,342,468,519,643,537,669,695,841,562,701,728,891,741,913,951,1133, 162,241,295,439,320,456,504,618,353,523,472,652,551,678,712,857,393,515,558,698,579,720,73 9,904,605,747,783,934,812,964,992,1187,435,569,599,736,636,762,800,957,663,803,839,980,862, 1018,1046,1231,706,853,898,1028,909,1048,1084,1266,945,1095,1124,1293,1151,1317,1357,1534, 217,289,325,512,368,534,544,709,412,555,582,733,608,760,770,955,448,586,615,765,646,798,83 2,984,675,834,855,1008,902,1040,1076,1253,480,627,666,810,681,836,869,1030,731,893,911,105 2,943,1093,1114,1291,768,928,960,1103,982,1144,1155,1313,1020,1171,1210,1347,1238,1376,143 4,1535,496,672,717,875,757,906,941,1099,780,947,968,1131,994,1153,1186,1337,827,986,1010,11 68,1050,1203,1234,1385,1068,1241,1271,1409,1301,1444,1464,1613,866,1032,1058,1215,1105,12 51,1276,1427,1150,1286,1315,1456,1348,1469,1514,1651,1184,1326,1359,1493,1373,1527,1546,1 681,1431,1556,1576,1675,1597,1704,1740,1841,256,358,379,576,417,589,621,795,421,624,655,81 7,687,859,878,1072,476,658,689,884,723,900,924,1074,744,922,953,1122,988,1148,1161,1312,488, 715,749,889,788,930,962,1146,807,976,996,1164,1016,1200,1222,1370,805,1012,1036,1198,1066, 1236,1256,1410,1109,1279,1302,1443,1325,1463,1497,1641,530,775,790,972,824,1004,1034,1189, 843,1044,1056,1233,1086,1265,1284,1440,949,1078,1107,1270,1135,1297,1323,1459,1175,1331,1 364,1490,1390,1526,1549,1670,1002,1127,1166,1310,1196,1345,1367,1515,1228,1380,1399,1533, 1435,1565,1584,1696,1273,1433,1446,1577,1460,1598,1570,1713,1504,1637,1652,1747,1658,178 2,1800,1859,548,820,829,1064,932,1091,1112,1278,974,1120,1137,1305,1173,1334,1362,1518,998, 1170,1195,1336,1214,1368,1393,1538,1243,1402,1425,1560,1457,1581,1611,1718,1070,1202,122 1,1391,1255,1418,1449,1572,1304,1450,1466,1609,1505,1594,1646,1749,1343,1484,1523,1638,15 40,1657,1672,1772,1566,1678,1677,1795,1714,1808,1821,1893,1126,1239,1281,1451,1333,1467,1 495,1620,1365,1516,1529,1653,1554,1661,1676,1780,1394,1544,1573,1671,1585,1680,1715,1809, 1619,1723,1736,1825,1760,1845,1857,1924,1441,1578,1606,1717,1645,1719,1755,1831,1650,175 1,1774,1852,1790,1867,1886,1944,1662,1783,1804,1873,1816,1889,1880,1951,1839,1902,1911,19 68,1928,1976,1986,2007,302,388,430,602,464,661,692,871,484,704,725,882,755,917,926,1139,49 2,752,773,915,793,1006,1022,1182,846,1026,1062,1229,1089,1258,1283,1454,500,785,822,1014,8 50,1060,1080,1248,873,1097,1116,1288,1142,1318,1340,1470,896,1129,1159,1329,1191,1361,137 7,1509,1205,1371,1403,1542,1407,1558,1580,1742,630,848,864,1087,887,1118,1140,1309,937,116 2,1177,1353,1209,1383,1400,1520,970,1180,1219,1374,1246,1406,1413,1550,1268,1415,1424,158 2,1483,1599,1632,1750,1000,1245,1261,1422,1296,1447,1453,1590,1321,1481,1500,1618,1531,16 42,1655,1775,1351,1512,1541,1656,1568,1669,1698,1791,1605,1702,1724,1810,1737,1828,1848,1 922,640,880,919,1157,966,1179,1212,1388,990,1224,1250,1416,1275,1430,1437,1586,1042,1263, 1294,1438,1320,1477,1494,1614,1350,1507,1530,1648,1552,1663,1687,1776,1082,1307,1339,149 8,1379,1525,1522,1665,1396,1545,1557,1682,1592,1699,1709,1812,1428,1569,1602,1706,1615,17 30,1738,1832,1636,1748,1765,1853,1794,1869,1887,1945,1111,1356,1382,1548,1412,1564,1593,1 703,1474,1603,1624,1734,1628,1741,1757,1844,1486,1625,1634,1754,1666,1763,1787,1866,1692, 1793,1803,1874,1820,1894,1905,1954,1508,1674,1685,1777,1711,1796,1807,1882,1725,1818,183 3,1901,1849,1912,1926,1971,1767,1835,1854,1915,1871,1930,1936,1983,1883,1941,1950,1989,19 61,1997,2006,2027,684,939,978,1226,1038,1260,1289,1462,1054,1299,1328,1480,1354,1502,1537, 1688,1101,1342,1387,1519,1405,1562,1553,1695,1419,1574,1596,1721,1622,1731,1744,1840,119 3,1397,1421,1561,1473,1589,1607,1735,1479,1623,1631,1746,1643,1759,1770,1861,1487,1639,16 60,1769,1691,1786,1801,1876,1707,1815,1819,1895,1834,1906,1918,1966,1207,1471,1476,1616,1 488,1627,1647,1762,1511,1667,1683,1781,1701,1797,1817,1891,1601,1690,1712,1802,1726,1826, 1836,1903,1761,1837,1855,1916,1872,1929,1935,1982,1629,1729,1753,1827,1768,1851,1863,192 1,1789,1868,1878,1934,1890,1942,1953,1992,1805,1884,1898,1949,1910,1956,1965,1999,1923,19 69,1975,2004,1980,2013,2015,2035,1217,1491,1501,1686,1588,1697,1708,1813,1610,1720,1732,1 829,1756,1843,1860,1919,1633,1743,1766,1846,1779,1864,1879,1932,1798,1888,1877,1939,1904, 1952,1960,1995,1693,1773,1785,1870,1811,1881,1897,1946,1824,1899,1909,1957,1917,1962,197 2,2003,1850,1913,1925,1967,1937,1977,1981,2011,1943,1988,1991,2017,1998,2020,2022,2032,17 27,1788,1823,1900,1842,1908,1914,1963,1858,1927,1931,1974,1940,1978,1990,2014,1862,1938,1 947,1987,1959,1993,1994,2021,1970,2000,2002,2023,2009,2028,2030,2040,1892,1955,1958,1996, 1973,2001,2005,2025,1979,2010,2012,2029,2018,2031,2036,2042,1985,2016,2019,2033,2024,203 4,2037,2043,2026,2038,2039,2044,2041,2045,2046,2047]
›APPENDIX · 15 of 21
Sequence Group 3: Q3_4096
[0,1,2,4,8,16,32,3,5,64,1024,2048,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,5 12,11,40,68,130,19,13,48,14,72,257,1025,21,132,35,258,26,2049,513,80,37,25,22,136,260,264,38, 514,96,67,41,144,28,69,42,516,49,1026,74,272,160,520,288,528,192,544,70,44,131,81,2050,50,73, 15,320,133,52,1028,23,134,384,76,137,82,56,27,97,39,259,84,138,145,261,1032,29,43,2052,98,51 5,88,140,30,146,71,262,265,161,576,45,1040,100,640,51,148,46,75,266,273,517,2056,104,162,53, 193,1056,152,77,164,768,268,274,518,54,83,57,521,1027,112,135,2064,78,289,194,85,276,522,58, 168,1029,139,99,86,60,280,89,290,529,2080,524,196,1088,141,101,147,176,142,530,321,31,200,1 033,90,545,292,2051,322,532,263,149,102,105,1030,304,296,163,92,47,267,385,546,2053,324,104 1,208,386,150,153,165,106,55,1034,328,536,577,548,2112,113,154,79,269,1042,108,578,224,166, 519,552,195,1152,270,3072,641,523,275,580,291,59,1036,169,560,114,277,156,2057,87,197,1057, 116,170,61,531,525,642,281,1089,278,526,2054,177,293,388,91,1044,584,769,198,172,120,201,20 65,336,1280,62,282,143,103,178,294,1058,93,644,2058,202,592,323,1048,392,297,770,107,180,15 1,1060,2066,209,284,648,94,204,298,1031,400,608,352,2176,325,533,1153,155,210,305,547,300,1 090,109,2060,184,534,537,115,167,1536,225,326,306,772,2081,157,1035,656,329,110,117,212,106 4,171,2113,776,330,226,549,1092,538,387,308,216,2068,1154,416,271,279,158,337,1043,550,672, 2304,118,332,579,1037,540,389,173,121,1072,2082,553,199,784,179,1038,228,338,312,2072,704, 390,1096,174,554,581,393,1281,283,2084,122,448,353,1045,561,203,63,340,2055,1156,394,527,5 82,556,181,1059,2177,295,285,232,124,1282,205,182,643,2114,562,1050,286,585,299,1537,354,2 11,2560,401,185,1104,396,344,586,645,2059,1061,593,535,240,206,1049,95,2088,327,564,1046,8 00,402,356,307,2116,1160,301,417,213,568,1284,832,2178,588,186,1288,646,404,227,896,2067,1 062,594,418,302,1538,649,771,2061,360,539,1120,111,331,214,1091,2096,309,188,449,1065,217,4 08,2062,609,596,1168,551,650,229,1052,2120,159,420,310,1093,541,773,2305,610,1066,657,333, 119,1540,3073,600,339,218,1073,368,652,230,2069,1098,391,313,450,1296,542,2180,334,233,118 4,555,774,175,2083,1544,123,658,612,1312,2306,341,777,220,1552,314,424,2074,395,1216,673,5 83,355,1568,2561,287,183,234,1094,125,557,2128,660,1068,616,342,316,2085,1155,241,778,1105, 563,345,2073,452,1074,397,403,207,2070,1097,674,558,1039,785,432,2184,357,1344,187,236,66 4,2308,1157,624,587,1076,780,2312,705,126,1047,242,565,1158,2086,398,346,456,1408,358,2562, 405,1100,303,569,244,2144,1161,595,189,1106,566,2115,676,361,1080,706,589,2089,1051,215,78 6,647,1121,2192,348,419,1063,406,464,2076,680,1283,801,362,1108,2117,590,409,1162,570,2090, 788,597,1169,572,219,2564,1285,311,708,1053,598,2097,601,1067,651,421,3074,792,1122,802,61 1,1539,2122,602,410,1112,231,688,2320,1164,653,248,1054,2208,369,190,364,1170,654,2568,659, 1095,335,480,2336,1286,315,221,1289,2576,370,613,1185,422,425,2240,1600,451,614,1069,2592, 543,235,1124,412,2118,343,372,1664,775,317,2092,1075,222,426,1172,2179,453,237,1070,559,21 29,833,1099,804,712,2098,1290,834,661,1297,2121,808,779,1541,617,1128,2063,604,433,1186,72 0,2368,816,1077,836,347,2181,1217,897,243,1176,2100,662,454,1101,318,3076,675,1188,618,898, 2071,1792,781,376,2182,1292,428,1298,665,2432,736,1542,567,840,2124,1078,625,238,1107,218 5,359,457,1081,399,2130,787,1545,591,1136,2104,678,434,1159,2075,677,349,1102,245,2145,458, 1313,666,1218,2087,620,363,1109,2307,127,191,1300,782,2132,1546,407,436,1082,2186,626,571, 1192,2193,465,1163,681,246,2309,1123,707,350,3080,1110,599,1084,668,2077,790,1304,460,2091, 249,1113,682,1314,2146,573,411,1553,2563,803,789,1548,709,2136,1220,365,440,2188,1165,628, 1125,689,2078,374,1171,423,2194,466,1200,793,2119,1166,250,371,1554,2310,481,1345,574,2313, 413,1055,603,2209,1224,366,468,1114,2624,655,1569,900,2093,805,1316,615,3088,1346,684,710, 2148,1556,429,1287,2688,794,252,1173,373,2099,1126,605,848,2196,1129,690,1328,2094,713,13 20,632,2123,482,1187,806,2314,1116,427,904,2321,1071,414,1291,2565,223,663,1409,2152,692,1 570,835,2210,1348,619,472,2101,1232,455,1410,2241,796,809,1174,3104,714,1177,721,2200,1189, 837,716,2125,1130,864,1079,2212,810,1352,606,2816,912,1560,722,2316,1601,696,1572,2322,37 7,435,1137,2566,817,1178,319,2102,1103,621,1293,2131,812,484,1132,2105,430,1602,838,2569,1 248,667,3075,488,1190,239,2160,1543,378,1576,2183,459,1219,622,2126,627,1294,437,2337,166 5,380,2242,1547,818,1299,2133,461,496,1604,2324,669,1315,2570,679,1083,724,2106,1193,841,6 29,2216,1584,351,1138,3077,467,1301,2187,438,1180,737,2147,1111,251,1221,2134,462,442,2108, 1140,441,1194,2328,469,1085,2137,247,1555,683,2338,1549,842,1666,2577,738,899,2572,1305,6 70,1302,2244,783,1550,3136,849,1201,820,2189,1317,728,2149,1412,928,1115,2195,791,367,222 4,1608,901,1793,2190,630,1222,2578,685,1196,844,2369,1144,633,2079,1225,711,1360,2248,253, 1086,3081,691,1306,824,2138,1167,902,2593,1127,686,740,2340,1202,850,2370,1318,375,2580,11 17,444,1668,2311,470,1226,2197,483,1616,415,2150,1347,485,2153,1416,905,3078,1321,795,179 4,2352,473,1131,2344,634,1204,2211,744,1175,852,2140,1233,960,2095,1308,865,2315,1672,693, 2433,1118,797,1228,2594,906,1322,2372,715,1424,3089,807,1632,474,2256,1376,636,2434,1349, 694,2198,1557,254,2201,1179,717,2213,1234,575,1329,2154,913,1571,2103,798,1324,3082,811,11 33,2376,379,1208,2584,697,1558,431,2625,607,489,2596,1561,866,2161,1139,723,2202,1191,486, 2127,1249,908,2317,1350,718,1330,3090,813,1796,2156,476,1181,2626,856,1680,2272,839,1353, 2214,725,1134,2567,698,1141,2600,914,1236,2243,752,1195,3200,868,1800,2318,819,1354,2689,8 14,1250,439,2571,1573,929,2323,1562,490,2628,1411,623,2339,1332,671,2107,1240,739,3084,14 40,916,2217,1295,463,2608,1303,843,2162,1182,381,2325,1361,497,2204,1574,930,2135,1696,82 1,2245,1142,726,3105,1356,1603,2164,961,2218,1564,872,2109,1413,492,2579,1197,631,2573,114 5,729,2690,1577,700,2329,1223,443,3137,1808,741,2326,1203,845,2574,1252,920,2225,1362,382, 2341,1336,822,2436,1728,2139,1414,851,3092,1198,730,2632,1578,498,2817,1605,880,2246,1417, 742,2220,1307,445,2168,1146,2249,471,1472,2384,1377,635,3328,1585,932,2110,1227,687,2330, 1087,903,2191,1364,2151,825,1418,2226,500,1551,2342,1606,846,3106,1580,745,2141,1205,2692, 826,1319,2250,732,1309,2640,446,1256,2371,1148,3096,962,1229,2440,936,1206,2345,475,1667, 2818,853,2155,1586,867,2228,1310,1609,2199,637,1323,3108,907,2257,1378,487,2332,1235,695, 2696,1425,2142,1209,746,2252,1420,828,2346,1368,3079,753,1610,2448,854,1669,2656,1617,240 0,857,1559,2373,504,1264,2581,799,3201,1230,1119,2203,255,1351,2258,964,2353,1588,909,259 5,1824,719,2348,1426,3138,1380,477,2157,1331,915,2232,1325,2582,638,1441,2585,1237,2163,7 48,1592,2215,944,1856,3584,869,2273,1612,1210,2374,491,2354,1670,699,2820,1428,1251,2205, 754,3083,1920,858,2704,1618,2377,478,1442,2158,1326,968,2165,1673,2260,383,1795,3112,910, 2219,1384,1563,2824,815,2378,1135,976,2274,1355,2597,1238,870,3140,1333,2586,917,1212,243 5,1473,2356,727,1241,2264,493,3202,1432,873,2464,1633,2319,1620,701,2327,1575,2206,931,16 74,2385,1253,3091,756,1183,2598,860,2720,1444,1334,2166,499,2380,1565,731,2627,1797,3085, 1634,823,2588,1681,2437,922,1357,2221,1143,2169,874,1624,3120,918,2601,1363,2247,1242,502, 2832,1392,2227,933,1676,3086,1254,2276,743,1415,2386,1337,2360,760,2752,1474,881,2438,15 66,3144,1358,494,2222,1257,2602,702,2629,1579,1798,2441,921,3329,1199,501,2331,1147,2170, 1682,2496,876,1636,2401,1365,3093,847,1801,2609,992,2251,1244,2111,1338,447,2388,1448,320 4,1419,2442,733,1697,2575,827,2630,1607,2604,1379,934,2229,1311,3107,1207,2343,882,1258,2 333,937,2280,1149,2172,1581,963,3330,1684,2253,1640,2230,747,1366,2691,505,2610,1340,3098, 1265,855,2334,1802,2633,1587,2347,924,3585,1369,734,2402,1476,2259,1421,2449,829,1427,22 33,1231,3152,965,2444,1698,2392,1582,938,2634,1809,2693,1456,3109,884,1381,2641,506,2583, 1211,2288,1260,2254,749,1688,3097,1648,2143,945,2375,1611,2612,1804,966,3094,1729,2848,11 50,2450,755,2404,1266,859,2355,1589,3208,1422,2349,940,2465,1370,2261,1480,830,2616,1382, 3332,1429,2880,911,2636,1327,1593,2234,871,3336,1268,2694,1619,2452,639,2275,1213,1590,29 44,888,3110,1700,2642,1385,2466,479,2350,1730,3586,1613,946,2697,1239,2819,750,2408,1810, 2587,1671,3168,969,2159,1372,1443,2379,508,2262,1430,3139,1488,2357,861,2236,1704,2497,18 25,757,3113,1386,2265,1614,2456,970,2657,1433,2644,1594,3216,919,2599,1812,1621,2698,1596, 2277,875,3100,1243,2207,1335,2468,862,2358,1732,3141,1622,2589,758,1625,2821,1675,2658,9 48,3114,1445,2705,1816,2381,977,2167,1826,3588,1635,2648,923,2387,1626,2266,1434,972,3121, 1255,2416,1712,2700,761,2278,1677,3146,1272,2439,877,2361,1393,2498,1214,3344,1388,2590, 952,2382,1678,2281,1683,495,3232,1359,2603,1504,2822,703,2223,1339,3592,1245,2171,935,270 6,1394,2660,1637,3360,978,2389,1446,2825,1449,2268,1475,3600,883,2362,1638,2472,1567,2443, 762,3264,1259,2721,1436,2631,503,2403,1367,3616,1396,2335,925,2231,1799,2282,1341,3142,1 246,2173,878,2605,1450,2708,1477,3116,735,2664,1261,2390,1583,2364,1857,3203,993,2289,182 8,2826,1736,3153,885,2611,1858,2393,1685,2500,939,3122,1832,2445,1803,2451,1641,2255,994, 3145,1628,2722,1457,2606,980,3087,1744,2833,1840,2480,1860,2405,926,3392,1371,2235,1921,2 284,764,2712,1267,3205,1686,2672,1478,2635,941,3124,1342,2828,1699,2753,967,2174,1642,309 5,1922,2290,1805,2613,886,1400,1452,3206,831,2446,1689,2394,1760,2504,1591,3456,947,2406, 1864,2453,1649,3148,507,2351,1262,2617,1383,2292,1481,3209,889,2643,1423,2237,1811,3154,1 615,2614,984,2724,1702,2409,1458,3128,751,2754,1701,2637,1373,3099,1269,2263,942,2834,148 2,2695,1690,3169,1644,2396,996,2467,1387,3111,1151,2454,1215,2512,971,2728,1806,3331,1431, 2849,890,2410,1460,3156,1650,2638,1595,2457,509,3210,1489,2618,1705,2836,1270,2645,949,32 17,1731,2620,1374,2267,1623,3333,973,2359,1692,2756,1814,3101,1484,2646,1000,2649,1273,31 15,1706,2699,1597,2469,892,2840,1435,3170,1827,2850,1813,2659,950,3587,1733,2650,1389,245 8,1464,3160,863,2279,2736,1652,3212,1713,2701,1398,2296,759,3102,1447,2417,1490,2238,1817, 2412,1008,3218,1274,2702,1395,2707,1505,3143,510,2383,1598,2528,3334,1437,2363,1627,2269, 979,3337,1390,2418,1492,2661,1679,3233,953,2470,1924,2473,1829,3648,1639,2499,2662,763,3 117,1708,2591,1734,2283,1453,3172,974,2460,1818,2391,1276,2420,1397,3712,2823,1629,2365,9 54,3123,1872,2270,1714,2474,1737,3220,879,2501,1656,2285,3118,1506,2607,1830,2881,981,314 7,1451,2852,1928,2760,1438,3338,2882,982,2709,1247,3345,1687,2856,1716,2827,1859,3589,927, 2665,3176,1643,2652,1496,2481,1479,3234,995,2768,1820,2864,1833,3125,2884,1738,2395,1745, 3265,765,2945,1861,2291,3224,1740,2710,1888,2502,956,3149,1834,2366,1630,2723,3236,1936, 2666,1746,2946,887,3840,1720,2829,1401,2424,3340,1459,2476,1841,3346,985,2713,1343,2784,3 590,1645,2615,1836,2888,997,3126,1508,2673,2286,1454,3155,1862,2407,1691,2505,986,3129,24 47,1512,2835,1263,3593,1402,2639,3184,1483,2726,943,2482,1646,3207,1651,2725,2397,1461,31 50,1404,2293,891,2506,3361,1842,2714,1485,3266,1520,2668,1693,2411,3157,998,2175,1703,223 9,1748,3348,2830,1865,3594,766,2455,1653,2484,3130,1375,2674,1491,2619,1462,3240,2513,511, 3211,1761,2729,1275,2294,3171,1486,2755,1466,2398,1465,3158,2647,988,3132,1493,2716,1271, 2838,3352,1707,2508,1866,2297,3161,1001,2730,1762,3362,1923,2621,2459,1694,3601,1807,285 1,951,2837,3596,1873,2757,1844,3268,2413,1752,2488,1952,3213,1002,2676,3173,1815,2737,139 1,2422,3219,1925,2471,1654,2514,1709,3248,2841,893,3214,1868,2298,2419,1657,3602,1735,252 9,3393,1277,2622,975,2461,1715,3103,2651,1848,3272,1926,2414,2516,1710,3162,894,2703,3617, 1764,2948,1874,2853,3364,1399,2663,1468,3394,2732,1494,2758,1009,3604,2477,1507,3335,143 9,2842,2300,1509,3221,1929,2421,3174,1819,2653,955,2896,3177,1497,2738,1658,3376,2761,176 8,3368,1876,2680,2530,1984,3235,1004,2854,3164,1889,2475,1717,2952,3119,1821,2462,1930,33 39,2271,1010,2711,1739,3457,2740,1831,3618,2883,1498,3396,1660,2667,2520,1718,3280,957,25 03,3458,1278,2844,1741,2857,3222,1599,2762,3225,1937,2769,1822,3237,2885,983,2764,1835,31 78,2912,1403,3127,2858,1721,3400,1455,2654,2960,1631,3608,1513,2770,3649,958,2744,3620,18 90,2425,1747,2483,3185,1510,2865,3226,1932,2367,1742,3151,2669,987,3341,2860,1837,2532,15 00,3180,2478,1880,3650,2886,1863,3296,1749,2715,2536,1012,3238,2287,1722,3591,1938,2426,3 624,1776,2507,3267,1892,2670,1843,2675,3342,1838,2485,3713,999,2428,1463,3595,2866,1953,3 347,2509,1514,2544,3652,1647,2717,1695,3363,2727,1763,3131,2772,1016,3241,2889,1940,2677, 1487,3632,2399,1867,3186,2515,1405,3349,2486,1521,3228,2785,767,3159,1954,2299,3269,1845, 2510,2490,1750,3188,2489,1985,3242,1896,2517,3133,1516,2295,3603,1655,2731,3597,989,2890, 3714,1753,2786,2947,1724,3353,1467,2718,3350,1765,2831,3598,1869,2897,3249,1944,2868,336 5,1003,2776,3460,1406,2976,3163,1846,2839,1875,2415,3656,1754,2949,3841,1522,2678,3270,19 04,2733,3244,990,2892,3192,1766,2681,3273,1469,2759,3408,1495,2301,3134,1659,2739,3354,19 56,2872,3215,1711,2950,3175,1927,2734,1005,2788,3250,1849,2898,3366,1524,2423,3165,1870,2 492,3716,1769,2518,3274,1850,2531,3664,1756,2463,3395,1470,2533,3464,959,2953,3369,1986,2 843,3842,1960,2521,3179,1499,2682,3252,1877,2792,3223,1891,2900,3281,3008,1661,3356,2913, 1931,3720,2741,1011,3166,2845,1511,3276,2954,1719,3370,2763,1770,3472,2855,1852,3680,252 2,1777,3424,2684,1878,3397,2742,1881,3605,2302,1013,3227,2765,1528,3282,2623,3377,1823,29 61,3619,1279,2846,3372,1988,2859,3181,1933,2427,3256,1743,2745,3606,1501,2479,2655,2537,1 939,3609,2914,895,3187,2771,1662,3239,2534,1772,3297,2956,1968,3398,2766,3378,1893,2861,3 844,1515,2524,3229,1723,2904,3728,1778,2887,3401,1882,2773,3182,2746,1006,3189,2962,1502, 3284,2800,1992,3243,2916,3848,1407,2867,3402,1934,2862,3298,1839,2487,3621,2000,2977,361 0,2538,1894,3459,2671,1941,3380,2719,1014,3288,2787,3488,1751,2964,3343,1517,2511,3351,28 91,1897,3230,2429,1725,3409,2545,1955,3622,2978,3744,1780,2869,3190,1884,2774,3404,1523,3 651,3009,3612,1755,2920,3461,1017,2540,3245,2679,1847,3193,2777,1946,3625,2748,3271,1898, 2491,3856,1942,2789,3251,2893,1526,3300,2968,1957,3410,2430,3384,1767,2870,3776,1784,346 2,2899,3246,1905,2778,3626,1018,2546,3653,2928,1518,3465,2790,1726,3355,2493,3194,1945,25 19,3520,1525,3425,2683,3633,1900,2980,3275,2735,1871,3135,2951,2016,3412,2873,3466,1471,2 548,3599,1757,3654,2894,3628,1851,2793,3253,2874,991,3367,2780,1958,3357,2494,3304,1906,3 196,3010,3277,1961,2984,3254,2523,1987,3715,2901,1771,3634,2915,3358,1529,3657,2685,3371, 1879,2955,3426,2535,1948,3283,2743,1758,3473,3257,2794,1853,3468,2876,3416,1020,2801,365 8,2902,1989,3717,3665,1962,2905,3607,2552,1908,3312,2847,3278,1530,3167,2303,3399,1773,30 12,3636,2957,1969,3872,2767,3474,1990,3428,2525,3379,1779,2963,3373,2686,1883,3489,3285,2 796,1964,3640,2992,3904,1854,2917,3660,3258,1935,2539,3718,2747,1007,3476,3299,2802,1895, 3968,2906,3666,1663,2526,3490,3374,1912,3016,3721,2431,1503,3843,2958,3432,1970,3611,286 3,3183,1774,3024,3403,3286,1993,2918,3381,2965,1532,3260,3521,2775,1885,3289,2541,3480,17 81,2921,3681,3668,1994,2749,3623,2979,3722,1943,3301,2804,3231,1015,2908,3492,3382,1899,2 547,3613,2779,1886,3845,3682,2871,3729,1782,2970,3405,3191,1972,2922,3672,2966,2001,3411, 3290,2550,1947,3440,2981,3724,3302,1996,2791,3463,3385,1785,2808,3522,2929,1901,3614,340 6,2542,3305,1976,2750,3627,3846,1519,2969,3247,2549,3195,1727,3730,2924,3684,1959,3413,28 95,3849,3040,2002,3292,3386,2495,1019,3496,3467,2781,3745,1907,2875,3655,3427,1786,2982,3 359,3255,2930,1527,3306,2985,3197,1949,3629,3011,3732,3688,1902,2795,3414,2553,3388,1759, 3313,2903,3850,2017,3635,2972,3417,2782,1909,3524,3469,2877,3475,1963,3279,3013,3746,201 8,3630,2986,3857,3504,2004,2932,3429,2554,3259,1950,3308,2797,3736,3696,1788,2993,3659,38 52,3014,1965,3777,3198,2803,3314,1991,2907,3637,3470,2988,1021,3418,3528,2878,1910,3430,3 477,2959,3375,1855,3641,2919,3316,3667,1971,2687,3261,3638,2936,1531,3748,3433,2527,3778, 1913,3661,2994,3287,2798,3858,2008,3719,3017,3420,3491,1775,2556,3478,3536,2909,1966,375 2,3873,2805,3434,2020,3662,3018,3481,3642,1995,2967,3860,3669,3644,2923,1914,3291,3383,29 10,3780,1533,3670,2806,3673,3723,1973,2996,3493,3864,3025,3874,1997,3683,2971,3674,3482,2 024,3020,3303,3760,2809,1916,3725,3320,2925,3441,3262,1974,3436,3000,3726,3731,1887,2543, 3407,3552,2751,3387,1783,3293,2983,3442,3685,3026,1022,3494,3497,3523,2931,2032,3686,361 5,2810,3307,3484,1534,2551,3415,3444,2973,3847,2003,3389,3294,2926,3498,3525,1977,2783,33 09,3631,3905,1787,3041,3876,3784,2933,3906,1998,3733,2987,3880,3851,3689,1978,3042,3676,3 505,3028,3792,1903,3888,3908,2974,3419,3969,2005,2812,3315,3734,3526,2989,2006,3390,3747, 3015,3690,3970,1951,3853,2934,3448,3500,2879,3737,2019,3808,3639,2995,3912,3697,1789,255 5,3310,3431,3529,2937,1980,3471,3859,3663,3032,3750,3506,1911,2799,3749,3421,3317,2990,20 09,3530,3738,3692,3044,3435,3199,2021,3263,3019,3854,3479,2938,2010,3508,3698,3643,2557,3 537,3753,1967,3318,2997,3779,3422,3671,3021,1915,3740,3862,3532,3048,3321,3754,2022,3645, 2940,3483,3875,3861,1790,2998,3781,3437,3512,2911,3700,1535,3761,3446,2807,3495,3538,386 5,3056,1023,3322,3443,3553,2558,3646,3485,2012,3675,3027,3438,3540,3727,3001,2025,3972,38 77,3687,2811,3756,3782,1975,3501,3022,3866,3324,3445,3677,3002,2026,3920,3762,3785,2927,3 704,3554,1917,3878,3029,3499,3976,3486,3030,3295,1999,3735,3764,3907,2975,3691,3544,3527, 1918,3043,3868,3881,3786,3793,2813,3909,2033,3788,3936,3004,3882,3678,3984,3794,1979,293 5,3768,3449,3507,3889,3033,3391,2028,3693,3884,3045,3556,3502,3910,3739,2034,3034,3560,33 11,3450,3531,2991,3694,1981,3699,3509,3452,2939,3890,3533,3568,3741,2007,3046,3751,3796,3 913,2814,3701,3423,3539,1982,3510,2559,3809,3323,3534,3514,3513,2011,3036,3541,3319,3755, 3914,3049,3810,3971,3742,2036,3855,2999,3921,3892,3800,4000,3050,3863,2023,3439,3973,370 2,3757,2941,3916,3705,3783,2040,3325,3023,3763,3896,3974,3758,2942,3812,3922,1791,3447,35 16,3542,3057,3555,3487,3557,3977,3867,2013,3003,3545,3706,3816,3924,4032,3052,3937,3765,2 027,3869,3978,3058,3787,3879,3546,3708,3766,3005,2014,3326,3789,3647,3985,3870,3031,3883, 3451,3769,3503,2029,3679,3561,3006,3938,3795,3558,3980,3790,3035,3885,1983,3548,3928,391 1,3797,3060,3770,3986,3824,3940,3891,2035,3886,3047,3511,4001,3562,3695,3743,3811,3064,39 88,3535,2037,3915,3453,3569,2815,4002,3893,3798,4033,3944,3564,3703,1919,3037,3801,3772,3 515,3813,3917,3992,3051,3454,3894,3923,3802,2030,3570,3952,3038,3814,3517,3543,3707,4004, 3759,3975,3053,3897,2038,3572,3918,3817,3898,3804,3518,3007,4034,4008,3547,3925,3939,204 1,3709,3979,3059,3559,3767,3818,3900,3825,3926,3929,3061,3576,3871,3327,2042,4036,3981,37 91,3549,3987,2943,3710,3820,4016,3941,3563,3771,3826,3930,2015,3054,3550,4040,3455,3982,3 887,4048,3942,3989,3062,3799,3565,3945,3773,4003,2044,3828,3932,3571,3803,3065,3895,3994, 3946,3990,3574,4005,3815,3832,3953,3066,3566,2031,3774,3993,3573,3948,3919,4064,3519,380 5,3899,3039,4006,3954,4009,4035,3819,3577,3927,2039,3996,3806,3901,3068,4037,4010,3956,35 78,3821,4017,4038,3827,3931,4012,3902,3983,3055,3943,3711,3960,2043,3551,4018,3822,4041,3 580,3933,3829,4042,3991,3063,3947,3934,3830,4020,4049,3995,4044,3833,3949,4024,3567,2045, 3775,4007,4050,3067,3955,3834,3575,3997,3950,3807,4065,3957,4011,4066,4052,3998,3836,401 3,4039,3069,3958,3903,4019,3579,3961,2046,4056,3823,4014,4068,4043,3962,3581,4021,4045,40 72,3964,4022,3935,3831,3070,4080,3582,4051,4025,3835,4046,4026,3951,4053,4054,3999,4067,3 837,4028,3959,4057,4069,2047,4058,4015,3963,4070,3838,3583,3071,4060,4073,4023,4074,3965, 4047,3966,4081,4027,4076,4082,4029,4055,4030,4059,4084,4071,4088,3839,4061,4075,4062,407 7,4031,4083,4085,3967,4078,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095]
›APPENDIX · 16 of 21
Sequence Group 3: Z3_4096
[0,1,2,7,3,8,13,26,4,12,15,30,18,35,37,82,5,14,16,34,21,41,51,87,24,50,45,94,61,103,11 0,177,6,19,23,43,25,49,55,96,31,59,63,104,76,117,123,195,36,65,80,121,85,131,141,208,93,143,15 5,235,161,248,271,391,9,20,28,58,32,62,75,112,38,81,67,124,90,135,149,217,48,78,92,142,98,152, 160,243,108,163,180,260,194,278,296,434,57,95,106,159,119,171,188,274,129,189,207,288,220,3 13,330,471,146,215,239,318,246,331,356,502,266,363,385,528,405,551,593,816,17,27,33,77,42,84, 88,147,52,91,99,158,109,170,174,273,60,100,111,172,122,187,204,290,134,205,216,307,241,326, 350,491,69,115,130,193,136,206,223,319,156,237,247,334,265,362,378,525,173,257,275,369,289, 399,408,548,315,421,453,582,477,613,681,817,73,132,151,226,168,244,264,367,178,267,281,390, 297,407,432,571,202,293,308,418,332,447,473,624,344,480,507,650,535,693,719,942,222,321,338, 457,371,488,511,672,404,521,549,708,583,724,785,1011,431,561,595,756,609,805,833,1072,677, 848,880,1059,914,1122,1203,1479,22,39,44,97,53,101,113,186,54,114,125,196,138,218,228,348,68, 126,139,232,153,240,254,349,162,252,272,383,294,403,413,547,71,150,164,234,182,258,276,402, 192,286,298,415,311,445,463,607,191,309,323,442,343,476,493,653,373,515,537,692,558,716,762, 992,83,176,184,283,200,304,322,436,210,329,337,472,357,501,520,688,269,351,372,506,392,533, 557,712,424,565,600,752,629,803,837,1048,302,387,417,544,441,580,603,788,468,618,638,813,68 2,863,893,1102,509,680,696,881,713,916,871,1140,771,986,1014,1221,1026,1306,1353,1539,89,1 97,203,342,259,361,376,514,285,381,395,540,423,569,599,791,300,420,440,570,456,605,632,822, 481,642,670,854,710,888,939,1151,347,446,462,630,492,661,699,873,538,700,720,935,774,910,10 02,1226,578,745,799,987,823,1023,1054,1279,864,1066,1063,1341,1143,1376,1417,1670,386,478, 516,703,567,723,760,955,601,789,807,1017,846,1032,1062,1300,633,830,875,1051,894,1069,1146, 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636,3827,1526,2023,2043,2436,2217,2463,2489,2771,2264,2519,2549,2819,2612,2862,2917,3130, 2315,2578,2638,2872,2674,2930,2981,3183,2727,3013,2974,3212,3072,3270,3308,3497,2453,265 7,2690,2950,2765,2988,3045,3243,2803,3053,3090,3294,3122,3318,3368,3549,2884,3106,3154,33 42,3204,3394,3416,3605,3230,3456,3473,3652,3516,3676,3694,3792,2537,2699,2800,3057,2859,3 087,3110,3323,2910,3162,3178,3378,3217,3400,3467,3628,2923,3208,3248,3450,3303,3485,3491, 3685,3358,3529,3542,3702,3591,3750,3770,3896,3027,3284,3298,3504,3373,3536,3563,3721,340 5,3598,3613,3760,3660,3781,3840,3929,3438,3644,3668,3803,3712,3815,3853,3947,3730,3866,38 81,3968,3912,3990,4016,4049,11,46,79,183,105,199,256,393,128,242,280,427,314,467,482,743,14 8,268,292,459,345,512,572,768,374,566,539,801,634,843,870,1117,166,325,365,526,384,559,598, 811,435,622,645,847,717,900,925,1175,475,657,732,917,758,953,993,1214,797,1001,1042,1292,1 064,1327,1388,1668,214,335,410,616,443,640,711,878,490,737,668,929,782,969,1020,1239,553,7 27,792,997,820,1031,1061,1313,861,1071,1128,1359,1172,1408,1451,1756,610,806,852,1057,908, 1096,1152,1396,945,1155,1211,1432,1249,1494,1533,1826,1012,1233,1304,1504,1322,1536,1591, 1884,1377,1608,1654,1930,1696,1970,2040,2386,303,401,451,722,519,753,772,1016,579,787,825, 1053,865,1093,1107,1394,628,829,874,1100,921,1148,1201,1438,965,1204,1236,1478,1310,1523,1 578,1863,679,891,949,1168,973,1207,1258,1507,1046,1298,1324,1543,1374,1606,1640,1926,1103, 1351,1399,1620,1435,1685,1703,1964,1497,1729,1792,2022,1837,2076,2187,2388,701,957,1027, 1267,1086,1316,1371,1615,1121,1379,1413,1666,1454,1701,1751,2004,1195,1443,1481,1724,153 8,1780,1831,2094,1566,1844,1892,2138,1942,2206,2246,2551,1255,1512,1551,1800,1625,1859,19 01,2174,1694,1917,1966,2229,2024,2254,2343,2635,1749,1986,2044,2302,2070,2372,2411,2705,2 181,2430,2473,2691,2516,2760,2845,3100,355,497,532,815,585,834,883,1145,591,887,933,1178,9 81,1242,1273,1573,674,937,985,1283,1035,1307,1345,1576,1068,1339,1391,1652,1446,1692,1713, 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2789,2621,2795,2880,3071,2632,2871,2926,3131,2968,3172,3228,3422,2661,2949,3003,3192,303 2,3237,3211,3445,3093,3278,3306,3511,3364,3546,3588,3696,419,546,604,856,651,941,989,1261, 685,1005,1038,1280,1082,1333,1348,1678,695,1079,1110,1330,1141,1473,1499,1747,1223,1502,1 558,1822,1601,1871,1913,2227,706,1131,1185,1486,1230,1553,1586,1854,1264,1613,1642,1922,1 682,1972,2010,2257,1301,1664,1708,1992,1760,2046,2080,2336,1783,2068,2128,2402,2136,2437, 2481,2851,896,1227,1252,1596,1286,1644,1680,1956,1365,1715,1738,2032,1789,2090,2122,2358, 1416,1745,1807,2074,1850,2132,2148,2419,1888,2150,2168,2486,2283,2523,2594,2870,1465,184 8,1876,2164,1934,2212,2223,2503,1978,2280,2316,2563,2381,2616,2645,2929,2030,2342,2400,26 47,2456,2675,2745,2970,2535,2754,2807,3018,2839,3066,3117,3343,912,1276,1336,1706,1410,17 40,1796,2098,1449,1816,1857,2154,1899,2179,2193,2495,1528,1880,1932,2195,1974,2270,2305,2 553,2026,2331,2377,2631,2423,2664,2719,2932,1588,1954,2008,2313,2082,2367,2361,2667,2112, 2409,2433,2708,2506,2748,2772,3023,2175,2459,2528,2763,2556,2821,2842,3074,2602,2866,290 3,3133,2976,3179,3231,3425,1632,2038,2088,2414,2144,2447,2508,2757,2265,2531,2576,2830,25 84,2848,2886,3108,2289,2579,2599,2877,2670,2901,2958,3169,2731,2973,3000,3194,3044,3255,3 288,3457,2333,2687,2714,2935,2774,2982,3008,3218,2810,3039,3078,3276,3121,3310,3356,3524, 2909,3084,3137,3321,3185,3371,3391,3579,3222,3409,3441,3602,3486,3642,3690,3819,977,1368, 1430,1818,1520,1874,1924,2240,1546,1940,1988,2276,2036,2322,2391,2722,1618,2014,2096,235 4,2130,2444,2425,2737,2158,2469,2515,2801,2571,2824,2857,3096,1765,2116,2162,2442,2263,25 00,2540,2833,2274,2573,2590,2860,2619,2889,2918,3156,2291,2610,2656,2915,2728,2955,2993,3 198,2766,3029,3041,3258,3081,3292,3331,3502,1787,2259,2268,2559,2294,2582,2627,2898,2338, 2673,2711,2943,2751,2984,3036,3245,2525,2725,2777,2997,2813,3059,3086,3282,2895,3091,314 0,3324,3188,3367,3387,3574,2587,2818,2874,3062,2912,3127,3163,3339,2965,3175,3205,3383,32 41,3413,3453,3617,3005,3224,3265,3437,3304,3465,3499,3653,3346,3515,3541,3680,3565,3726,3 737,3887,1803,2300,2318,2715,2498,2742,2769,3026,2545,2798,2827,3069,2883,3105,3152,3335, 2595,2854,2906,3115,2938,3165,3207,3379,2987,3235,3201,3402,3286,3448,3482,3632,2734,292 4,2952,3181,3021,3214,3262,3429,3054,3268,3300,3469,3327,3490,3528,3674,3124,3314,3354,35 07,3395,3551,3570,3714,3418,3597,3612,3751,3647,3769,3784,3860,2815,2962,3051,3272,3103,3 296,3317,3494,3147,3360,3375,3538,3406,3555,3607,3732,3159,3398,3432,3593,3477,3622,3626, 3776,3520,3658,3669,3790,3703,3828,3843,3939,3247,3462,3474,3637,3533,3663,3686,3805,356 0,3708,3719,3835,3757,3851,3897,3964,3583,3744,3763,3869,3797,3877,3906,3978,3812,3917,39 27,3994,3951,4010,4031,4056,229,504,662,1008,763,1050,1158,1459,838,1124,1217,1525,1295,1 598,1623,2012,904,1191,1246,1583,1362,1661,1763,2042,1421,1754,1710,2092,1861,2146,2183,2 485,961,1319,1405,1687,1441,1742,1805,2106,1541,1842,1878,2152,1976,2225,2255,2546,1611,1 895,1998,2244,2034,2293,2340,2589,2086,2351,2398,2669,2421,2703,2761,3025,1089,1342,1491, 1833,1556,1869,1968,2197,1637,2006,1903,2261,2064,2309,2370,2615,1731,1990,2078,2345,212 0,2384,2418,2689,2172,2431,2493,2735,2541,2781,2823,3099,1824,2100,2160,2412,2231,2457,25 21,2770,2281,2526,2586,2805,2623,2861,2902,3157,2359,2608,2680,2876,2697,2905,2956,3203,2 752,2972,3012,3238,3050,3269,3320,3535,1270,1475,1568,1984,1673,2028,2050,2365,1774,2072, 2126,2407,2177,2454,2471,2767,1852,2134,2191,2462,2250,2518,2574,2811,2303,2577,2611,284 7,2686,2893,2945,3186,1920,2214,2287,2538,2314,2581,2634,2879,2404,2672,2700,2911,2749,29 69,2998,3236,2468,2726,2775,2983,2808,3040,3055,3264,2864,3077,3129,3307,3167,3344,3415,3 537,1952,2298,2379,2643,2449,2692,2746,2977,2488,2755,2787,3022,2826,3052,3097,3295,2566, 2814,2850,3073,2908,3120,3161,3355,2934,3171,3210,3385,3249,3428,3452,3627,2629,2882,291 9,3136,2986,3184,3216,3407,3048,3229,3267,3442,3309,3458,3512,3671,3095,3281,3322,3487,33 40,3527,3550,3705,3412,3561,3585,3698,3609,3731,3771,3880,1385,1649,1699,2114,1785,2140,2 202,2513,1794,2208,2267,2550,2325,2618,2648,2939,1911,2272,2329,2658,2390,2683,2720,2942, 2426,2717,2764,3010,2817,3046,3063,3263,1936,2375,2435,2666,2501,2729,2778,3043,2533,279 9,2829,3067,2858,3116,3145,3336,2530,2852,2887,3113,2931,3164,3190,3386,2991,3220,3250,34 26,3279,3451,3492,3659,2020,2479,2505,2793,2561,2841,2885,3101,2592,2899,2916,3160,2959,3 202,3227,3423,2758,2948,2989,3209,3028,3244,3277,3446,3082,3287,3329,3483,3361,3526,3553, 3692,2838,3017,3070,3260,3111,3305,3333,3513,3153,3349,3372,3534,3417,3572,3594,3722,321 3,3414,3430,3586,3447,3610,3578,3741,3500,3655,3672,3778,3679,3817,3836,3900,2058,2555,25 69,2928,2732,2966,2996,3219,2796,3007,3030,3254,3080,3291,3326,3517,2832,3076,3109,3293,3 135,3334,3365,3540,3173,3376,3404,3566,3443,3590,3625,3746,2936,3119,3144,3362,3189,3396, 3434,3580,3253,3435,3454,3623,3501,3606,3665,3780,3302,3476,3522,3656,3543,3678,3695,380 6,3573,3701,3700,3831,3742,3845,3859,3936,3015,3168,3223,3436,3290,3455,3489,3635,3330,35 14,3530,3673,3559,3682,3699,3814,3366,3547,3581,3693,3595,3704,3743,3846,3634,3752,3766,3 863,3793,3885,3898,3969,3424,3587,3619,3745,3664,3747,3787,3870,3670,3783,3808,3892,3825, 3908,3928,3989,3683,3818,3841,3915,3854,3932,3922,3997,3878,3945,3955,4014,3973,4023,403 3,4055,1510,1719,1813,2166,1886,2278,2334,2637,1928,2356,2393,2655,2445,2709,2723,3033,19 44,2440,2476,2706,2510,2844,2867,3092,2597,2873,2925,3155,2963,3193,3226,3440,1960,2496,2 558,2855,2603,2922,2951,3180,2640,2975,3001,3232,3037,3271,3299,3459,2677,3019,3061,3285, 3104,3325,3345,3506,3123,3338,3377,3545,3382,3564,3589,3773,2220,2600,2626,2961,2662,300 4,3035,3259,2740,3065,3085,3315,3128,3353,3374,3519,2790,3089,3141,3341,3177,3381,3390,35 54,3206,3392,3403,3592,3475,3611,3649,3782,2835,3176,3197,3401,3242,3431,3439,3601,3274,3 472,3495,3633,3532,3661,3675,3809,3312,3509,3544,3677,3575,3691,3724,3826,3618,3728,3753, 3847,3767,3867,3888,3966,2239,2651,2712,3058,2784,3088,3132,3359,2820,3148,3182,3393,321 5,3411,3419,3596,2896,3199,3240,3420,3273,3468,3488,3629,3311,3503,3531,3667,3557,3684,37 11,3810,2953,3256,3297,3493,3348,3525,3521,3687,3369,3548,3562,3706,3603,3725,3736,3849,3 408,3577,3615,3733,3630,3759,3768,3871,3654,3779,3798,3893,3830,3910,3930,3991,2994,3319, 3351,3552,3388,3571,3604,3729,3464,3616,3640,3764,3645,3772,3789,3884,3478,3641,3651,378 6,3688,3796,3822,3907,3717,3829,3839,3916,3858,3937,3949,4000,3505,3697,3709,3811,3738,38 32,3844,3924,3754,3856,3872,3944,3889,3956,3971,4018,3800,3874,3894,3959,3913,3975,3981,4 030,3925,3986,3996,4036,4007,4044,4054,4075,2320,2743,2802,3151,2890,3196,3233,3449,2913, 3246,3283,3471,3316,3498,3539,3713,2980,3301,3357,3518,3380,3568,3558,3720,3397,3582,360 8,3749,3638,3761,3775,3879,3107,3370,3399,3567,3463,3600,3621,3765,3470,3639,3648,3777,36 62,3791,3804,3902,3480,3657,3681,3802,3716,3821,3837,3918,3734,3852,3857,3938,3873,3950,3 962,4012,3125,3460,3466,3631,3481,3643,3666,3795,3508,3689,3707,3816,3727,3833,3855,3934, 3614,3715,3739,3838,3755,3864,3875,3946,3794,3876,3895,3960,3914,3974,3980,4029,3646,375 8,3785,3865,3801,3891,3904,3965,3824,3909,3920,3979,3933,3987,3999,4039,3842,3926,3941,39 95,3954,4002,4011,4046,3967,4015,4022,4052,4027,4061,4063,4083,3139,3484,3496,3710,3599,3 723,3735,3850,3624,3748,3762,3868,3788,3883,3901,3963,3650,3774,3799,3886,3813,3905,3921, 3977,3834,3931,3919,3984,3948,3998,4006,4042,3718,3807,3820,3911,3848,3923,3940,3992,386 2,3942,3953,4003,3961,4008,4019,4051,3890,3957,3970,4013,3982,4024,4028,4059,3988,4035,40 38,4065,4045,4068,4070,4080,3756,3823,3861,3943,3882,3952,3958,4009,3899,3972,3976,4021,3 985,4025,4037,4062,3903,3983,3993,4034,4005,4040,4041,4069,4017,4047,4050,4071,4057,4076, 4078,4088,3935,4001,4004,4043,4020,4048,4053,4073,4026,4058,4060,4077,4066,4079,4084,409 0,4032,4064,4067,4081,4072,4082,4085,4091,4074,4086,4087,4092,4089,4093,4094,4095]
›APPENDIX · 17 of 21
Sequence Group 3: Q3_8192
[0,1,2,4,8,16,32,3,5,64,1024,2048,4096,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,12 9,66,512,11,40,68,130,19,13,48,14,72,257,1025,21,132,35,258,26,2049,513,80,37,25,22,4097,136, 260,264,38,514,96,67,41,144,28,69,42,516,49,1026,74,272,160,520,288,528,192,544,70,44,131,81, 2050,50,73,15,320,133,52,1028,23,134,384,76,4098,137,82,56,27,97,39,259,84,138,145,261,1032, 29,43,2052,98,515,88,140,30,146,71,262,265,161,576,45,1040,100,640,51,148,46,75,4100,266,273, 517,2056,104,162,53,193,1056,152,77,164,768,268,274,518,54,83,57,521,1027,112,135,2064,78,2 89,194,85,276,4104,522,58,168,1029,139,99,86,60,280,89,290,529,2080,524,196,1088,141,101,14 7,176,142,530,321,31,200,1033,4112,90,545,292,2051,322,532,263,149,102,105,1030,304,296,163, 92,47,267,385,546,2053,324,1041,208,386,4128,150,153,165,106,55,1034,328,536,577,548,2112, 113,154,79,269,1042,108,578,224,166,519,552,195,4099,1152,270,3072,641,523,275,580,291,59,1 036,169,560,114,277,156,2057,87,197,1057,116,170,4101,61,531,525,642,281,1089,278,526,2054, 177,293,388,91,1044,584,769,198,172,120,4160,201,2065,336,1280,62,282,143,103,178,294,1058, 93,644,2058,202,592,323,1048,392,5120,297,770,107,180,151,1060,2066,209,284,648,94,204,298, 1031,400,608,352,2176,6144,325,533,1153,155,210,305,547,300,1090,109,2060,184,534,537,115, 167,1536,4105,225,326,306,772,2081,157,1035,656,329,110,117,212,1064,171,2113,776,4102,330, 226,549,1092,538,387,308,216,2068,1154,416,271,279,158,337,1043,4113,550,672,2304,118,332,5 79,1037,540,389,173,121,1072,2082,553,199,784,4106,179,1038,228,338,312,2072,704,390,1096, 174,554,581,393,1281,4114,283,2084,122,448,353,1045,561,203,63,340,2055,1156,394,527,582,4 224,556,181,1059,2177,295,285,232,124,1282,205,182,643,2114,4108,562,1050,286,585,299,1537, 354,211,2560,401,185,1104,396,344,4129,586,645,2059,1061,593,535,240,206,1049,95,2088,327, 564,4161,1046,800,402,356,307,2116,1160,301,417,213,568,1284,832,4116,2178,588,186,1288,64 6,404,227,896,2067,1062,594,418,4352,302,1538,649,771,2061,360,539,1120,111,331,214,1091,20 96,4130,309,188,449,1065,217,408,2062,609,596,1168,551,650,4120,229,1052,2120,159,420,310, 1093,541,773,2305,610,4132,1066,657,333,119,1540,3073,600,339,218,1073,368,652,4103,230,20 69,1098,391,313,450,1296,542,2180,334,233,4225,1184,555,774,175,2083,1544,123,658,612,1312, 2306,4162,341,777,220,1552,314,424,2074,395,1216,673,583,4608,355,1568,2561,287,183,234,1 094,125,557,2128,4107,660,1068,616,342,316,2085,1155,241,778,1105,563,4136,345,2073,452,10 74,397,403,207,2070,1097,674,4164,558,1039,785,432,2184,357,1344,187,236,664,4226,2308,115 7,624,587,1076,780,2312,705,126,1047,4115,242,565,1158,2086,398,346,456,1408,358,2562,4109, 405,1100,303,569,244,2144,1161,595,189,4144,1106,566,2115,676,361,1080,706,589,2089,1051,4 110,215,786,647,1121,2192,348,419,1063,406,4168,464,2076,680,1283,801,362,1108,2117,590,43 53,409,1162,570,2090,788,597,1169,572,219,5121,2564,1285,311,708,1053,598,2097,601,1067,41 17,651,421,3074,792,1122,802,611,1539,2122,4228,602,410,1112,231,688,2320,1164,653,248,413 1,1054,2208,369,190,364,1170,654,2568,4354,659,1095,335,480,2336,1286,315,221,1289,4122,25 76,370,613,1185,422,425,2240,1600,6145,451,614,1069,2592,543,235,1124,412,4609,2118,343,37 2,1664,775,317,2092,1075,222,4176,426,1172,2179,453,237,1070,559,2129,4133,833,1099,804,71 2,2098,1290,834,661,4121,1297,2121,808,779,1541,617,1128,2063,4118,604,433,1186,720,2368,8 16,1077,4232,836,347,2181,1217,897,243,1176,2100,4356,662,454,1101,318,3076,675,1188,618,4 360,898,2071,1792,781,376,2182,1292,4134,428,1298,665,2432,736,1542,567,840,4610,2124,107 8,625,238,1107,2185,359,4192,457,1081,399,2130,787,1545,591,1136,4163,2104,678,434,1159,20 75,677,349,4137,1102,245,2145,458,1313,666,1218,4240,2087,620,363,1109,2307,127,191,4124,1 300,782,2132,1546,407,436,1082,4165,2186,626,571,1192,2193,465,1163,681,4138,246,2309,1123, 707,350,3080,4612,1110,599,1084,668,2077,790,1304,4145,460,2091,249,1113,682,1314,2146,51 22,573,411,1553,2563,803,789,1548,4170,709,2136,1220,365,440,2188,1165,4368,628,1125,689,2 078,374,1171,4256,423,2194,466,1200,793,2119,1166,4616,250,371,1554,2310,481,1345,574,4384, 2313,413,1055,603,2209,1224,4624,366,468,1114,2624,655,1569,900,4288,2093,805,1316,615,30 88,1346,4640,684,710,2148,1556,429,1287,4166,2688,794,252,1173,373,2099,1126,4140,605,848, 2196,1129,690,1328,4227,2094,713,1320,632,2123,482,4177,1187,806,2314,1116,427,904,6146,23 21,1071,414,1291,2565,223,663,4146,1409,2152,692,1570,835,2210,4169,1348,619,472,2101,123 2,455,4111,1410,2241,796,809,1174,3104,4416,714,1177,721,2200,1189,837,4229,716,2125,1130, 864,1079,2212,4148,810,1352,606,2816,912,5124,1560,722,2316,1601,696,1572,4119,2322,377,4 35,1137,2566,817,4230,1178,319,2102,1103,621,1293,4480,2131,812,484,1132,2105,430,4172,160 2,838,2569,1248,667,4233,3075,488,1190,239,2160,1543,4178,378,1576,2183,459,1219,622,4152, 2126,627,1294,437,2337,4123,1665,380,2242,1547,818,1299,4193,2133,461,496,1604,2324,4135, 669,1315,2570,679,1083,724,4355,2106,1193,841,629,2216,4180,1584,351,1138,3077,467,1301,4 234,2187,438,1180,737,2147,4241,1111,251,1221,2134,462,4357,442,2108,1140,441,1194,2328,51 28,469,1085,2137,247,1555,4125,683,2338,1549,842,1666,4139,2577,738,899,2572,1305,6148,67 0,1302,2244,783,1550,3136,4194,849,1201,820,2189,1317,4611,728,2149,1412,928,1115,4184,219 5,791,367,2224,1608,4236,901,1793,2190,630,1222,4126,2578,685,1196,844,2369,4242,1144,633, 2079,1225,711,4167,1360,2248,253,1086,3081,4358,691,1306,824,2138,1167,4361,902,2593,1127, 686,740,4257,2340,1202,850,2370,1318,4672,375,2580,1117,444,1668,4141,2311,470,1226,2197,4 83,5136,1616,415,2150,1347,485,4196,2153,1416,905,3078,1321,4736,795,1794,2352,473,4147,1 131,2344,634,1204,2211,4244,744,1175,852,2140,1233,4142,960,2095,1308,865,2315,4171,1672, 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721,3400,4549,1455,4333,2654,5166,2960,1631,4655,3608,6225,1513,2770,4929,3649,5195,958,4 900,2744,3620,4808,1890,6194,2425,5386,1747,2483,4930,3185,4757,1510,5393,2865,3226,6217, 1932,4904,2367,4875,1742,3151,5637,2669,4713,987,3341,5224,2860,6159,1837,4700,2532,1500, 4529,3180,5282,2478,4816,1880,3650,6464,2886,4912,1863,5173,3296,1749,4932,2715,4443,253 6,6277,1012,3238,5313,2287,4993,1722,4339,3591,1938,5272,2426,6196,3624,4758,1776,2507,45 50,3267,5197,1892,4414,2670,7172,1843,2675,4771,3342,5284,1838,4714,2485,3713,4994,999,61 67,2428,5888,1463,3595,4877,2866,4472,1953,6278,3347,2509,5388,1514,4524,2544,5394,3652,4 761,1647,2717,6528,1695,4832,3363,5638,2727,1763,4663,3131,4936,2772,6220,1016,3241,5174, 2889,4721,1940,4334,2677,5203,1487,3632,6281,2399,4455,1867,4553,3186,5177,2515,1405,449 5,3349,6226,2486,4883,1521,3228,5641,2785,4687,767,5232,3159,6200,1954,2299,4774,3269,453 0,1845,5255,2510,6171,2490,1750,4773,3188,4445,2489,5198,1985,4341,3242,1896,6241,2517,45 54,3133,5409,1516,4762,2295,3603,5314,1655,6183,2731,4716,3597,4459,989,2890,5205,3714,64 03,1753,4223,2786,4287,2947,1724,5396,3353,4878,1467,6228,2718,5642,3350,1765,4503,2831,4 532,3598,5178,1869,6282,2897,4722,3249,1944,4667,2868,5288,3365,6289,1003,4561,2776,3460, 5259,1406,4777,2976,4342,3163,6405,1846,5219,2839,1875,4803,2415,4446,3656,7176,1754,520 6,2949,3841,4695,1522,5180,2678,4764,3270,6173,1904,4886,2733,3244,5400,990,4556,2892,618 7,3192,4345,1766,5209,2681,3273,4778,1469,5410,2759,6242,3408,4669,1495,4507,2301,5649,31 34,1659,6659,2739,4899,3354,4885,1956,5644,2872,4805,3215,1711,6232,2950,5316,3175,4461,1 927,4536,2734,6284,1005,5261,2788,3250,4724,1849,5221,2898,4785,3366,6174,1524,4470,2423, 5267,3165,1870,4519,2492,6290,3716,4562,1769,5296,2518,4889,3274,6215,1850,2531,5262,366 4,4346,1756,4467,2463,5650,3395,6406,1470,4577,2533,3464,5441,959,4670,2953,6409,3369,450 9,1986,5151,2843,4699,3842,6305,1960,2521,5320,3179,4462,1499,4564,2682,5210,3252,6720,18 77,4751,2792,5665,3223,1891,4996,2900,6189,3281,4901,3008,5412,1661,4711,3356,7184,2913,5 442,1931,4780,3720,2741,4806,1011,6244,3166,5652,2845,4525,1511,5383,3276,6784,2954,4890, 1719,4348,3370,5269,2763,1770,4469,3472,6195,2855,5222,1852,4701,3680,4944,2522,6292,177 7,5225,3424,4786,2684,5424,1878,3397,6190,2742,4809,1881,5416,3605,4728,2302,6219,1013,45 78,3227,5283,2765,4902,1528,6410,3282,5212,2623,3377,4523,1823,5000,2961,6417,3619,5167,1 279,4510,2846,5387,3372,6661,1988,4319,2859,4759,3181,5505,1933,6248,2427,4788,3256,1743, 5666,2745,4931,3606,6306,1501,5444,2479,4715,2655,4568,2537,6197,1939,5328,3609,4551,291 4,5506,895,6337,3187,4892,2771,4905,1662,3239,5270,2534,7200,1772,4810,3297,5273,2956,481 7,1968,6296,3398,5285,2766,4933,3378,4812,1893,6221,2861,5226,3844,4960,1515,5175,2524,63 08,3229,4906,1723,5448,2904,4702,3728,6912,1778,5008,2887,3401,5656,1882,4818,2773,6412,3 182,5697,2746,4792,1006,5668,3189,6418,2962,4473,1502,4531,3284,5233,2800,6662,1992,4913, 3243,5274,2916,4415,3848,6198,1407,5199,2867,4717,3402,5389,1934,6227,2862,4908,3298,458 0,1839,5228,2487,6201,3621,4526,2000,5698,2977,4934,3610,6665,2538,5344,1894,4763,3459,71 71,2671,4584,1941,5286,3380,4335,2719,6256,1014,5639,3288,4474,2787,5672,3488,6279,1751,4 555,2964,5315,3343,4718,1517,6222,2511,4723,3351,5390,2891,1897,4533,6433,3230,5761,2429, 4476,1725,6338,3409,5643,2545,4914,1955,5395,3622,6229,2978,4557,3744,4592,1780,5700,286 9,6420,3190,4765,1884,5411,2774,6666,3404,4775,1523,5179,3651,4820,3009,6202,3612,5289,17 55,4937,2920,4725,3461,6312,1017,5680,2540,4447,3245,5234,2679,7173,1847,4563,3193,5397,2 777,6283,1946,4534,3625,5276,2748,4833,3271,6243,1898,5207,2491,4347,3856,5317,1942,6230, 2789,4558,3251,4538,2893,6204,1526,5236,3300,4537,2968,5290,1957,6424,4565,3410,5181,243 0,6233,3384,4343,1767,5651,2870,4779,3776,6434,1784,5645,3462,4938,2899,5762,3246,6673,19 05,4834,2778,4995,3626,6668,1018,5401,2546,4766,3653,5398,2928,6340,1518,4879,3465,2790,1 726,5646,3355,7232,2493,4945,3194,5297,1945,4916,2519,6285,3520,5413,1525,4824,3425,6245, 2683,5508,3633,5024,1900,5211,2980,6291,3275,4887,2735,4463,1871,6320,3135,5704,2951,499 7,2016,3412,5889,2873,6286,3466,4726,1471,5318,2548,6674,3599,4781,1757,5292,3654,4940,28 94,6465,3628,5240,1851,4729,2793,6175,3253,5321,2874,4807,991,5456,3367,6344,2780,4349,19 58,5182,3357,7177,2494,4787,3304,5402,1906,4920,3196,6234,3010,5263,3277,4998,1961,6689,2 984,5223,3254,4782,2523,4836,1987,6436,3715,5298,2901,4946,1771,6466,3634,5414,2915,4471, 3358,6676,1529,5213,3657,4540,2685,5764,3371,6407,1879,4566,2955,5322,3426,6293,2535,457 9,1948,5712,3283,4511,2743,6246,1758,5443,3473,4581,3257,6249,2794,5512,1853,5001,3468,71 74,2876,5417,3416,4891,1020,5890,2801,6448,3658,4569,2902,5227,1989,6440,3717,4730,3665,5 300,1962,6307,2905,4840,3607,5271,2552,4948,1908,6236,3312,5329,2847,5056,3278,6191,1530, 5404,3167,4961,2303,6411,3399,5768,1773,4789,3012,6529,3636,5214,2957,4893,1969,5324,387 2,6690,2767,5002,3474,5418,1990,6468,3428,4811,2525,5520,3379,7185,1779,4903,2963,5728,33 73,4570,2686,6352,5472,1883,4732,3489,6530,3285,5445,2796,4790,1964,6294,3640,5653,2992,4 350,3904,6297,1854,5275,2917,4813,3660,6309,3258,5330,1935,4671,2539,5425,3718,6250,2747, 5009,1007,5667,3476,6199,4894,3299,5420,2802,7178,1895,4907,3968,5229,2906,6472,3666,447 5,1663,5304,2526,6680,3490,4793,3374,5654,1912,4527,3016,6721,3721,4703,2431,4585,6692,15 03,5657,3843,4962,2958,6257,3432,5235,1970,4819,3611,6298,2863,5287,3183,4582,1774,6223,3 024,5345,3403,5004,3286,6413,5446,1993,4814,2918,5426,3381,7186,2965,4909,1532,5892,3260, 6252,3521,4572,2775,5277,1885,6722,3289,4952,5776,2541,6368,3480,4935,1781,5449,2921,631 0,3681,4821,3668,5230,1994,6663,2749,4794,3623,5237,6696,2979,5010,3722,5332,1943,6339,33 01,4848,2804,5291,3231,7296,1015,4964,2908,5896,3492,6414,4915,3382,5450,1899,6785,2547,4 910,3613,5346,2779,4535,1886,6667,3845,5669,5025,3682,6419,2871,5658,3729,4586,1782,6724, 2970,5507,3405,4719,3191,6435,1972,5428,4767,2922,6203,3672,5336,2966,4835,2001,7180,341 1,5536,3290,5012,2550,6313,5391,1947,4559,3440,6704,2981,5399,3724,4939,3302,6258,1996,52 78,4477,2791,6421,3463,5457,3385,4593,1785,6300,2808,5670,3522,5026,6231,2929,5792,1901,4 917,3614,6341,3406,5238,2542,4822,3305,7201,5452,1976,5699,2750,6260,3627,5057,3846,6314, 1519,5660,2969,4968,6205,3247,5509,2549,4588,3195,6675,1727,5293,3730,4727,6669,2924,524 1,3684,4825,1959,6786,3413,5673,2895,4796,3849,6425,5319,3040,4539,2002,7233,3292,5904,33 86,4837,2495,6422,5299,1019,4941,3496,6670,3467,5348,2781,5016,6321,3745,5458,1907,4478,2 875,6437,3655,5432,3427,4918,6532,1786,5824,2982,6235,3359,5510,3255,4947,2930,7188,5294, 1527,4826,3306,6728,2985,5674,3197,4594,6913,1949,5701,3629,4976,3011,6342,3732,5513,368 8,4838,6316,1902,5403,2795,4541,3414,6264,2553,5242,6345,3388,4567,1759,5568,3313,6480,29 03,5473,4731,3850,7424,2017,5681,3635,5028,2972,6206,5323,3417,4783,2782,6426,1909,5183,3 524,4999,6287,3469,5460,2877,6247,3475,4921,1963,5514,6322,3279,4596,3013,5647,3746,6438, 2018,5702,4942,3630,7202,2986,5676,3857,4841,3504,6237,5301,2004,6788,2932,4922,3429,541 5,6346,2554,4828,3259,5405,1950,6736,3308,4542,5352,2797,6467,3736,5244,3696,7192,5058,17 88,5325,2993,6536,3659,5032,3852,5302,6441,3014,4571,1965,5763,3777,6914,4949,3198,6251,2 803,5682,3314,4963,1991,6324,5406,2907,5705,3637,6295,3470,4733,5419,2988,7204,1021,5003, 3418,6353,5474,3528,4583,2878,6428,1910,5331,4791,3430,6792,3477,5521,2959,6238,3375,530 5,4842,1855,6348,3641,5516,2919,4924,6442,3316,5464,3667,7175,1971,4849,5706,2687,6544,32 61,4950,3638,5765,6752,2936,5713,1531,6496,3748,4953,5655,3433,6469,2527,4600,3778,5360,6 677,1913,4895,3661,7297,2994,5326,5215,3287,6299,2798,4351,5447,3858,6354,2008,5060,3719, 6449,5684,3017,5005,3420,6691,3491,5920,4815,1775,6444,2556,5522,3478,7234,5476,3536,457 3,2909,6253,5427,1966,5011,3752,6328,3873,5421,6678,2805,4734,3434,5537,2020,6681,5333,36 62,6259,3018,4844,5688,3481,6311,3642,5040,1995,5952,7680,2967,4965,3860,6369,3669,5708,5 306,3644,6470,2923,4587,6450,1914,5766,3291,4795,3383,6916,5524,2910,5347,3780,6301,4850, 1533,7179,3670,6016,2806,4954,6800,3673,5714,3723,6473,4574,1973,5538,2996,6254,5422,349 3,5064,3864,6261,3025,5769,6356,3874,4479,1997,5891,7208,3683,5006,2971,6315,3674,5480,56 59,3482,6920,2024,4911,6474,3020,5231,3303,5072,6370,3760,5451,2809,6693,5334,1916,4966,3 725,7236,3320,5429,6682,2925,5013,3441,5308,6531,3262,5569,1974,6452,4823,3436,5337,3000, 6360,4589,3726,7298,3731,5528,4969,1887,6560,2543,5729,3407,6415,5716,3552,4797,2751,642 3,5671,3387,6302,1783,5027,5770,3293,6481,2983,5349,7187,3442,4852,3685,5279,6694,3026,49 56,1022,6816,5540,3494,5430,3497,6262,4595,3523,6476,2931,5661,4827,2032,6723,3686,5893,7 181,3615,5730,2810,4919,6684,3307,5777,3484,6533,5018,1534,5453,2551,6317,5239,3415,6265, 3444,4970,5720,2973,7216,3847,5014,6697,2003,5459,3389,6343,5338,3294,4598,2926,6928,548 8,3498,6323,3525,5029,5772,1977,7182,2783,5350,6372,3309,4839,3631,5511,6482,3905,5433,17 87,6456,4856,3041,6848,5570,3876,4977,3784,6534,5662,2933,7240,3906,5454,4590,1998,6318,3 733,5353,6698,2987,4798,3880,6725,5675,3851,5894,6537,3689,5017,1978,7425,5295,3042,4597, 3676,6427,5243,3505,6266,3028,5778,6592,3792,4972,1903,5732,6497,3888,5461,7189,3908,494 3,2974,5897,6705,3419,5088,3969,6347,5340,2005,6207,5434,2812,4543,3315,6484,5544,3734,73 00,3526,5515,6538,2989,4829,5793,2006,6671,3390,4923,6726,3747,5703,3015,6700,5475,3690,5 030,6325,3970,5407,1951,7203,5303,3853,6439,2934,4978,5354,3448,6429,5033,3500,6376,2879, 5245,6268,3737,5677,2019,5059,7426,3808,5780,6349,3639,5736,2995,6326,4843,3912,5462,678 7,3697,4601,1789,6706,5436,2555,7194,5361,3310,4951,3431,6430,5898,3529,6729,5683,2937,64 43,1980,5020,7681,3471,5465,4830,3859,6498,3663,5572,6355,3032,5517,6545,3750,4925,3506,5 523,6329,1911,5327,7248,2799,5061,3749,6540,5794,3421,6488,5678,3317,5034,2990,6730,5905, 2009,6789,5552,3530,7205,3738,4980,5477,3692,6737,4602,3044,6679,3435,5307,6384,3199,535 6,6350,2021,4845,3263,5784,7193,3019,5744,6239,3854,5041,6471,3479,5707,2938,6708,5900,20 10,5062,7190,3508,5825,3698,6944,5246,3643,6546,4851,2557,6500,5362,3537,4955,3753,6451,5 685,1967,7304,5518,3318,6445,5036,2997,6561,3779,5466,6357,3422,5576,4926,3671,6712,5478, 3021,7428,1915,5525,6976,3740,5007,6732,3862,5423,5689,3532,6330,3048,4967,7432,3321,536 4,6790,3754,5715,6548,2022,4735,3645,6371,5309,2940,5686,7040,3483,4984,7206,3875,5796,67 38,3861,5481,1790,6562,4575,2998,6446,5826,3781,7682,5709,3437,5042,3512,6793,5335,2911,6 915,4846,3700,6504,5906,1535,6683,5767,3761,7264,3446,5065,6255,2807,5468,5539,3495,6475, 4604,3538,6358,5526,3865,7235,5584,3056,6453,1023,4957,6332,3322,5800,6593,3443,5921,485 3,3553,7209,5482,2558,6361,5710,3646,6552,3485,5066,6753,2012,5529,6740,3675,5690,7312,30 27,5015,6695,3438,5908,5717,3540,6794,3727,5692,6373,3001,4971,7196,2025,5339,6303,3972,5 431,6564,3877,4958,6454,3687,5828,7237,2811,5718,6685,3756,4854,3782,5721,6917,1975,5771, 6754,3501,5044,7210,3022,5541,6801,3866,5912,6477,3324,5073,6263,3445,5922,7684,3677,573 1,6744,3002,5019,6483,2026,5722,3920,6362,5530,3762,5068,7217,3785,5351,6512,2927,5808,67 96,3704,4857,6374,3554,5773,7242,1917,5368,6535,3878,4973,6457,3029,5489,6594,3499,5310,7 440,3976,5484,6686,3486,5048,6478,3030,5774,6377,3295,5779,1999,4591,7328,3735,5455,6699, 3764,5600,6918,3907,4799,6319,2975,5435,7688,3691,5341,6267,3544,5031,6802,3527,5490,675 6,1918,5733,7456,3043,5074,6485,3868,5542,6921,3881,5545,6364,3786,5571,7696,3793,4979,64 58,2813,5734,6568,3909,5663,6539,2033,4858,7360,3788,5355,6817,3936,5532,6727,3004,4599,6 499,3882,5463,7712,3678,5492,6431,3984,5021,6327,3794,5895,6378,1979,5437,7238,2935,5342, 6269,3768,4974,6701,3449,5546,6804,5573,3507,7212,4831,3889,6760,5357,3033,6486,5679,339 1,6460,5953,2028,7299,5089,3693,6385,5924,3884,6922,5832,3045,7249,4981,3556,6707,5954,35 02,6489,5781,3910,6596,5035,3739,7218,5928,2034,6541,5899,3034,6547,5737,6351,3560,5090,7 241,3311,5724,6818,3450,5553,6702,3531,5076,7183,2991,5840,6929,3694,5936,6576,1981,5956, 6501,3699,5022,7488,3509,5467,6331,6017,3452,6380,4860,2939,6808,5363,3890,7301,5782,353 3,6768,5574,3568,6731,5037,3741,7220,5438,2007,6924,5795,6849,3046,5063,6270,3751,5738,71 91,3796,6018,6386,3913,5901,6709,2814,4982,5496,3701,5548,7302,4927,3423,6542,5785,3539,6 490,5856,1982,6600,5687,3510,7552,5043,2559,6502,5960,6549,3809,5745,7244,3323,4603,6447, 3534,5358,6713,3514,5479,6388,3513,5577,7305,4985,2011,6739,5519,3036,6333,5907,3541,725 0,5711,3319,6710,5080,3755,6820,5798,6505,3914,5554,7224,3049,4847,6850,3810,5797,6733,39 71,5469,7195,5365,3742,6359,5038,2036,6930,5578,3855,6791,5786,2999,7265,5740,6492,3921,5 092,6563,3892,5483,7207,3800,5247,6550,5311,4000,6608,5067,3050,6824,5902,3863,7427,5527, 2023,6945,4986,6506,3439,5556,7252,3973,5746,6734,3702,5691,6553,4605,3757,7306,5585,294 1,6714,5801,3916,6932,5366,6741,3705,5045,7313,3783,5827,6716,2040,5470,6363,5719,3325,74 29,5069,3023,6455,5788,3763,6852,5910,7197,3896,5580,6742,3974,5096,6745,5369,3758,7211,5 802,2942,6795,5693,3812,6565,4988,6936,3922,5531,7266,1791,5923,6946,3447,5909,6755,5046, 3516,7683,5829,3542,6746,5485,6554,3057,5560,7256,3555,4959,6375,3487,6832,5748,7308,355 7,5809,6797,3977,5494,6392,4855,3867,7198,5543,2013,6513,5586,6334,3003,5913,6508,3545,51 04,7314,3706,5370,6798,5491,3816,6803,5601,3924,7239,4606,6479,4032,5694,6624,3052,7430,5 533,6459,3937,5723,6365,3765,5075,7433,5486,2027,6514,5588,3869,6757,5775,7329,3978,5049, 6566,3058,6020,6569,5925,3787,7744,5735,3879,6595,6758,4859,3546,7213,5804,3708,6687,583 0,6379,3766,5549,7268,3005,5070,6556,5914,2014,6487,5372,3326,6516,5493,7808,3789,6919,57 25,6461,3647,5050,7219,3985,5968,6366,5810,3870,6570,5833,3031,7316,4975,6597,3883,5752,6 381,3451,7214,5602,6703,3769,5926,6977,5077,3503,7243,5547,2029,6948,6024,6856,3679,5534, 7434,3561,6978,5078,6805,3006,5343,7441,5783,3938,6952,5812,3795,6923,5955,7685,3558,502 3,6761,3980,7272,5739,6748,3790,5592,6577,5575,3035,7330,5091,3885,6864,5916,6960,1983,59 29,7221,6980,3548,5834,6491,3928,5841,7361,4861,3911,7041,5957,6387,3797,7320,5836,3060,6 806,5984,6598,3770,5052,7245,5930,3986,6462,5726,6819,3824,7332,6032,3940,6762,5842,7042, 3891,4983,7936,5816,2035,6925,5497,3886,6520,7436,5555,3047,6572,5937,7442,3511,5081,680 9,5439,4001,6880,7686,5741,3562,6711,5932,3695,6984,5093,7222,3743,5604,6769,6382,3811,55 50,7251,5958,3064,6503,5787,3988,6601,5082,7225,3535,6543,5608,6931,2037,5359,7689,5498,3 915,6735,7280,5579,3453,6822,5039,3569,6578,5742,7303,2815,5747,6821,6493,4002,5557,7246, 5500,3893,6389,4987,6602,3798,7457,5938,6810,4033,5581,7362,5616,3944,6764,5789,3564,650 7,7253,5094,3703,6271,5799,6335,1919,5844,7444,6926,3037,5961,7690,4862,3801,6551,5749,65 80,3772,7226,5471,6770,3515,5587,6715,5558,3813,7336,6609,4607,3917,7307,5857,6825,3992,5 371,6390,7267,3051,5582,6851,5562,3454,6494,5561,7254,3894,6743,5084,7228,3923,5589,6812, 5367,3802,6934,7448,5803,2030,6604,5962,6393,3570,7257,5097,6826,3952,5858,7458,6019,303 8,6717,6555,5790,3814,7697,5903,6947,3517,5047,6933,7692,3543,5969,6853,5940,3707,7364,65 09,5848,4004,6584,6048,7309,3759,5098,6772,7269,3975,5911,6833,5487,3053,6518,7315,6021,3 897,6567,5750,6610,2038,5805,7344,6937,3572,4989,7310,5964,3918,6394,6515,5753,3817,7698, 5831,6625,7489,3898,5373,6718,5071,3804,6557,5811,7199,3518,6747,5944,7368,3007,6022,651 0,6612,4034,5806,7258,4990,4008,6799,7713,5860,3547,7044,5970,6949,7460,3925,5495,6759,55 64,3939,7490,6828,5590,2041,6854,5105,7700,3709,6573,5603,7431,5535,3979,6938,6396,5605,3 059,7317,6025,6517,3559,7270,5915,6749,3767,5051,6992,7273,5593,3818,6834,5754,7472,3900, 6857,5864,7464,3825,5972,6776,6626,3926,6080,7331,5100,6950,3929,7260,5985,6571,3061,581 3,7048,7215,3576,5917,6558,6026,7435,3871,6367,5106,6807,3327,5835,7553,6836,2042,5927,77 14,6979,5594,4036,7492,5756,6763,3981,6616,5814,7376,3791,5053,6599,7554,5374,3549,6940,5 837,6953,3987,7318,5695,6858,7321,2943,6033,6865,5918,3710,7333,6981,5079,3820,6860,5931, 7274,7008,4016,5499,7223,6954,3941,5817,7496,5551,6750,3563,7056,5727,7704,3771,5609,686 6,7745,5054,3826,6840,7716,5986,3930,6521,5843,6579,7281,2015,5606,6961,7322,3054,6028,64 63,5838,7247,3550,6765,5083,7437,4040,6956,5933,6628,5596,3455,7276,6574,5976,7746,3982,6 982,5959,7392,3887,5845,6811,6632,5108,4048,7334,6383,5818,3942,7687,6034,6522,7720,3989, 5872,6603,7363,5988,3062,6766,5939,6771,3799,7438,5934,6581,7809,3565,5095,6524,5559,394 5,7691,6962,6049,7443,3773,6605,5610,6640,7748,4003,5743,6813,5791,7459,2044,6823,5859,72 27,3828,6868,5112,7337,6985,3932,6036,6773,5583,7728,3571,6495,5963,7282,3803,6611,5501,7 445,6582,3065,5617,7324,6881,4863,3895,7255,6050,6395,7365,3994,5941,6606,6586,5846,3946, 7284,6585,6081,3990,7338,5992,6613,7229,3574,5612,6391,7699,5751,4005,6827,7693,5085,698 6,3815,7810,5849,6882,7043,3832,5820,7449,5563,6814,3953,7446,5861,6927,7694,3066,5965,69 93,7345,6040,3566,6964,7461,5099,2031,6872,7556,5502,7072,3774,7259,5942,6935,5971,3993,6 511,7752,5850,7045,3573,7937,5618,6774,7366,3948,6000,6829,7340,5086,3919,6988,7288,5862, 6777,4064,7369,5565,6855,7504,3519,5591,6397,7230,5755,3805,6835,7450,6052,6968,3899,731 1,5807,7046,7271,6023,3039,6830,5101,6884,7346,4006,5945,6994,7462,5620,3954,6519,7261,59 66,6588,4009,7812,5865,6614,7370,4035,5946,6627,7760,5852,3819,6559,7491,5566,6629,3577,7 560,5055,7049,7465,6082,3927,6939,7938,6056,6617,2039,7275,5595,6778,7348,3996,5973,6888, 7319,5987,3806,6996,7377,7104,5757,7452,3901,7009,6027,7816,6837,3068,5107,7262,6941,560 7,4037,7372,7050,5815,7466,6859,4010,5866,7568,6951,5948,3956,7776,6618,5873,7520,3578,67 80,5974,7493,6838,5977,3821,7701,6398,5109,7323,4017,6861,5624,7378,6719,4038,7473,5919,7 057,7715,5375,3827,6942,7468,6084,6955,3931,7277,6029,6523,7352,5839,4012,6841,7702,5597, 6575,3902,6751,6633,6035,7705,7010,3983,4991,7283,6867,5758,3055,7335,6630,5868,7393,705 2,3943,6064,7494,6862,7474,3711,5989,6957,7940,5611,6620,3960,7325,5819,7000,7824,5874,20 43,6983,7497,5978,6869,3551,7278,6842,5102,7285,7058,4018,5598,7380,6896,6088,7339,3822,7 012,7944,5503,6963,4041,7498,6030,6958,7394,5935,3580,6583,7717,6096,7073,7706,3933,6634, 5990,7555,6767,6037,3829,7476,6815,5110,7384,6883,4042,7584,5847,7060,7439,3991,5613,660 7,7447,6987,5993,3063,7326,6525,5821,7505,6641,3947,6051,7718,7074,7840,5876,3934,6965,72 86,5980,6870,7500,3830,5619,7747,7105,7708,5851,4020,7016,7557,5113,6636,7341,4049,6775,5 943,7289,6873,6042,3995,7721,6844,7367,5994,6587,4044,7952,6038,6885,7347,6989,3833,5622, 7396,7064,6053,7506,3949,6526,7480,5863,6966,7872,4024,5880,7558,6995,7342,6001,3567,687 4,7722,5114,6642,7749,2045,7024,5614,7561,6886,5822,7451,3775,6589,7290,6041,6615,7616,40 07,5621,7521,6779,7729,5996,4050,7076,7371,6831,5967,7231,3067,7047,6112,7508,6969,7562,5 567,3955,6644,7695,5853,7750,6990,3834,7724,5947,6889,7349,6970,5087,3575,7463,6876,6054, 7453,6590,3997,7400,6002,7292,7106,7373,3950,6057,7080,7350,6619,6083,7811,3807,6997,586 7,7730,7011,7454,4065,5625,7753,6781,7467,5975,7051,3957,7522,6631,6044,7379,6839,4011,58 54,7569,7353,6890,5949,7564,4066,6972,7512,5116,6897,7754,6998,4052,6085,7813,7761,6058,7 001,3998,7703,6648,6004,7408,6943,7374,3836,5626,7263,6399,7495,5869,7108,4013,7732,7053, 6065,7968,6863,7570,4039,6086,7524,6621,7475,5875,7059,3069,7469,6782,5979,7585,7381,395 8,6892,6060,7736,7088,8000,5950,3903,7013,7756,7354,6031,6635,7814,4019,6843,5103,7572,73 95,6898,5991,3579,8064,7002,7762,5759,6622,7586,3961,7470,6008,7112,7817,6527,5599,7939,2 046,7054,7528,6066,7707,6959,7279,4056,5870,7120,7499,7382,6089,7014,3823,7477,7061,5628, 7356,7617,6871,4014,5981,7385,6637,7576,5877,7017,4068,7777,7764,6090,6845,7719,7075,781 8,4043,6039,7397,6900,7327,5111,7004,3962,7588,7478,5995,6643,7709,6875,3581,5982,7941,77 78,6967,7825,5878,7066,4021,7501,7287,6068,7018,7768,7062,4045,6097,7507,7386,6646,6043,7 536,7077,4072,7820,7398,6092,6887,7559,7481,5881,3964,6904,7618,7025,5997,7710,7502,4022, 6638,7401,6072,6846,7723,7942,5615,3935,7065,7343,6645,7291,5823,7826,7020,3831,7780,605 5,7509,6991,7945,7136,6098,3070,7388,7482,6591,5115,7592,7563,6877,4080,7841,6003,6971,77 51,7523,5882,7078,3582,7455,7351,7026,5623,7402,7081,7293,4051,6045,7725,7107,7828,7784,5 998,6891,4025,7510,6649,7484,5855,7409,6999,7946,3835,6113,7731,7068,7513,6878,6005,7620, 4046,7565,6973,7571,6059,7375,7109,7842,4026,6114,7726,7082,7953,7600,6100,7028,7525,395 1,6650,7355,6046,7404,6893,7832,7792,4053,5884,7089,7755,7948,7110,6061,7873,7294,4054,68 99,7410,6087,7003,7733,7566,7084,3999,5117,7514,7624,6974,6006,7526,7573,7055,4067,7471,5 951,7737,7015,7412,7763,6067,6783,3837,7357,7734,7032,5627,7844,7529,6623,4028,7874,6009, 7757,7090,7383,6894,7954,6104,3959,7815,7113,7516,7587,5871,6652,7574,7632,4057,7005,606 2,7848,7969,6901,7530,6116,7758,7114,4069,7577,7738,6091,7063,7956,7765,7740,7019,2047,60 10,7387,7479,7006,7876,5629,7766,6902,4058,7769,7819,6069,7092,7589,7960,7121,7970,4015,6 093,7779,7067,7770,7578,6120,7116,7399,7856,3963,6905,6012,7821,7416,7021,7537,7358,6070, 4070,7532,7096,7822,7827,5983,6639,7503,7648,6847,3838,7483,5879,7389,7079,7538,7781,712 2,5118,7590,3583,7593,7619,7027,6128,7782,7711,6906,7403,7580,3071,5630,6647,7511,7540,70 69,7943,6099,7485,7390,4060,7022,7594,7621,6073,6879,7405,7727,8001,5883,4073,7137,7972,7 880,7029,8002,6094,7829,7083,7976,4023,7947,7785,6074,7138,7772,7601,7124,7888,5999,7984, 4074,8004,7070,7515,8065,6101,6908,7411,7830,7622,7085,3965,6102,7486,7843,7111,7786,8066, 6047,7949,7030,4047,7544,7596,6975,7833,6115,7904,7735,7091,8008,7793,3966,5885,6651,740 6,7527,7625,7033,6076,7567,7955,7759,4081,7128,7846,7602,6007,6895,7845,7517,7413,7086,61 05,4027,7626,7834,7788,7140,7531,7295,6117,7359,7115,7950,7575,4076,7034,6106,7604,7794,7 739,6653,7633,7849,6063,7414,4082,7093,7875,7518,7767,7117,6011,7836,7958,7628,7144,7417, 4029,7850,6118,7741,7036,7579,7971,7957,5886,7094,7877,7533,4055,7608,7007,7796,5631,785 7,7542,6903,7591,7634,7961,7152,4030,5119,7418,7539,7649,6654,7742,7581,6108,7771,7123,75 34,7636,4059,7823,7097,6121,8068,7973,7783,6907,7852,7878,6071,7597,7118,4084,7962,7420,7 541,7773,7098,6122,8016,7858,7881,7023,7800,4071,7650,6013,7974,7125,7595,8072,7582,7126, 7391,6095,7831,7860,8003,4088,7071,7787,7640,7623,6014,7139,7964,7977,7882,7889,6909,800 5,3839,6129,7884,8032,7100,7978,7774,8080,7890,6075,7031,7864,7545,7603,4061,7985,7129,74 87,6124,7789,7980,7141,7652,7598,8006,7835,6130,7130,4075,7656,7407,7546,7627,7087,7790,6 077,7795,7605,7548,7035,7986,7629,7664,4062,7837,6103,7142,7847,7892,8009,6910,7797,7519, 7635,6078,7606,6655,4077,7905,7419,7630,7610,7609,6107,7132,7637,7415,7851,8010,7145,790 6,8067,7838,4031,6132,7951,7095,8017,7988,7896,8096,7146,7959,6119,7535,8069,7798,7853,70 37,4083,8012,7801,7879,6136,7421,7119,7859,7992,8070,7854,7038,7908,8018,5887,7543,4085,7 612,7638,7153,7651,7583,7653,8073,7963,6109,7099,7641,7802,7912,8020,8128,7148,3967,8033, 7861,6123,7965,8074,7154,7883,7975,7642,7804,7862,7101,6110,7422,7885,7743,4078,8081,796 6,7127,7979,7547,7865,7599,6125,7775,7657,7102,8034,7891,7654,8076,7886,7131,4086,7981,60 79,7644,8024,8007,7893,7156,7866,8082,7920,8036,7987,6131,7982,7143,7607,8097,7658,4089,7 791,7839,7907,7160,8084,7631,6133,8011,7549,7665,6911,8098,7989,7894,8129,8040,7660,7799, 6015,4090,7133,7897,7868,7611,7909,8013,8088,7147,7550,7990,8019,7898,6126,7666,8048,713 4,7910,7613,7639,7803,4063,8100,7855,8071,7149,7993,6134,7668,8014,7913,7994,7900,7614,71 03,8130,8104,7643,8021,8035,6137,7805,4092,8075,7155,7655,7863,7914,7996,7921,8022,8025,7 157,7672,7967,7423,6138,8132,8077,7887,7645,8083,7039,7806,7916,8112,4079,8037,7659,7867, 7922,8026,6111,7150,7646,8136,7551,8078,7983,8144,8038,8085,7158,7895,7661,8041,7869,809 9,6140,7924,8028,4087,7667,7899,7161,7991,8090,8042,8086,7670,8101,7911,7928,8049,7162,76 62,6127,7870,8089,7669,8044,8015,8160,7615,7901,7995,7135,8102,4091,8050,8105,8131,7915,7 673,8023,6135,8092,7902,7997,7164,8133,8106,8052,7674,7917,8113,8134,7923,8027,8108,7998, 8079,7151,8039,7807,8056,6139,7647,8114,4093,7918,8137,7676,8029,7925,8138,8087,7159,804 3,8030,7926,8116,8145,8091,8140,7929,8045,8120,7663,6141,7871,8103,8146,7163,8051,7930,76 71,8093,8046,7903,8161,8053,8107,4094,8162,8148,8094,7932,8109,8135,7165,8054,7999,8115,7 675,8057,6142,8152,7919,8110,8164,8139,8058,7677,8117,8141,8168,8060,8118,8031,7927,7166, 8176,7678,8147,8121,7931,8142,8122,8047,8149,8150,8095,4095,8163,7933,8124,8055,8153,816 5,6143,8154,8111,8059,8166,7934,7679,7167,8156,8169,8119,8170,8061,8143,8062,8177,8123,81 72,8178,8125,8151,8126,8155,8180,8167,8184,7935,8157,8171,8158,8173,8127,8179,8181,8063,8 174,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191]
›APPENDIX · 18 of 21
Sequence Group 3: Z3_8192
[0,1,2,7,3,8,14,27,4,13,16,31,19,36,38,84,5,15,17,35,22,42,52,89,25,51,46,97,63,106,11 3,182,6,20,24,44,26,50,57,99,32,61,65,107,78,120,126,201,37,67,82,124,87,135,145,215,96,147,16 0,243,166,257,281,408,9,21,29,60,33,64,77,115,39,83,69,127,92,139,153,224,49,80,95,146,101,15 6,165,251,111,168,186,269,200,288,307,454,59,98,109,164,122,176,194,284,133,195,214,299,227, 325,343,494,150,222,247,330,254,344,371,528,275,378,402,556,423,581,627,877,18,28,34,79,43,8 6,90,151,54,94,102,163,112,175,179,283,62,103,114,177,125,193,211,301,138,212,223,319,249,33 9,364,516,71,118,134,199,140,213,230,331,161,245,255,347,274,377,394,553,178,266,285,385,30 0,417,426,578,327,440,475,615,501,649,725,878,75,136,155,233,173,252,273,382,183,277,291,40 7,308,425,452,603,208,304,320,437,345,468,496,662,358,504,533,690,564,738,767,1022,229,334, 352,479,387,513,538,715,422,548,579,755,616,773,842,1103,451,592,630,809,645,865,897,1175,7 20,914,951,1160,990,1235,1333,1678,23,40,45,100,55,104,116,192,56,117,129,202,142,225,236,36 2,70,130,143,240,157,248,263,363,167,261,282,400,305,421,432,577,73,154,169,242,188,267,286, 420,198,297,309,434,323,466,486,643,197,321,336,463,357,500,518,694,389,542,566,737,589,764, 816,1081,85,181,190,293,206,316,335,456,217,342,351,495,372,527,547,733,279,365,388,532,40 9,562,588,760,443,597,635,805,667,862,901,1147,313,404,436,574,462,613,638,845,491,655,677, 874,726,931,966,1211,535,724,742,952,761,992,940,1257,826,1074,1107,1355,1121,1459,1518,17 55,91,203,209,356,268,376,392,541,295,397,412,569,442,601,634,849,311,439,461,602,478,641,6 70,884,505,682,713,921,757,960,1019,1270,361,467,484,668,517,703,745,943,567,746,769,1014,8 30,985,1092,1361,611,797,858,1075,885,1117,1154,1426,932,1168,1165,1503,1260,1547,1599,192 8,403,502,543,750,599,772,814,1037,636,847,867,1110,912,1128,1163,1452,672,893,945,1150,967, 1172,1264,1552,1034,1284,1322,1613,1390,1696,1745,2117,734,955,1008,1267,1089,1273,1376, 1634,1101,1365,1433,1725,1488,1791,1886,2269,1129,1463,1535,1824,1577,1902,1857,2323,166 7,1977,2030,2480,2145,2568,2678,3005,30,48,58,110,66,131,144,231,72,148,159,239,172,259,264, 413,74,170,180,258,191,317,328,450,218,329,355,492,375,520,545,754,76,187,204,322,220,353,3 68,510,232,381,395,551,416,582,608,775,246,406,430,595,457,631,652,836,469,644,684,890,689, 920,957,1340,119,219,228,373,241,396,414,572,271,433,445,622,474,658,680,853,292,449,483,64 8,508,687,697,905,531,699,712,962,796,996,1062,1363,312,507,523,708,558,743,751,977,587,792, 820,1033,873,1084,1112,1437,621,841,889,1115,936,1143,1218,1492,1006,1228,1288,1557,1326, 1626,1705,2102,123,238,260,427,289,446,477,664,306,488,511,702,536,719,728,970,341,526,557, 731,585,785,813,1023,617,832,869,1098,907,1133,1190,1441,369,571,606,818,654,861,857,1136,6 74,895,916,1178,981,1222,1248,1564,716,938,1000,1239,1027,1305,1329,1638,1070,1358,1405,1 729,1499,1802,1892,2278,391,626,657,900,695,928,982,1231,781,1004,1046,1316,1053,1336,138 3,1689,799,1048,1067,1372,1138,1401,1474,1788,1203,1495,1532,1828,1595,1936,1996,2352,834, 1156,1185,1445,1249,1507,1543,1869,1292,1586,1644,1973,1711,2038,2130,2512,1412,1653,173 6,2060,1814,2160,2203,2654,1876,2243,2315,2718,2421,2834,2985,3484,141,272,298,489,337,52 1,552,763,349,563,593,790,624,825,881,1193,383,610,663,851,686,925,909,1210,705,947,989,128 1,1041,1309,1347,1671,460,676,707,924,780,975,1011,1319,789,1042,1060,1351,1088,1387,1424, 1765,801,1078,1124,1420,1199,1471,1522,1835,1241,1573,1591,1940,1648,2004,2079,2459,471,7 78,784,1029,804,1051,1095,1398,837,1142,1181,1456,1224,1510,1582,1917,997,1197,1253,1528,1 294,1616,1657,1984,1394,1663,1739,2064,1818,2153,2195,2640,1056,1301,1368,1620,1416,1719, 1776,2094,1484,1795,1847,2187,1910,2251,2343,2760,1539,1880,1954,2306,2026,2372,2453,286 6,2109,2491,2557,2952,2616,3109,3149,3832,480,808,822,1186,972,1215,1245,1568,1015,1277,1 312,1630,1379,1685,1759,2087,1064,1344,1409,1699,1448,1781,1851,2177,1514,1898,1840,2227, 1992,2332,2413,2803,1206,1430,1467,1807,1561,1862,1946,2286,1609,1958,2018,2381,2072,243 3,2524,2934,1715,2045,2124,2471,2210,2580,2628,3065,2262,2704,2747,3199,2848,3272,3331,36 83,1298,1481,1605,1965,1681,2011,2052,2442,1750,2138,2169,2548,2234,2592,2730,3129,1769,2 219,2295,2692,2401,2774,2787,3300,2503,2883,2915,3359,3027,3524,3596,4162,1921,2364,2392, 2817,2536,2897,2971,3420,2604,3047,3085,3560,3225,3639,3888,4347,2666,3174,3247,3730,338 7,3776,3946,4458,3454,4014,4085,4599,4244,4770,5021,5420,10,41,68,149,88,162,196,310,105,1 84,216,340,244,374,386,609,121,207,226,366,270,405,459,628,294,453,431,660,514,696,722,961, 137,253,287,418,302,448,482,669,346,503,525,700,586,752,774,1018,379,534,600,766,623,802,84 0,1057,656,848,886,1137,906,1173,1236,1567,174,262,324,497,354,519,580,732,393,605,540,779, 642,815,864,1083,441,594,651,843,678,875,904,1159,714,915,968,1207,1013,1259,1307,1675,493, 665,706,899,756,937,994,1247,793,999,1055,1286,1090,1352,1403,1768,854,1076,1148,1371,116 7,1406,1473,1844,1227,1494,1549,1905,1602,1961,2057,2542,235,318,360,591,411,620,632,859,4 65,647,683,894,718,934,949,1243,509,688,727,941,770,991,1043,1293,810,1047,1080,1335,1155, 1392,1458,1815,550,744,798,1010,819,1050,1102,1374,891,1141,1169,1414,1223,1490,1530,1901, 946,1198,1252,1509,1289,1588,1610,1952,1356,1643,1723,2033,1782,2105,2257,2545,570,807,87 0,1111,930,1161,1219,1502,964,1230,1265,1563,1310,1606,1674,2008,1036,1296,1339,1637,1410, 1708,1775,2127,1443,1789,1856,2189,1924,2284,2341,2791,1097,1378,1425,1733,1513,1811,186 6,2237,1600,1889,1956,2318,2035,2355,2483,2923,1669,1982,2062,2424,2097,2521,2577,3034,22 48,2607,2669,3011,2736,3126,3278,3795,280,398,424,675,470,693,736,986,476,739,783,1020,828, 1085,1116,1451,544,787,831,1125,880,1151,1191,1454,910,1188,1240,1546,1300,1596,1623,1949, 559,868,917,1134,976,1201,1255,1592,1005,1279,1313,1628,1349,1702,1749,2090,1001,1341,13 84,1698,1440,1778,1822,2192,1520,1873,1926,2281,1980,2338,2436,2886,614,956,979,1272,1032, 1328,1382,1679,1061,1399,1421,1772,1477,1841,1885,2272,1233,1462,1517,1853,1571,1914,197 4,2326,1651,1995,2075,2416,2141,2518,2586,2993,1324,1556,1633,1945,1694,2027,2082,2486,17 62,2115,2163,2539,2260,2634,2695,3093,1860,2254,2289,2672,2329,2740,2651,3163,2455,2872,2 926,3309,2948,3473,3565,3908,637,1025,1039,1436,1205,1487,1527,1870,1276,1542,1575,1933,1 647,2001,2069,2494,1317,1641,1692,2005,1732,2084,2148,2554,1794,2171,2233,2619,2321,2686, 2783,3183,1447,1706,1746,2142,1820,2213,2298,2657,1930,2301,2346,2777,2456,2727,2905,331 7,2023,2398,2509,2877,2559,2945,3000,3424,2637,3023,3019,3538,3166,3607,3678,4140,1553,17 85,1878,2303,1999,2349,2430,2814,2078,2489,2527,2931,2601,2960,3016,3463,2151,2571,2660,2 997,2698,3031,3171,3613,2811,3205,3261,3700,3367,3818,3894,4381,2275,2675,2767,3179,2900, 3188,3345,3736,2920,3326,3434,3863,3513,3960,4093,4559,2963,3479,3585,4000,3650,4111,405 0,4630,3782,4206,4274,4814,4414,4914,5049,5398,332,435,487,709,529,791,835,1105,555,852,88 3,1123,926,1180,1194,1578,565,922,953,1176,984,1332,1360,1665,1066,1367,1432,1763,1483,182 7,1882,2312,575,971,1028,1345,1071,1428,1466,1805,1108,1498,1534,1894,1585,1964,2016,2358, 1146,1559,1619,1989,1684,2067,2106,2468,1712,2091,2174,2565,2184,2613,2681,3286,748,1069, 1094,1478,1130,1538,1581,1942,1213,1624,1655,2047,1721,2123,2166,2500,1269,1661,1742,209 9,1801,2181,2201,2589,1848,2205,2230,2689,2395,2744,2855,3322,1321,1798,1833,2224,1912,22 92,2309,2713,1970,2389,2445,2808,2533,2891,2937,3440,2042,2477,2562,2940,2645,2988,3101,3 518,2763,3118,3208,3618,3264,3719,3838,4364,762,1120,1182,1614,1261,1658,1728,2135,1304,1 752,1809,2208,1864,2245,2265,2701,1395,1837,1908,2268,1968,2378,2427,2794,2039,2462,2530, 2912,2595,2966,3058,3443,1469,1937,2014,2439,2112,2515,2506,2974,2156,2574,2610,3039,272 1,3104,3146,3629,2240,2648,2753,3133,2797,3233,3269,3742,2869,3314,3392,3869,3534,3974,40 97,4570,1524,2054,2120,2583,2198,2631,2724,3121,2369,2757,2828,3250,2842,3281,3354,3812,2 404,2831,2863,3340,2977,3381,3498,3954,3078,3529,3580,4008,3672,4146,4228,4661,2465,3008, 3050,3448,3154,3543,3602,4065,3213,3661,3747,4198,3843,4282,4397,4852,3401,3759,3875,430 6,3988,4431,4486,5006,4071,4531,4619,5091,4736,5218,5378,5901,824,1216,1282,1756,1388,183 1,1896,2335,1417,1918,1987,2387,2050,2450,2551,3062,1505,2020,2133,2497,2180,2625,2598,30 90,2216,2663,2733,3196,2820,3238,3295,3789,1688,2159,2222,2622,2366,2710,2770,3255,2384,2 823,2852,3303,2894,3364,3415,3920,2407,2880,2956,3410,3073,3493,3571,4022,3138,3644,3667, 4154,3753,4236,4331,4791,1716,2361,2375,2800,2410,2837,2908,3378,2474,2982,3042,3468,311 3,3549,3655,4127,2750,3070,3158,3574,3216,3706,3765,4214,3373,3770,3880,4315,3994,4422,44 75,4992,2845,3230,3336,3711,3406,3857,3934,4356,3507,3967,4036,4467,4119,4540,4650,5137,3 591,4079,4176,4610,4266,4681,4779,5253,4372,4826,4902,5342,4965,5524,5571,6216,1738,2418, 2448,3053,2707,3098,3141,3635,2780,3191,3242,3725,3350,3807,3914,4339,2859,3291,3395,382 6,3459,3940,4042,4450,3554,4105,4028,4512,4222,4639,4724,5184,3081,3429,3488,3980,3624,40 56,4168,4579,3695,4184,4258,4692,4323,4747,4864,5323,3849,4290,4389,4802,4494,4926,4979,5 480,4551,5079,5122,5619,5234,5693,5750,6084,3221,3504,3689,4192,3801,4252,4298,4758,3900, 4406,4439,4887,4522,4940,5107,5547,3926,4503,4590,5064,4713,5153,5169,5721,4840,5269,530 4,5776,5440,5935,6005,6505,4133,4670,4701,5202,4875,5288,5362,5837,4952,5460,5504,5970,56 44,6044,6268,6660,5034,5595,5668,6125,5808,6170,6320,6752,5867,6374,6438,6866,6579,6995,7 168,7433,11,47,81,189,108,205,265,410,132,250,290,447,326,490,506,794,152,278,303,481,359,5 39,604,823,390,598,568,860,673,908,939,1229,171,338,380,554,401,590,633,872,455,659,685,913, 765,974,1003,1299,498,698,782,993,811,1035,1082,1346,856,1091,1140,1442,1166,1485,1562,19 25,221,348,428,653,464,679,759,948,515,788,710,1007,839,1054,1114,1377,583,776,850,1087,88 2,1127,1162,1468,929,1174,1242,1525,1295,1587,1642,2043,646,866,918,1157,983,1204,1271,157 2,1026,1275,1343,1618,1389,1697,1747,2139,1104,1369,1457,1710,1479,1751,1823,2220,1548,18 45,1906,2285,1962,2342,2443,2972,314,419,473,771,546,806,827,1109,612,844,888,1153,933,120 0,1217,1569,666,892,944,1209,998,1266,1330,1625,1049,1334,1373,1676,1464,1734,1806,2191,7 23,963,1030,1290,1058,1338,1400,1714,1144,1449,1482,1760,1544,1843,1888,2279,1212,1515,15 76,1861,1621,1948,1972,2333,1701,2007,2093,2417,2155,2496,2662,2976,747,1040,1122,1411,11 92,1472,1541,1855,1234,1551,1593,1922,1646,1969,2037,2391,1323,1632,1680,2000,1754,2076,2 146,2522,1790,2164,2231,2588,2302,2691,2752,3245,1396,1720,1771,2104,1868,2185,2244,2642, 1960,2267,2336,2726,2420,2764,2904,3390,2034,2365,2449,2839,2487,2950,3013,3515,2653,304 4,3114,3489,3186,3615,3774,4278,370,522,560,876,619,898,954,1263,625,959,1012,1302,1068,13 80,1419,1799,717,1017,1073,1431,1131,1461,1508,1803,1170,1500,1566,1904,1635,1957,1985,23 31,735,1118,1179,1438,1251,1519,1580,1953,1287,1611,1649,1991,1690,2071,2119,2481,1283,16 83,1727,2065,1786,2152,2196,2594,1874,2253,2308,2687,2359,2746,2853,3352,800,1225,1254,16 01,1315,1666,1724,2046,1354,1743,1767,2144,1826,2217,2264,2680,1554,1810,1872,2229,1929,2 296,2356,2735,2015,2376,2464,2830,2534,2943,3021,3466,1662,1913,1997,2325,2061,2411,2472, 2910,2131,2508,2558,2968,2665,3076,3143,3576,2238,2659,2697,3116,2738,3193,3095,3652,287 4,3338,3397,3809,3422,3972,4061,4378,833,1306,1327,1784,1523,1839,1881,2250,1607,1897,193 4,2313,2012,2385,2461,2918,1656,2003,2058,2388,2101,2475,2543,2987,2167,2567,2636,3057,27 32,3131,3240,3674,1797,2073,2116,2537,2194,2615,2706,3099,2311,2709,2755,3232,2878,3178,3 371,3820,2408,2812,2936,3341,2990,3417,3477,3922,3080,3502,3497,4038,3657,4101,4172,4596, 1909,2157,2255,2715,2379,2761,2847,3274,2467,2913,2953,3402,3040,3432,3495,3962,2546,300 3,3103,3472,3144,3509,3663,4107,3267,3696,3757,4190,3865,4302,4366,4821,2683,3123,3220,36 68,3366,3680,3841,4220,3385,3824,3932,4341,4016,4427,4546,4994,3436,3978,4087,4469,4142,4 566,4509,5051,4264,4656,4720,5221,4854,5315,5432,5756,438,576,639,923,692,1021,1077,1404, 729,1096,1135,1427,1187,1493,1512,1938,741,1184,1221,1489,1258,1670,1703,2031,1357,1707,1 780,2134,1836,2202,2261,2723,753,1246,1311,1687,1366,1773,1816,2178,1407,1852,1890,2274,1 944,2345,2400,2769,1453,1919,1978,2374,2049,2452,2502,2893,2080,2484,2573,2998,2585,3055, 3128,3786,969,1362,1393,1829,1435,1893,1941,2322,1533,1988,2019,2431,2088,2517,2564,2928, 1597,2028,2113,2493,2173,2579,2603,3026,2226,2606,2633,3136,2809,3198,3319,3822,1660,217 0,2209,2627,2291,2700,2717,3164,2353,2805,2861,3266,2964,3357,3408,3938,2429,2902,2995,34 11,3086,3461,3587,4020,3218,3604,3702,4115,3763,4210,4312,4805,988,1422,1497,1976,1590,20 22,2098,2528,1639,2126,2182,2612,2241,2650,2671,3151,1741,2215,2288,2674,2348,2789,2844,3 249,2423,2885,2958,3383,3032,3441,3540,3944,1819,2319,2397,2856,2505,2942,2932,3447,2549, 3010,3049,3520,3169,3593,3637,4125,2643,3091,3206,3620,3254,3728,3768,4226,3333,3814,388 6,4345,4032,4441,4553,5001,1877,2440,2514,3018,2597,3071,3173,3609,2781,3211,3288,3746,33 02,3780,3853,4294,2819,3293,3327,3836,3452,3882,3996,4420,3562,4026,4081,4473,4166,4605,4 679,5081,2888,3482,3531,3950,3641,4044,4096,4525,3708,4156,4234,4652,4321,4729,4835,5256, 3898,4246,4354,4754,4454,4871,4918,5406,4533,4962,5041,5472,5156,5589,5737,6185,1063,153 7,1615,2128,1730,2206,2277,2743,1764,2299,2368,2798,2437,2870,2980,3545,1858,2405,2525,29 21,2576,3067,3036,3573,2618,3108,3184,3691,3279,3734,3797,4270,2056,2555,2624,3063,2778,3 159,3227,3751,2795,3283,3312,3803,3362,3859,3916,4393,2822,3347,3427,3910,3556,3990,4067, 4482,3626,4136,4160,4612,4240,4688,4777,5197,2086,2772,2786,3259,2826,3298,3376,3877,289 6,3457,3525,3966,3598,4048,4150,4583,3201,3551,3646,4075,3713,4196,4250,4665,3871,4260,43 60,4761,4460,4861,4909,5392,3307,3723,3830,4202,3904,4333,4408,4795,4010,4433,4497,4899,4 575,4972,5071,5515,4091,4538,4627,5031,4715,5102,5189,5622,4812,5232,5301,5706,5367,5854, 5891,6465,2108,2836,2864,3533,3156,3582,3631,4131,3235,3685,3740,4216,3847,4288,4385,478 6,3321,3791,3892,4308,3956,4412,4501,4890,4054,4561,4488,4945,4674,5059,5145,5559,3567,39 28,3984,4446,4121,4516,4621,5011,4186,4634,4706,5112,4768,5166,5266,5687,4327,4738,4830,5 210,4928,5329,5381,5814,4984,5457,5501,5939,5604,6001,6055,6349,3717,4004,4180,4643,4284, 4697,4745,5176,4374,4845,4880,5293,4955,5340,5486,5874,4399,4935,5019,5446,5132,5530,554 2,6026,5245,5638,5671,6077,5779,6220,6280,6711,4588,5094,5125,5574,5280,5653,5725,6132,53 53,5795,5831,6248,5959,6312,6509,6843,5418,5915,5980,6387,6102,6421,6551,6923,6159,6602,6 651,7020,6773,7126,7280,7500,237,530,704,1100,817,1149,1278,1652,902,1237,1350,1737,1446, 1832,1865,2402,978,1318,1385,1812,1529,1916,2053,2446,1604,2041,1981,2519,2188,2600,2656, 3134,1044,1476,1583,1950,1629,2024,2110,2540,1758,2162,2212,2609,2351,2720,2766,3237,184 9,2236,2382,2749,2434,2825,2899,3310,2511,2916,2992,3450,3029,3511,3617,4129,1195,1504,16 93,2149,1777,2199,2339,2677,1884,2394,2247,2775,2478,2850,2947,3355,2009,2371,2499,2907,2 561,2969,3024,3486,2639,3045,3148,3569,3228,3654,3732,4276,2137,2531,2621,3014,2729,3088, 3194,3633,2806,3203,3305,3698,3369,3805,3884,4395,2929,3343,3470,3834,3500,3890,3992,449 2,3600,4024,4103,4568,4178,4636,4752,5285,1415,1672,1793,2362,1932,2426,2458,2939,2068,24 90,2570,3006,2647,3083,3111,3628,2175,2582,2668,3096,2758,3189,3284,3710,2841,3290,3348,3 778,3480,3867,3970,4456,2271,2703,2815,3223,2858,3296,3388,3839,3001,3455,3506,3902,3594, 4018,4077,4564,3106,3553,3642,4046,3704,4158,4188,4625,3811,4232,4337,4722,4416,4807,497 7,5290,2316,2833,2961,3404,3075,3491,3589,4034,3139,3605,3665,4123,3738,4182,4272,4695,32 71,3715,3784,4224,3896,4319,4403,4833,3948,4424,4507,4904,4592,5009,5069,5545,3380,3845,3 918,4352,4052,4452,4520,4957,4174,4548,4632,5044,4726,5084,5224,5678,4268,4663,4756,5158, 4798,5264,5326,5785,4969,5356,5423,5763,5492,5871,6008,6434,1558,1900,1966,2552,2083,259 1,2684,3181,2095,2694,2784,3243,2875,3360,3413,3958,2258,2792,2881,3431,2979,3475,3542,39 64,3037,3536,3622,4099,3721,4170,4204,4623,2294,2955,3052,3445,3161,3558,3648,4164,3215,3 687,3744,4212,3799,4310,4370,4788,3210,3787,3855,4304,3942,4410,4465,4906,4063,4529,4594, 5004,4659,5066,5171,5641,2414,3124,3168,3676,3262,3766,3851,4280,3315,3878,3912,4401,399 8,4490,4544,4996,3611,3976,4059,4505,4134,4581,4654,5054,4242,4677,4772,5148,4847,5261,53 34,5744,3761,4113,4218,4616,4300,4717,4782,5226,4387,4819,4873,5282,4982,5387,5449,5841,4 514,4974,5014,5426,5056,5495,5403,5904,5192,5628,5681,6033,5703,6178,6252,6523,2469,3252, 3276,3936,3563,4012,4073,4527,3681,4095,4138,4603,4238,4686,4765,5237,3749,4230,4296,469 0,4349,4784,4856,5299,4429,4883,4950,5370,5046,5437,5539,5921,3952,4317,4368,4849,4462,49 31,5024,5409,4601,5026,5074,5533,5195,5483,5659,6041,4710,5130,5250,5632,5307,5699,5753,6 136,5389,5772,5769,6232,5908,6288,6345,6695,4109,4418,4535,5029,4683,5076,5163,5568,4775, 5229,5272,5684,5351,5712,5766,6166,4859,5318,5412,5747,5452,5782,5911,6292,5565,5942,599 1,6361,6088,6456,6514,6871,4999,5429,5521,5918,5656,5925,6066,6391,5675,6051,6144,6487,62 08,6560,6656,6989,5715,6181,6272,6593,6324,6675,6626,7040,6425,6741,6794,7153,6894,7218,7 296,7490,1717,1993,2121,2630,2223,2801,2889,3394,2282,2924,2984,3425,3068,3522,3547,4144, 2305,3060,3119,3516,3176,3772,3816,4262,3324,3828,3930,4391,4006,4471,4542,5039,2328,315 3,3257,3793,3334,3924,3982,4443,3399,4030,4083,4555,4152,4641,4704,5086,3464,4117,4200,46 72,4286,4763,4809,5208,4325,4793,4885,5312,4897,5364,5435,6016,2712,3329,3374,4002,3438,4 089,4148,4614,3578,4208,4248,4740,4335,4828,4878,5242,3670,4256,4362,4800,4437,4894,4916, 5337,4499,4921,4947,5443,5127,5498,5610,6048,3755,4435,4480,4943,4577,5016,5036,5469,464 7,5120,5179,5562,5277,5647,5690,6147,4733,5216,5309,5696,5395,5740,5847,6212,5518,5861,59 45,6296,5994,6378,6469,6854,2741,3418,3527,4194,3659,4254,4343,4842,3727,4376,4448,4923,4 518,4967,4987,5454,3873,4484,4572,4989,4645,5109,5161,5550,4731,5200,5274,5665,5345,5718, 5805,6151,3986,4608,4699,5174,4816,5258,5248,5728,4866,5320,5359,5788,5475,5851,5888,630 4,4960,5401,5509,5877,5553,5966,5998,6395,5625,6037,6106,6491,6228,6569,6665,7002,4069,47 49,4823,5331,4911,5384,5477,5864,5099,5512,5583,5984,5598,6012,6073,6451,5135,5586,5616,6 062,5731,6099,6197,6555,5824,6224,6264,6597,6341,6700,6762,7059,5205,5760,5798,6155,5894, 6236,6284,6636,5949,6332,6400,6736,6473,6800,6883,7182,6114,6408,6496,6816,6583,6906,694 1,7272,6641,6971,7033,7320,7105,7388,7480,7719,2867,3583,3693,4383,3861,4477,4557,5061,39 06,4585,4668,5117,4742,5187,5296,5811,4040,4708,4838,5240,4892,5376,5348,5834,4933,5415,5 489,5932,5577,5973,6023,6430,4292,4868,4938,5373,5097,5466,5527,5987,5114,5580,5607,6030, 5650,6080,6128,6532,5140,5635,5709,6121,5821,6193,6256,6607,5881,6316,6337,6705,6404,676 8,6832,7139,4329,5089,5104,5556,5143,5592,5662,6095,5213,5734,5792,6174,5857,6240,6328,66 85,5506,5818,5898,6260,5952,6366,6412,6747,6091,6417,6500,6821,6588,6900,6935,7264,5601,5 963,6059,6370,6117,6482,6541,6849,6205,6564,6617,6929,6680,6977,7052,7345,6276,6646,6721, 7027,6789,7072,7132,7405,6860,7160,7211,7461,7249,7552,7573,7841,4358,5150,5182,5801,546 3,5844,5884,6308,5536,5928,5977,6383,6069,6447,6528,6838,5613,6019,6110,6460,6162,6546,66 21,6917,6244,6670,6612,6959,6757,7046,7098,7370,5828,6140,6189,6574,6300,6631,6716,7008,6 357,6726,6784,7078,6827,7112,7189,7451,6478,6805,6877,7146,6947,7226,7256,7530,6983,7312, 7336,7595,7396,7630,7654,7792,5956,6201,6353,6731,6443,6778,6810,7119,6518,6888,6912,720 4,6965,7233,7328,7562,6537,6953,7014,7304,7092,7353,7362,7642,7175,7414,7442,7667,7510,77 33,7762,7936,6690,7065,7085,7379,7196,7424,7470,7692,7241,7520,7541,7747,7607,7776,7858,7 981,7288,7584,7618,7808,7680,7824,7876,8006,7706,7895,7915,8033,7957,8064,8098,8138,12,53, 93,234,128,256,350,537,158,333,384,584,429,640,661,1038,185,367,399,629,472,701,795,1072,5 12,786,740,1119,879,1177,1220,1579,210,444,499,721,524,777,829,1132,596,863,896,1183,995,12 62,1297,1664,650,911,1024,1285,1059,1342,1397,1722,1113,1408,1470,1838,1501,1891,1983,240 6,276,458,561,855,607,887,987,1232,671,1031,927,1303,1093,1364,1439,1761,768,1009,1106,140 2,1145,1455,1496,1871,1208,1511,1594,1939,1659,2010,2077,2541,846,1126,1196,1491,1274,155 0,1631,1994,1331,1636,1718,2048,1774,2140,2200,2652,1423,1753,1854,2158,1883,2204,2290,27 42,1963,2314,2386,2816,2451,2879,2991,3530,415,549,618,1002,711,1052,1079,1429,803,1099,1 152,1486,1214,1545,1565,1990,871,1158,1226,1555,1291,1627,1704,2055,1359,1709,1757,2118,1 863,2186,2270,2711,942,1250,1337,1654,1370,1713,1787,2161,1475,1846,1887,2214,1959,2310,2 363,2807,1560,1927,1998,2334,2051,2432,2460,2871,2147,2501,2599,2962,2670,3043,3214,3532, 973,1348,1450,1800,1536,1875,1955,2327,1584,1967,2021,2403,2081,2457,2535,2933,1695,2066, 2122,2492,2207,2581,2658,3072,2249,2679,2756,3137,2835,3244,3306,3802,1783,2168,2228,261 1,2340,2702,2768,3192,2447,2796,2873,3280,2965,3318,3460,3943,2532,2906,2996,3393,3033,35 05,3568,4064,3204,3601,3671,4039,3743,4167,4328,4836,485,681,730,1139,812,1164,1238,1622, 821,1244,1308,1668,1381,1766,1808,2263,935,1314,1386,1825,1460,1859,1915,2266,1506,1907,1 986,2380,2070,2444,2476,2868,958,1444,1516,1834,1603,1931,2002,2441,1650,2040,2085,2482,2 132,2575,2629,3028,1645,2125,2176,2566,2246,2667,2716,3145,2347,2779,2840,3241,2898,3299, 3407,3905,1045,1574,1612,2029,1686,2107,2172,2547,1731,2197,2225,2655,2293,2739,2793,323 1,1975,2273,2344,2754,2409,2829,2895,3289,2510,2917,3009,3384,3084,3501,3577,4017,2100,23 93,2488,2860,2563,2957,3017,3467,2644,3056,3107,3523,3217,3634,3699,4126,2762,3212,3251,3 673,3292,3748,3651,4203,3428,3893,3949,4363,3973,4524,4611,4939,1086,1673,1700,2242,1935, 2307,2357,2776,2036,2373,2419,2849,2507,2927,3007,3474,2092,2498,2560,2930,2608,3022,309 2,3544,2682,3117,3187,3614,3285,3688,3796,4225,2259,2578,2626,3087,2714,3165,3258,3656,28 43,3260,3308,3788,3435,3735,3925,4373,2951,3368,3492,3895,3546,3968,4029,4474,3636,4053,4 047,4589,4209,4653,4727,5157,2390,2673,2782,3268,2922,3316,3403,3829,3012,3469,3510,3955, 3597,3985,4045,4513,3094,3561,3660,4023,3701,4058,4215,4660,3823,4249,4311,4746,4419,486 0,4925,5380,3234,3679,3777,4221,3919,4231,4396,4776,3939,4379,4485,4900,4567,4986,5106,55 48,3987,4530,4637,5028,4696,5126,5070,5605,4822,5217,5279,5764,5411,5850,5954,6239,573,75 8,838,1202,903,1320,1391,1792,950,1413,1465,1821,1531,1899,1920,2422,965,1521,1570,1895,1 617,2111,2150,2529,1735,2154,2239,2646,2304,2722,2788,3277,980,1598,1677,2129,1744,2232,2 280,2696,1796,2324,2367,2802,2428,2882,2944,3323,1850,2399,2470,2914,2550,2999,3048,3449, 2584,3030,3122,3555,3135,3612,3684,4340,1256,1740,1779,2297,1830,2370,2425,2857,1947,247 9,2513,2978,2596,3064,3115,3483,2025,2526,2623,3041,2690,3130,3152,3584,2751,3157,3185,36 92,3365,3754,3872,4377,2096,2688,2731,3177,2821,3253,3270,3720,2892,3358,3416,3821,3521,3 911,3959,4491,2975,3458,3552,3963,3643,4011,4139,4573,3773,4155,4255,4667,4316,4766,4872, 5363,1280,1817,1903,2463,2013,2516,2605,3077,2074,2635,2699,3162,2765,3202,3222,3707,219 3,2737,2818,3226,2887,3344,3400,3804,2967,3439,3514,3935,3588,3993,4088,4496,2283,2854,29 41,3412,3054,3499,3490,3999,3100,3566,3606,4068,3726,4145,4189,4678,3195,3647,3762,4173,3 810,4283,4322,4781,3887,4369,4442,4905,4584,5000,5113,5557,2354,2989,3061,3575,3147,3627, 3729,4161,3335,3769,3844,4301,3856,4334,4407,4851,3372,3848,3881,4390,4003,4436,4547,498 1,4112,4578,4631,5033,4721,5167,5239,5634,3444,4033,4080,4502,4191,4595,4648,5085,4261,47 09,4790,5212,4881,5289,5394,5796,4453,4803,4913,5314,5015,5428,5476,5931,5093,5519,5596,5 990,5705,6094,6223,6606,1375,1951,2044,2638,2179,2725,2804,3297,2221,2832,2909,3353,2983, 3426,3537,4094,2330,2949,3074,3478,3127,3623,3592,4124,3170,3664,3741,4243,3835,4289,435 1,4827,2556,3105,3175,3621,3332,3716,3781,4307,3351,3837,3868,4357,3917,4413,4470,4953,33 77,3901,3979,4464,4106,4541,4617,5042,4177,4691,4716,5172,4796,5249,5336,5743,2590,3328,3 342,3815,3382,3854,3929,4430,3451,4009,4074,4519,4149,4600,4703,5144,3756,4102,4197,4626, 4265,4751,4808,5225,4425,4817,4919,5319,5020,5421,5467,5919,3862,4277,4384,4757,4459,489 1,4966,5354,4562,4991,5057,5458,5136,5528,5626,6028,4642,5098,5190,5587,5275,5655,5738,61 22,5371,5775,5839,6195,5896,6325,6356,6839,2614,3391,3419,4082,3712,4132,4183,4684,3790,4 237,4295,4771,4402,4846,4944,5346,3876,4346,4447,4865,4508,4973,5062,5447,4606,5121,5048, 5502,5235,5614,5697,6067,4118,4479,4536,5007,4673,5077,5180,5566,4741,5194,5265,5664,532 8,5717,5807,6180,4886,5297,5388,5755,5484,5862,5907,6289,5540,5978,6017,6396,6107,6452,64 95,6743,4271,4556,4735,5203,4841,5257,5305,5726,4932,5404,5438,5830,5510,5873,6002,6340,4 958,5493,5575,5967,5685,6040,6053,6472,5787,6137,6164,6516,6258,6634,6684,7039,5149,5646, 5676,6079,5819,6149,6211,6561,5885,6274,6305,6659,6415,6713,6874,7148,5943,6376,6432,677 4,6536,6803,6909,7209,6585,6950,6992,7284,7088,7371,7488,7655,296,691,919,1418,1065,1480, 1640,2089,1171,1589,1726,2190,1842,2300,2337,2946,1268,1691,1770,2276,1943,2396,2553,299 4,2032,2538,2473,3069,2705,3150,3207,3690,1353,1879,2006,2435,2059,2523,2620,3089,2211,26 76,2734,3160,2890,3273,3320,3794,2317,2759,2925,3304,2981,3379,3456,3864,3059,3471,3548,4 001,3586,4060,4169,4682,1540,1911,2136,2661,2235,2719,2876,3229,2360,2938,2773,3330,3025, 3405,3503,3909,2504,2911,3046,3462,3110,3526,3581,4037,3190,3603,3703,4120,3785,4207,428 7,4832,2649,3079,3172,3572,3282,3645,3752,4187,3361,3760,3860,4251,3921,4359,4438,4956,34 85,3897,4019,4388,4051,4444,4545,5053,4153,4576,4657,5129,4732,5198,5311,5825,1804,2114,2 256,2903,2415,2973,3002,3494,2572,3038,3120,3564,3200,3640,3669,4181,2693,3132,3219,3653, 3311,3745,3840,4263,3396,3846,3903,4332,4031,4421,4523,5017,2799,3256,3370,3779,3414,385 2,3941,4394,3557,4007,4055,4455,4147,4571,4629,5124,3662,4104,4195,4598,4257,4712,4743,51 86,4365,4789,4896,5283,4975,5366,5534,5827,2851,3389,3517,3957,3632,4041,4141,4587,3697,4 159,4217,4676,4291,4737,4831,5254,3827,4269,4338,4780,4449,4877,4964,5391,4500,4983,5068, 5461,5152,5563,5623,6056,3933,4400,4472,4910,4604,5012,5082,5513,4728,5110,5191,5599,528 6,5637,5767,6171,4824,5223,5317,5708,5357,5804,5859,6263,5525,5887,5946,6245,6007,6338,64 55,6815,1979,2377,2454,3102,2587,3142,3239,3737,2602,3246,3339,3798,3433,3913,3965,4511,2 785,3346,3437,3981,3535,4025,4090,4517,3595,4086,4175,4651,4275,4723,4760,5183,2824,3512, 3608,3995,3718,4110,4201,4718,3771,4241,4297,4767,4353,4869,4930,5349,3764,4342,4409,486 3,4495,4970,5025,5464,4615,5090,5155,5560,5220,5620,5720,6139,2959,3682,3724,4229,3819,43 20,4405,4837,3870,4432,4466,4961,4550,5050,5105,5551,4163,4528,4609,5065,4687,5141,5214,5 608,4799,5238,5332,5700,5407,5802,5868,6230,4314,4666,4774,5178,4858,5276,5339,5770,4948, 5377,5431,5822,5537,5913,5969,6311,5073,5531,5569,5948,5611,6010,5929,6367,5739,6127,617 3,6479,6192,6599,6663,6886,3015,3806,3831,4489,4116,4565,4624,5087,4235,4646,4693,5164,47 94,5246,5325,5778,4303,4785,4855,5251,4908,5343,5414,5836,4990,5441,5508,5899,5602,5961,6 049,6382,4506,4874,4927,5408,5023,5487,5578,5934,5160,5581,5629,6043,5741,5999,6156,6485, 5271,5682,5793,6131,5842,6190,6235,6563,5916,6254,6251,6644,6369,6692,6739,7026,4662,497 8,5096,5584,5243,5631,5714,6076,5335,5773,5810,6177,5882,6202,6249,6591,5417,5853,5937,62 33,5972,6261,6373,6696,6074,6399,6442,6754,6522,6830,6878,7166,5554,5951,6035,6380,6152,6 386,6506,6777,6168,6492,6571,6858,6627,6918,6997,7263,6204,6603,6677,6942,6720,7009,6972, 7300,6807,7066,7106,7392,7185,7439,7501,7646,2165,2485,2632,3180,2745,3356,3446,3947,281 3,3481,3541,3977,3625,4072,4098,4698,2838,3616,3675,4066,3733,4326,4371,4818,3879,4382,44 83,4949,4560,5032,5101,5593,2862,3709,3813,4348,3889,4478,4534,5003,3951,4582,4635,5116,4 707,5201,5263,5640,4015,4671,4755,5231,4844,5322,5368,5752,4882,5350,5444,5848,5455,5893, 5957,6462,3265,3885,3927,4552,3989,4640,4702,5175,4130,4762,4804,5300,4895,5386,5434,578 4,4223,4813,4922,5360,4998,5451,5473,5870,5058,5478,5505,5964,5679,6014,6112,6489,4309,49 95,5040,5499,5138,5572,5590,5986,5209,5673,5729,6071,5816,6143,6183,6575,5294,5761,5845,6 186,5923,6226,6318,6630,6031,6331,6402,6699,6445,6766,6842,7157,3294,3971,4076,4748,4211, 4810,4903,5400,4281,4936,5008,5481,5078,5522,5543,5975,4426,5045,5133,5546,5206,5661,571 1,6058,5291,5746,5813,6161,5876,6207,6283,6577,4539,5168,5260,5723,5374,5799,5790,6214,54 24,5856,5890,6267,5993,6321,6354,6707,5516,5926,6022,6343,6061,6422,6449,6781,6124,6483,6 540,6862,6642,6926,7000,7269,4620,5308,5383,5865,5470,5910,5996,6334,5652,6025,6089,6435, 6101,6458,6512,6826,5688,6092,6119,6502,6217,6533,6616,6914,6299,6638,6673,6946,6735,703 0,7079,7316,5749,6242,6277,6581,6360,6648,6688,6980,6406,6728,6785,7061,6846,7110,7176,74 10,6547,6792,6865,7124,6934,7194,7224,7482,6984,7248,7294,7519,7354,7574,7638,7822,3423,4 135,4245,4941,4415,5037,5118,5617,4461,5146,5228,5670,5303,5735,5833,6286,4593,5268,5397, 5781,5450,5905,5879,6309,5490,5940,6004,6393,6082,6426,6468,6812,4850,5427,5496,5902,564 9,5983,6038,6439,5667,6085,6109,6475,6146,6520,6557,6893,5691,6134,6199,6553,6295,6613,66 67,6955,6347,6717,6732,7035,6788,7083,7138,7381,4888,5643,5658,6064,5694,6097,6158,6530,5 758,6221,6270,6595,6327,6652,6724,7018,6020,6293,6363,6669,6409,6758,6796,7070,6526,6799, 6869,7129,6938,7190,7219,7475,6104,6419,6499,6761,6550,6855,6902,7152,6623,6922,6963,721 4,7013,7253,7310,7539,6681,6988,7048,7290,7101,7326,7375,7588,7162,7398,7434,7624,7463,76 94,7711,7914,4917,5702,5732,6279,5981,6315,6350,6710,6046,6389,6428,6770,6510,6823,6890,7 143,6116,6466,6543,6835,6589,6905,6967,7205,6655,7005,6958,7238,7075,7305,7348,7559,6302, 6567,6609,6930,6703,6975,7043,7274,6750,7053,7096,7332,7134,7359,7416,7616,6850,7115,717 1,7386,7229,7445,7469,7677,7259,7514,7533,7728,7580,7754,7773,7878,6413,6620,6746,7057,68 19,7093,7120,7365,6881,7180,7199,7427,7244,7452,7526,7702,6897,7234,7279,7507,7342,7546,7 553,7764,7404,7594,7609,7782,7662,7833,7854,7987,7022,7321,7337,7567,7421,7602,7632,7802, 7457,7670,7686,7844,7737,7866,7928,8021,7494,7720,7745,7889,7793,7902,7942,8040,7812,795 5,7971,8061,8003,8084,8111,8145,315,749,1016,1608,1189,1682,1923,2412,1325,1867,2017,2520, 2143,2641,2685,3363,1434,1971,2063,2617,2252,2771,2935,3421,2350,2919,2846,3496,3097,359 0,3649,4157,1526,2183,2320,2810,2383,2901,3004,3519,2544,3066,3125,3599,3301,3714,3767,42 73,2664,3155,3337,3750,3398,3825,3907,4350,3487,3923,4005,4498,4049,4563,4675,5154,1748,2 218,2466,3051,2569,3112,3287,3666,2708,3349,3182,3775,3453,3858,3961,4398,2884,3325,3476, 3915,3539,3983,4043,4537,3630,4062,4179,4622,4267,4711,4787,5295,3035,3508,3610,4035,373 1,4114,4227,4689,3808,4233,4344,4753,4417,4862,4929,5405,3945,4386,4521,4879,4554,4934,50 27,5494,4655,5055,5131,5564,5199,5624,5727,6213,2103,2438,2593,3313,2790,3386,3430,3953,2 954,3465,3550,4027,3638,4108,4137,4685,3082,3559,3658,4122,3758,4219,4324,4764,3850,4330, 4392,4834,4532,4912,5005,5462,3209,3694,3817,4259,3866,4336,4434,4884,4013,4510,4558,494 6,4649,5052,5108,5558,4128,4607,4694,5075,4759,5181,5211,5615,4867,5252,5352,5701,5422,57 80,5938,6215,3263,3833,3975,4451,4092,4543,4644,5067,4165,4658,4719,5151,4792,5207,5287,5 674,4313,4773,4839,5244,4937,5333,5413,5806,4985,5433,5507,5869,5582,5965,6021,6431,4428, 4893,4959,5365,5083,5456,5520,5920,5196,5544,5618,5997,5704,6032,6154,6539,5284,5648,573 3,6098,5771,6194,6246,6628,5930,6271,6329,6610,6385,6697,6802,7108,2287,2728,2827,3528,29 70,3570,3677,4213,2986,3686,3783,4279,3883,4404,4463,4997,3197,3792,3891,4481,3991,4526,4 597,5002,4057,4586,4680,5128,4778,5193,5227,5612,3236,3969,4070,4493,4193,4613,4700,5188, 4253,4744,4797,5233,4853,5327,5382,5765,4247,4843,4901,5321,4980,5419,5468,5875,5092,552 9,5588,5962,5642,6015,6111,6511,3375,4151,4199,4730,4299,4820,4898,5298,4361,4924,4954,54 10,5030,5491,5541,5955,4664,5010,5088,5503,5159,5576,5639,6006,5262,5660,5748,6090,5817,6 188,6253,6594,4815,5139,5241,5606,5316,5695,5757,6160,5396,5791,5840,6209,5941,6298,6351, 6671,5514,5936,5971,6330,6009,6390,6313,6722,6129,6501,6544,6824,6562,6925,6978,7165,344 2,4285,4318,4976,4618,5047,5100,5526,4739,5119,5165,5594,5259,5669,5745,6167,4806,5247,53 13,5672,5361,5759,5826,6225,5436,5849,5914,6282,6003,6342,6427,6737,4993,5330,5379,5820,5 465,5895,5979,6317,5591,5982,6024,6420,6133,6379,6525,6831,5692,6075,6182,6503,6227,6558, 6601,6895,6301,6619,6615,6964,6725,7003,7045,7283,5134,5425,5532,5988,5663,6029,6105,645 3,5751,6163,6196,6548,6269,6570,6614,6919,5829,6238,6319,6598,6352,6624,6729,7006,6448,67 51,6791,7056,6859,7122,7158,7395,5958,6335,6411,6733,6521,6740,6845,7074,6535,6834,6901,7 144,6951,7192,7257,7476,6572,6928,6993,7215,7028,7267,7237,7502,7100,7314,7346,7575,7411, 7613,7659,7775,2495,2865,3020,3619,3140,3800,3899,4440,3224,3931,3997,4476,4084,4574,460 2,5170,3248,4078,4143,4569,4205,4825,4870,5281,4367,4876,4971,5399,5043,5474,5538,5995,32 75,4185,4293,4848,4380,4963,5018,5448,4445,5063,5111,5552,5177,5627,5683,6036,4515,5147,5 219,5657,5302,5736,5786,6145,5338,5768,5855,6234,5866,6281,6339,6809,3705,4375,4423,5035, 4487,5115,5173,5603,4633,5230,5267,5716,5347,5800,5846,6175,4725,5278,5375,5777,5442,586 0,5883,6257,5500,5886,5912,6346,6072,6394,6486,6833,4811,5439,5482,5906,5570,5974,5989,63 68,5636,6068,6118,6446,6206,6515,6552,6904,5713,6153,6231,6554,6306,6590,6678,6954,6410,6 689,6755,7011,6795,7068,7128,7387,3739,4468,4580,5215,4714,5270,5358,5812,4783,5390,5453, 5892,5517,5927,5947,6358,4920,5488,5567,5950,5630,6054,6103,6433,5707,6138,6200,6534,626 2,6576,6645,6908,5022,5600,5680,6113,5789,6187,6179,6580,5832,6243,6275,6632,6372,6682,67 12,7017,5922,6310,6401,6701,6437,6772,6798,7077,6497,6828,6873,7147,6961,7200,7260,7479,5 095,5724,5797,6250,5878,6294,6375,6693,6047,6405,6463,6783,6474,6806,6852,7117,6081,6467, 6493,6841,6584,6870,6939,7188,6661,6957,6990,7217,7042,7287,7325,7515,6141,6605,6639,691 1,6714,6968,6999,7245,6759,7036,7082,7311,7133,7350,7402,7589,6880,7089,7151,7363,7207,74 19,7441,7649,7250,7462,7497,7674,7547,7717,7769,7906,3874,4638,4750,5393,4907,5479,5555,6 013,4951,5579,5651,6063,5722,6126,6219,6649,5072,5689,5809,6169,5858,6290,6265,6668,5897, 6323,6384,6748,6457,6776,6817,7103,5310,5838,5903,6287,6045,6364,6416,6787,6060,6459,648 1,6820,6519,6856,6891,7173,6083,6507,6566,6887,6657,6936,6981,7222,6704,7024,7038,7291,70 86,7330,7374,7565,5344,6039,6052,6441,6087,6471,6529,6867,6148,6587,6635,6921,6686,6970,7 032,7276,6397,6653,6718,6986,6763,7060,7091,7318,6863,7097,7155,7366,7210,7415,7437,7644, 6477,6769,6837,7063,6884,7140,7181,7383,6948,7195,7230,7432,7271,7466,7511,7690,6996,725 2,7299,7493,7343,7524,7561,7729,7391,7579,7608,7758,7634,7807,7819,7977,5369,6096,6120,66 40,6362,6674,6708,7021,6423,6744,6780,7071,6848,7114,7169,7378,6488,6813,6876,7125,6915,7 184,7232,7428,6974,7265,7225,7454,7323,7505,7543,7707,6664,6898,6932,7202,7015,7240,7295, 7484,7054,7302,7339,7528,7369,7551,7593,7752,7136,7355,7400,7570,7446,7619,7639,7795,747 2,7669,7685,7834,7723,7853,7869,7949,6765,6944,7050,7307,7111,7334,7358,7556,7163,7407,74 23,7604,7458,7623,7679,7814,7177,7449,7487,7664,7537,7696,7700,7861,7585,7735,7746,7875,7 783,7916,7931,8031,7278,7521,7534,7712,7599,7740,7765,7891,7628,7788,7800,7923,7840,7940, 7988,8057,7653,7827,7847,7959,7883,7967,7997,8072,7899,8009,8019,8088,8044,8105,8126,815 2,1813,2748,3167,3937,3409,4021,4239,4801,3579,4171,4355,4915,4504,5038,5080,5686,3722,43 05,4411,5013,4628,5142,5306,5730,4734,5292,5222,5803,5459,5880,5933,6344,3842,4549,4705,5 185,4769,5273,5372,5823,4942,5430,5485,5889,5633,5992,6034,6424,5060,5511,5666,6018,5719, 6086,6150,6480,5794,6165,6229,6582,6259,6625,6698,7019,4100,4591,4857,5416,4968,5471,562 1,5953,5103,5677,5523,6042,5762,6108,6191,6513,5255,5654,5783,6157,5843,6210,6255,6608,59 17,6273,6355,6666,6418,6723,6775,7107,5402,5815,5900,6247,6000,6307,6392,6709,6070,6398,6 476,6753,6524,6822,6872,7174,6176,6504,6596,6840,6618,6875,6937,7228,6687,6956,7004,7268, 7049,7303,7361,7601,4457,4829,4988,5645,5162,5710,5742,6184,5324,5774,5852,6241,5924,630 3,6326,6706,5445,5863,5944,6314,6027,6388,6461,6760,6100,6464,6508,6804,6604,6861,6924,72 08,5549,5976,6078,6414,6115,6470,6538,6844,6237,6586,6622,6882,6683,6952,6987,7266,6322,6 654,6715,6969,6756,7037,7055,7298,6825,7081,7142,7347,7186,7389,7468,7603,5597,6093,6203, 6549,6297,6611,6679,6962,6348,6691,6730,7016,6779,7051,7104,7333,6450,6764,6808,7076,687 9,7131,7179,7401,6910,7191,7236,7435,7281,7483,7509,7701,6531,6847,6892,7150,6973,7206,72 43,7459,7047,7258,7301,7498,7349,7516,7576,7749,7102,7317,7364,7548,7384,7592,7617,7785,7 465,7629,7656,7778,7682,7813,7855,7970,4669,5123,5204,5835,5341,5872,5960,6381,5355,5968, 6050,6429,6130,6517,6556,6916,5535,6057,6135,6568,6218,6600,6647,6920,6266,6643,6702,700 1,6767,7044,7064,7297,5573,6198,6278,6578,6365,6658,6719,7041,6407,6745,6782,7069,6818,71 27,7161,7380,6403,6811,6853,7123,6907,7183,7213,7436,6979,7247,7282,7481,7315,7508,7554,7 736,5698,6336,6371,6738,6444,6797,6851,7109,6484,6868,6889,7178,6940,7227,7255,7477,6694, 6927,6976,7235,7023,7275,7313,7503,7087,7324,7372,7544,7408,7591,7621,7771,6793,7010,707 3,7293,7121,7344,7376,7577,7170,7394,7420,7600,7471,7641,7665,7803,7239,7467,7485,7657,75 04,7683,7648,7823,7563,7731,7750,7863,7757,7904,7924,7991,5754,6436,6454,6903,6662,6949,6 985,7246,6742,6998,7025,7286,7084,7329,7368,7581,6786,7080,7118,7331,7149,7377,7412,7606, 7193,7425,7456,7635,7499,7661,7699,7829,6913,7130,7159,7409,7212,7447,7489,7650,7285,749 1,7512,7697,7564,7678,7742,7865,7341,7536,7587,7732,7610,7756,7774,7892,7643,7781,7780,79 19,7825,7933,7948,8028,7007,7187,7251,7492,7327,7513,7550,7710,7373,7578,7596,7751,7627,7 760,7779,7901,7413,7614,7651,7772,7666,7784,7826,7934,7709,7835,7850,7952,7879,7975,7989, 8062,7478,7658,7693,7828,7741,7830,7872,7960,7748,7868,7894,7983,7912,7999,8020,8083,776 1,7905,7929,8007,7943,8024,8014,8091,7968,8038,8048,8109,8067,8118,8128,8151,4889,5236,53 85,5909,5497,6065,6142,6542,5561,6172,6222,6565,6291,6633,6650,7029,5585,6285,6333,6629,6 377,6801,6829,7099,6490,6836,6899,7172,6945,7216,7254,7496,5609,6359,6440,6814,6498,6896, 6931,7201,6545,6960,6991,7261,7034,7306,7338,7517,6592,7012,7062,7322,7113,7367,7390,756 9,7135,7382,7426,7612,7431,7633,7660,7857,5985,6494,6527,6943,6573,6994,7031,7292,6672,70 67,7090,7356,7141,7399,7422,7583,6734,7095,7156,7385,7198,7430,7440,7622,7231,7443,7455,7 663,7535,7684,7725,7867,6790,7197,7221,7453,7273,7486,7495,7673,7309,7532,7557,7708,7598, 7738,7753,7896,7352,7572,7611,7755,7645,7770,7805,7913,7691,7810,7836,7935,7851,7956,797 8,8059,6011,6559,6637,7058,6727,7094,7145,7406,6771,7164,7203,7444,7242,7464,7473,7668,68 64,7223,7270,7474,7308,7527,7549,7703,7351,7566,7597,7744,7625,7763,7791,7897,6933,7289,7 335,7555,7393,7590,7586,7766,7417,7615,7631,7786,7675,7806,7818,7938,7460,7647,7688,7815, 7704,7843,7852,7961,7730,7864,7884,7984,7918,8001,8022,8085,6982,7360,7397,7620,7438,764 0,7676,7811,7523,7689,7715,7848,7721,7856,7874,7974,7538,7716,7727,7871,7767,7882,7909,79 98,7798,7917,7927,8008,7947,8029,8042,8094,7568,7777,7789,7898,7820,7920,7932,8016,7837,7 945,7962,8037,7979,8049,8065,8113,7886,7964,7985,8052,8004,8069,8075,8125,8017,8080,8090, 8131,8102,8140,8150,8171,6123,6676,6749,7167,6857,7220,7262,7506,6885,7277,7319,7531,735 7,7560,7605,7794,6966,7340,7403,7582,7429,7637,7626,7801,7448,7652,7681,7832,7713,7845,78 60,7969,7116,7418,7450,7636,7522,7672,7695,7849,7529,7714,7724,7862,7739,7877,7890,7993,7 540,7734,7759,7888,7797,7908,7925,8010,7816,7941,7946,8030,7963,8043,8055,8107,7137,7518, 7525,7705,7542,7718,7743,7881,7571,7768,7787,7903,7809,7921,7944,8026,7687,7796,7821,792 6,7838,7953,7965,8039,7880,7966,7986,8053,8005,8068,8074,8124,7722,7842,7870,7954,7887,79 82,7995,8058,7911,8000,8012,8073,8025,8081,8093,8134,7930,8018,8034,8089,8047,8096,8106,8 142,8060,8110,8117,8148,8122,8157,8159,8179,7154,7545,7558,7790,7671,7804,7817,7939,7698, 7831,7846,7958,7873,7973,7992,8056,7726,7859,7885,7976,7900,7996,8013,8071,7922,8023,801 1,8078,8041,8092,8101,8137,7799,7893,7907,8002,7937,8015,8032,8086,7951,8035,8046,8097,80 54,8103,8114,8147,7980,8050,8063,8108,8076,8119,8123,8155,8082,8130,8133,8161,8141,8164,8 166,8176,7839,7910,7950,8036,7972,8045,8051,8104,7990,8066,8070,8116,8079,8120,8132,8158, 7994,8077,8087,8129,8100,8135,8136,8165,8112,8143,8146,8167,8153,8172,8174,8184,8027,809 5,8099,8139,8115,8144,8149,8169,8121,8154,8156,8173,8162,8175,8180,8186,8127,8160,8163,81 77,8168,8178,8181,8187,8170,8182,8183,8188,8185,8189,8190,8191]
›APPENDIX · 19 of 21
Sequence Group 4: Q4_2048
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,41,144,28,6 9,42,516,49,74,272,160,1024,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134,384,7 6,137,82,56,27,97,39,259,84,138,145,261,29,43,98,515,88,140,30,146,1025,71,262,265,161,576,45, 100,640,1026,51,148,46,75,266,273,517,104,162,53,193,1028,152,77,164,768,268,274,518,54,83, 57,521,112,1032,135,78,289,194,85,276,522,58,168,139,99,86,60,280,89,290,529,524,196,141,104 0,101,147,176,142,530,321,31,200,90,1056,545,292,322,532,263,149,102,105,304,296,1027,163,9 2,1029,47,267,385,546,324,208,386,150,153,165,106,55,328,1088,536,577,548,1033,113,154,79,2 69,108,578,224,166,519,552,195,270,1030,641,1041,523,275,580,291,59,169,560,114,277,156,87, 1034,197,116,170,61,1042,531,525,642,281,278,526,177,293,388,1152,91,584,769,198,172,120,20 1,336,62,282,143,1036,1057,103,178,294,93,1089,644,202,592,323,392,297,770,107,180,1044,151, 209,284,1280,648,94,204,298,400,608,1058,352,325,533,155,210,305,547,300,109,1048,184,534, 1060,537,115,1031,167,225,326,306,772,157,656,329,110,117,212,171,1153,776,1090,330,1536,22 6,549,1035,538,387,308,216,416,271,279,158,337,550,672,1064,118,332,579,540,1092,389,173,11 54,121,553,199,784,179,228,338,312,1043,704,1037,390,174,554,581,1072,393,283,122,448,353,5 61,1038,203,63,340,394,1096,1281,527,582,556,181,295,1045,285,232,124,205,182,643,1156,562, 286,585,299,354,1059,211,401,1282,185,1050,396,344,586,645,1537,593,535,240,1104,206,95,32 7,564,800,402,356,307,301,417,1061,213,1049,568,1046,832,588,1160,1284,186,646,404,1288,22 7,896,594,418,302,649,771,360,539,111,1062,331,1538,214,309,1120,1091,188,449,1065,217,408, 609,596,551,650,229,159,420,310,1168,541,1052,773,610,657,333,1093,119,1066,600,339,1540,2 18,368,652,1073,230,391,313,450,542,1098,334,1296,233,555,774,175,123,1184,658,612,341,777, 220,314,1544,424,1312,395,673,583,355,1552,1216,287,183,234,1568,125,557,1094,660,616,342, 316,1068,241,778,563,1155,345,452,397,403,1105,207,1074,674,558,785,1097,432,1039,357,187, 1344,236,664,1157,624,587,780,1076,1047,705,126,242,1158,565,398,346,456,358,405,303,569,1 408,244,1100,1161,595,1106,189,566,676,1080,1051,1121,361,706,589,1063,215,786,647,348,419, 406,464,680,801,1283,362,1108,590,409,1162,570,1169,788,1285,1053,597,1067,572,1122,219,31 1,708,598,1539,601,651,421,792,802,611,1112,602,1164,410,231,688,653,1054,248,1170,369,190, 364,1095,654,1286,659,1289,335,480,315,221,370,1185,613,1600,422,425,451,1069,614,543,1124, 235,412,343,372,1664,775,317,1075,222,1172,426,453,237,1070,559,1099,1290,833,804,712,129 7,834,661,1541,808,779,1128,617,604,1186,433,720,816,1077,1217,836,347,897,1176,243,1101,66 2,1188,454,318,675,1792,618,1292,898,781,1298,1542,376,428,1078,665,736,567,1107,1081,1545, 840,625,238,1136,359,457,399,787,591,678,434,677,1159,1102,349,1313,1218,245,1109,458,666, 1300,620,1546,1082,1192,363,127,1163,191,1123,782,407,436,626,1110,571,465,681,246,707,108 4,350,1304,599,668,1113,790,1314,1553,460,1548,1220,249,682,1165,573,1125,411,803,1171,789, 1200,709,365,440,628,689,374,1166,423,1554,466,793,1345,250,371,1055,481,574,1224,413,1114, 603,366,1569,1316,1346,468,1556,655,900,805,615,1287,684,1173,710,1126,429,794,252,1129,37 3,605,1328,848,690,713,632,1320,482,806,1187,1116,427,1071,904,1291,414,1409,223,1570,1348, 663,692,835,1232,619,472,1410,455,796,1174,1177,809,714,1189,721,837,716,1130,1079,1352,86 4,810,1560,606,1601,912,1572,722,696,377,1137,435,1178,1103,817,1293,1132,319,621,1602,812, 484,1248,430,1190,1543,1576,838,667,1219,488,1294,239,378,459,622,1665,627,437,380,1547,12 99,818,1604,1315,461,1083,496,669,1193,1584,679,1138,1301,1180,724,841,1111,629,1221,351,4 67,1140,438,1194,737,251,462,442,441,1085,469,1555,247,683,1549,1666,842,1305,1302,738,155 0,1201,899,1317,670,1412,783,1115,849,1608,1793,820,1222,728,928,791,367,1196,901,1144,630, 1225,685,844,1360,633,711,1086,253,691,1306,824,1167,902,686,1127,1202,1318,1117,740,1668, 850,375,1226,444,1616,470,1347,483,1416,415,485,905,1321,795,473,1794,634,744,1131,852,960, 1204,865,693,1175,1233,1308,797,1672,1118,1228,906,1322,715,1424,1632,807,474,636,1376,69 4,254,1349,1557,717,1179,1234,575,913,1329,798,811,379,1571,1324,1133,697,1208,431,1558,60 7,1561,489,1139,866,723,486,1191,1249,1350,908,1330,1796,718,813,1181,476,856,1680,1353,83 9,1134,1141,1236,725,698,1195,914,1800,752,868,819,1354,814,439,929,1250,1573,490,1562,141 1,623,1332,1240,671,1440,1295,739,1303,1182,1361,916,1574,463,1696,843,1142,381,1356,1603, 497,1564,930,821,726,961,1413,1197,872,1145,492,1577,1223,631,1808,1203,729,1252,1362,700, 1336,443,1728,741,1414,1198,1578,1605,845,1417,920,382,1307,822,1146,851,1472,730,1377,49 8,880,1585,742,445,1227,471,635,1087,1364,932,1418,687,1551,1606,1580,1205,1319,903,1309,8 25,1256,1148,500,1229,846,1206,1667,745,826,732,1586,446,962,1310,1609,936,1323,475,853,13 78,867,637,1235,1425,1209,907,1420,1368,1610,1669,487,1617,695,1559,1264,746,828,753,1230, 854,1119,1351,857,1588,1824,504,799,1426,255,964,1380,909,1331,1325,1441,719,1237,477,159 2,915,1856,1612,638,748,944,1210,1670,1428,869,1251,1920,491,699,1618,1442,754,1326,1673,8 58,1795,1384,1563,478,968,1135,383,1355,910,1238,815,1333,976,870,1212,1473,917,1241,1432, 1633,1620,727,1575,1674,493,1253,1183,1444,873,1334,701,1565,931,1797,1634,1681,1357,756, 1143,860,499,731,1624,1363,823,1242,922,1392,1676,874,1254,1415,918,1337,1474,502,1566,93 3,1358,1257,1579,1798,1199,1147,743,1682,760,1636,1365,881,1801,494,1244,1338,702,921,144 8,501,876,1419,847,1697,1607,992,1379,447,1311,1207,1258,1149,1581,733,1684,1640,1366,134 0,827,1265,934,1802,1587,882,937,963,1369,747,1476,1421,505,1427,855,924,1231,734,829,1698, 1582,1809,1456,1381,1211,1260,1688,965,1648,1611,1804,938,884,506,1729,1150,1266,749,1589, 1422,945,966,1370,1480,755,1382,859,1429,1327,1593,940,1268,830,1619,911,1213,1590,1700,8 71,639,1385,1730,1613,888,1239,1810,479,1671,1372,946,1443,1430,750,1488,1704,1825,969,50 8,1386,861,1614,1433,1594,757,1812,970,1621,1596,919,1243,1335,1732,1622,875,1625,1675,86 2,1445,1816,1826,758,1635,948,1626,1434,1255,1712,1677,977,1272,923,1393,972,1214,1388,16 78,761,1683,877,1359,1504,1339,1245,952,1394,495,1637,1446,1449,1475,1638,1567,703,1259,1 436,1367,1396,935,1799,978,1341,883,762,1246,503,1450,925,1477,1261,878,1583,735,1857,182 8,1736,1858,1685,1832,1803,1641,1628,993,1457,1744,1840,885,939,994,1860,1371,1921,980,12 67,926,764,1686,941,1478,1342,1699,1642,1922,1805,1400,1452,967,1689,1760,1591,886,831,18 64,1649,1262,947,1383,1481,507,1423,1811,889,1615,984,1702,1458,1701,751,1373,942,1269,14 82,1690,1644,996,1387,1151,1215,971,1806,1431,1460,1650,890,1595,1489,509,1705,1270,1731, 949,973,1374,1623,1692,1814,1000,1484,892,1273,1706,1597,1435,1827,1813,950,1733,1389,146 4,1652,1713,863,1398,759,1447,1490,1817,1274,1395,1008,1505,1598,1437,510,1627,1390,979,1 492,953,1679,1924,1829,1639,763,1708,974,1734,1453,1818,1276,1397,1629,1872,1714,1737,165 6,954,1506,1830,879,981,1451,1928,982,1438,927,1247,1687,1716,1859,1643,1496,1479,1820,18 33,1738,995,1745,1861,1740,765,956,1888,1834,887,1630,985,1936,997,1746,1720,1401,1459,18 41,1343,1645,1836,1508,1454,986,1862,1691,1512,943,1263,1402,1483,1646,891,1651,998,1461, 1404,766,1842,1485,1520,1693,1703,511,1748,1865,1653,1375,1491,1462,988,1761,1275,1486,14 66,1465,1001,951,1493,1271,1707,1866,1002,1762,1923,1694,1807,1873,1844,893,1752,1952,181 5,1391,975,1925,894,1654,1709,1868,1657,1735,1277,1715,1848,1009,1926,1710,955,1764,1874, 1399,1468,1004,1494,1507,1439,1509,1929,1819,1497,1658,1768,1876,1984,1010,1889,1717,957, 1821,983,1930,958,1739,1831,1498,1660,1718,1278,1741,1599,1937,1822,1835,1403,987,1721,14 55,1012,1631,1513,999,1890,1747,1510,1932,1742,1837,1500,1880,1863,1016,1749,1722,1938,17 76,1892,1843,767,1838,1463,1953,989,1514,1647,1695,1763,1940,1487,1867,1405,1521,1003,195 4,1845,1750,1985,990,1005,1896,1516,1655,1753,1724,1467,1765,1869,1944,1406,1846,959,1875, 1754,1522,1904,1766,1469,1495,1659,1956,1011,1711,1927,1849,1524,1013,1870,1769,1850,175 6,1470,1986,1960,1499,1877,1891,1661,895,1931,1006,1511,1719,1770,1852,1777,1878,1881,152 8,1823,1279,1988,1933,1014,1743,1501,1939,1017,1662,1772,1968,1893,1515,1723,1778,1882,15 02,1992,1407,1934,1839,1018,2000,1894,991,1941,1751,1517,1897,1725,1955,1780,1884,1523,17 55,1020,1847,1946,1898,1942,1526,1957,1767,1784,1905,1007,1518,1726,1945,1525,1900,1871,2 016,1471,1757,1851,1958,1906,1961,1987,1771,1529,1879,1948,1758,1853,1015,1989,1962,1908, 1530,1773,1969,1990,1779,1883,1964,1854,1935,1019,1895,1663,1912,1503,1970,1774,1993,153 2,1885,1781,1994,1021,1943,1899,1886,1782,1972,2001,1947,1996,1022,1785,1901,1976,1519,17 27,1959,2002,1907,1786,1527,1949,1902,1759,2017,1909,1963,2018,2004,1950,1788,1965,1991,1 910,1855,1971,1531,1913,2008,1775,1966,2020,1995,1914,1533,1973,1997,2024,1916,1023,1974, 1887,1783,2032,1534,2003,1977,1787,1998,1978,1903,2005,2006,1951,2019,1789,1980,1911,200 9,2021,2010,1967,1915,2022,1790,153 5,2012,2025,1975,2026,1917,1999,1918,2033,1979,2028,20 34,1981,2007,1982,2011,2036,2023,2040,1791,2013,2027,2014,2029,1983,2035,2037,1919,2030,2 038,2041,2042,2015,2044,2031,2039,2043,2045,2046,2047]
›APPENDIX · 20 of 21
Sequence Group 4: Z4_2048
[0,1,2,7,3,8,11,24,4,10,13,28,16,33,35,77,5,12,14,32,19,38,47,81,22,46,42,88,57,96,102, 166,6,17,21,40,23,45,51,90,29,55,59,97,72,110,116,184,34,61,75,114,80,123,133,195,87,135,146,2 21,151,232,252,363,9,18,26,54,30,58,71,105,36,76,62,117,84,127,140,204,44,74,86,134,92,143,15 0,227,100,153,168,244,182,260,277,402,53,89,98,149,111,160,176,257,121,177,194,269,206,291,3 07,433,137,202,224,297,230,308,331,462,249,339,357,483,376,504,541,725,15,25,31,73,39,79,82, 139,48,85,93,148,101,158,163,254,56,94,103,161,115,175,191,272,126,192,203,286,226,304,326,4 51,64,108,122,181,128,193,209,299,147,222,231,310,248,337,351,482,162,240,258,343,270,371,3 78,501,293,390,420,530,441,558,614,727,69,124,142,212,157,229,247,341,167,250,263,362,278,3 77,401,521,189,273,287,387,309,412,437,568,322,444,467,592,489,624,644,819,208,300,316,424, 344,450,471,607,375,479,502,636,532,648,700,874,399,512,542,675,553,715,737,915,611,751,773, 908,799,951,1005,1192,20,37,41,91,49,95,106,174,50,107,118,185,130,205,213,324,63,119,131,21 8,144,225,238,325,152,237,253,356,274,374,382,500,67,141,154,220,171,241,259,372,179,267,27 9,384,290,409,428,550,178,288,302,408,321,438,453,593,346,473,490,623,510,642,680,859,78,16 5,172,265,188,284,301,403,196,306,314,435,332,460,477,621,251,327,345,465,364,487,509,638,3 93,516,546,672,571,712,740,902,283,359,385,497,407,529,548,702,431,564,578,724,615,762,782, 939,468,613,625,774,639,801,766,965,689,851,875,1016,881,1081,1115,1229,83,186,190,320,242, 336,350,472,266,355,365,494,392,518,545,704,280,388,406,519,422,549,573,730,445,581,606,756, 637,779,817,973,323,410,427,572,452,599,629,768,492,630,646,813,690,797,865,1022,527,666,7 08,853,731,880,905,1058,763,911,910,1105,967,1127,1155,1308,358,442,474,631,517,647,679,829, 547,703,717,876,748,887,909,1077,574,735,770,903,786,913,969,1129,827,978,1001,1161,1040,1 201,1226,1385,622,776,809,971,863,974,1030,1174,872,1026,1062,1215,1094,1247,1294,1444,88 9,1084,1123,1263,1146,1300,1278,1463,1189,1331,1352,1516,1396,1544,1581,1667,27,43,52,99,6 0,120,132,210,66,136,145,217,156,235,239,368,68,155,164,234,173,285,294,398,198,296,319,432, 334,455,475,634,70,170,187,289,200,317,328,448,211,340,352,480,370,505,524,650,223,360,381, 514,404,544,559,694,414,551,583,734,590,754,777,1011,109,199,207,333,219,353,369,496,245,38 3,394,536,417,566,580,706,264,397,426,556,447,588,595,742,464,597,604,781,664,802,845,1024, 281,446,458,602,486,627,633,791,508,663,683,826,720,860,877,1065,535,699,732,879,764,900,94 3,1097,807,948,980,1130,1002,1165,1206,1378,112,215,236,379,262,395,421,570,276,429,449,598, 469,609,617,788,305,459,485,619,507,658,677,822,533,692,718,870,743,890,927,1068,329,495,5 23,681,560,709,707,893,575,736,752,916,793,945,957,1135,608,765,805,952,823,987,1004,1176,8 50,1020,1049,1216,1103,1253,1297,1451,348,540,565,738,594,761,795,949,655,806,834,997,838, 1008,1037,1199,667,836,849,1029,897,1048,1088,1244,936,1100,1121,1264,1153,1314,1336,1470, 693,907,922,1071,962,1107,1126,1287,981,1151,1179,1328,1207,1356,1391,1525,1053,1181,1219, 1363,1260,1402,1419,1571,1289,1435,1461,1591,1493,1628,1661,1772,129,246,268,430,303,457, 481,641,312,488,513,661,537,686,729,929,342,525,569,705,585,759,745,938,600,771,798,977,830, 991,1014,1190,405,576,601,757,654,790,810,1000,660,833,843,1015,862,1038,1057,1233,668,85 6,884,1055,934,1087,1117,1267,954,1143,1152,1319,1180,1337,1371,1509,416,653,657,824,671,8 37,869,1044,698,898,919,1079,946,1112,1148,1303,804,931,964,1119,983,1162,1183,1333,1041,1 186,1222,1365,1262,1398,1415,1569,842,986,1028,1164,1054,1212,1236,1377,1092,1251,1272,14 12,1301,1437,1468,1607,1124,1292,1324,1460,1351,1484,1508,1632,1382,1519,1541,1656,1556,1 693,1700,1831,425,673,685,925,789,941,956,1141,815,975,995,1169,1034,1195,1231,1373,847,10 12,1051,1203,1075,1239,1275,1407,1114,1298,1269,1429,1334,1465,1492,1613,937,1059,1086,12 55,1133,1280,1321,1456,1159,1325,1350,1485,1369,1495,1527,1651,1208,1359,1388,1513,1421,1 548,1563,1681,1442,1586,1604,1712,1629,1732,1736,1804,984,1089,1156,1326,1193,1346,1360,1 504,1227,1395,1404,1536,1431,1549,1593,1698,1235,1427,1458,1584,1490,1608,1611,1734,1521, 1634,1647,1749,1674,1776,1791,1867,1306,1480,1486,1624,1532,1636,1658,1755,1554,1680,168 6,1786,1717,1792,1833,1888,1577,1709,1729,1814,1752,1819,1846,1909,1765,1850,1864,1922,18 78,1934,1943,1982,65,104,113,180,125,183,214,298,138,201,228,318,255,349,361,528,159,216,23 3,347,271,373,415,539,292,413,391,562,456,587,610,775,169,256,282,386,295,411,434,567,330,4 43,463,589,511,632,649,814,354,470,522,643,538,669,691,840,561,696,722,888,739,912,950,1131, 197,261,313,440,335,461,506,616,366,526,476,651,554,676,711,855,400,520,557,695,579,716,73 3,899,603,744,780,930,812,961,993,1184,439,563,591,728,635,755,796,958,662,800,839,982,858, 1019,1045,1228,701,852,894,1027,904,1046,1080,1261,942,1093,1118,1286,1145,1312,1354,1534, 243,311,338,515,380,534,543,710,418,555,582,726,605,753,767,955,454,584,612,758,645,794,831, 988,674,832,854,1009,896,1039,1073,1249,484,626,665,811,678,835,866,1031,723,891,906,1050, 940,1091,1109,1285,760,924,959,1099,985,1139,1149,1310,1021,1168,1209,1343,1237,1374,1432, 1535,499,670,714,871,750,901,935,1096,778,944,966,1128,994,1147,1182,1335,825,989,1010,116 6,1047,1200,1232,1383,1067,1240,1268,1408,1295,1441,1462,1614,864,1032,1060,1213,1101,124 8,1273,1424,1144,1282,1311,1452,1344,1467,1512,1652,1178,1320,1355,1491,1370,1528,1546,16 83,1428,1557,1575,1676,1597,1706,1742,1843,275,367,389,577,419,586,618,792,423,620,652,816, 684,857,873,1070,478,656,687,883,719,895,921,1072,741,920,953,1116,990,1142,1157,1309,493, 713,746,886,784,926,960,1140,808,976,996,1160,1018,1197,1220,1367,803,1013,1035,1196,1066, 1234,1252,1409,1104,1276,1296,1440,1318,1459,1497,1642,531,772,785,970,821,1006,1033,1185, 841,1043,1056,1230,1082,1259,1281,1438,947,1074,1102,1266,1132,1291,1317,1454,1171,1327,1 361,1488,1387,1526,1550,1671,1003,1122,1163,1307,1194,1342,1364,1514,1224,1379,1397,1533, 1433,1565,1583,1697,1270,1430,1443,1576,1455,1598,1570,1715,1502,1639,1653,1748,1660,178 4,1802,1861,552,818,828,1064,928,1090,1108,1274,972,1113,1134,1302,1170,1330,1358,1517,998, 1167,1191,1332,1211,1366,1390,1538,1241,1400,1423,1560,1453,1580,1612,1720,1069,1198,121 8,1389,1250,1416,1446,1572,1299,1447,1464,1609,1503,1595,1646,1751,1341,1481,1523,1640,15 39,1659,1673,1774,1566,1679,1678,1798,1716,1810,1824,1896,1120,1238,1277,1448,1329,1466,1 496,1620,1362,1515,1529,1654,1555,1663,1677,1782,1392,1543,1573,1672,1585,1682,1718,1811, 1619,1724,1739,1827,1762,1848,1859,1926,1439,1578,1605,1719,1645,1721,1758,1834,1650,175 4,1777,1855,1794,1870,1889,1947,1664,1785,1807,1876,1818,1892,1883,1953,1841,1904,1913,19 69,1930,1977,1987,2008,315,396,436,596,466,659,688,867,491,697,721,882,749,917,923,1136,49 8,747,769,914,787,1007,1023,1177,844,1025,1063,1225,1085,1254,1279,1450,503,783,820,1017,8 48,1061,1076,1245,868,1095,1110,1283,1138,1313,1339,1469,892,1125,1154,1323,1187,1357,137 5,1507,1202,1368,1401,1542,1406,1559,1579,1744,628,846,861,1083,885,1111,1137,1305,932,115 8,1172,1348,1205,1381,1399,1520,968,1175,1217,1372,1243,1405,1411,1551,1265,1413,1422,158 2,1479,1599,1633,1753,999,1242,1257,1420,1290,1445,1449,1590,1316,1478,1499,1618,1531,164 3,1655,1778,1347,1511,1540,1657,1567,1670,1701,1795,1603,1704,1725,1812,1740,1830,1851,19 24,640,878,918,1150,963,1173,1210,1386,992,1221,1246,1414,1271,1426,1434,1587,1042,1258,1 288,1436,1315,1475,1494,1615,1345,1505,1530,1649,1552,1665,1689,1779,1078,1304,1338,1498, 1376,1524,1522,1666,1393,1545,1558,1684,1592,1702,1711,1815,1425,1568,1601,1707,1616,173 1,1741,1835,1638,1750,1767,1856,1797,1872,1890,1948,1106,1353,1380,1547,1410,1564,1594,17 05,1473,1602,1623,1737,1627,1743,1760,1847,1482,1625,1637,1757,1668,1766,1789,1869,1694,1 796,1806,1877,1823,1897,1907,1956,1506,1675,1687,1780,1713,1799,1809,1885,1726,1821,1836, 1903,1852,1914,1928,1972,1769,1838,1857,1917,1874,1932,1938,1985,1886,1944,1952,1990,196 3,1998,2007,2027,682,933,979,1223,1036,1256,1284,1457,1052,1293,1322,1477,1349,1501,1537, 1690,1098,1340,1384,1518,1403,1562,1553,1696,1417,1574,1596,1723,1621,1733,1746,1842,118 8,1394,1418,1561,1472,1589,1606,1738,1476,1622,1631,1747,1644,1761,1773,1863,1483,1641,16 62,1771,1692,1788,1803,1879,1708,1817,1822,1898,1837,1908,1920,1967,1204,1471,1474,1617,1 487,1626,1648,1764,1510,1669,1685,1783,1703,1800,1820,1894,1600,1691,1714,1805,1727,1828, 1839,1905,1763,1840,1858,1918,1875,1931,1937,1984,1630,1730,1756,1829,1770,1854,1866,192 3,1793,1871,1881,1936,1893,1945,1955,1993,1808,1887,1900,1951,1912,1958,1966,2000,1925,19 70,1976,2005,1981,2013,2015,2035,1214,1489,1500,1688,1588,1699,1710,1816,1610,1722,1735,1 832,1759,1845,1862,1921,1635,1745,1768,1849,1781,1868,1882,1935,1801,1891,1880,1941,1906, 1954,1962,1996,1695,1775,1787,1873,1813,1884,1899,1949,1826,1901,1911,1959,1919,1964,197 3,2004,1853,1915,1927,1968,1939,1978,1983,2011,1946,1989,1992,2017,1999,2020,2022,2032,17 28,1790,1825,1902,1844,1910,1916,1965,1860,1929,1933,1975,1942,1979,1991,2014,1865,1940,1 950,1988,1961,1994,1995,2021,1971,2001,2003,2023,2009,2028,2030,2040,1895,1957,1960,1997, 1974,2002,2006,2025,1980,2010,2012,2029,2018,2031,2036,2042,1986,2016,2019,2033,2024,203 4,2037,2043,2026,2038,2039,2044,2041,2045,2046,2047]
›APPENDIX · 21 of 21
Sequence Group 4: Q4_4096
[0,1,2,4,8,16,32,3,5,64,9,6,17,10,18,128,12,33,65,20,256,34,24,36,7,129,66,512,11,40,6 8,130,19,13,48,14,72,257,21,132,35,258,26,513,80,37,25,22,136,260,264,38,514,96,67,41,144,28,6 9,42,516,49,74,272,160,1024,520,288,528,192,544,70,44,131,81,50,73,15,320,133,52,23,134,384,7 6,137,82,56,27,97,39,259,84,138,145,261,29,43,98,515,88,140,30,146,1025,71,262,265,2048,161,5 76,45,100,640,1026,51,148,46,75,266,273,517,104,162,53,193,1028,152,77,164,768,268,274,518,5 4,83,57,521,112,1032,135,78,289,194,85,276,522,58,168,139,99,86,60,280,89,290,529,524,196,14 1,1040,101,147,176,2049,142,530,321,31,200,90,1056,545,292,322,532,2050,263,149,102,105,304, 296,1027,163,92,1029,47,267,385,546,324,2052,208,386,150,153,165,106,55,328,1088,536,577,5 48,1033,113,154,79,269,108,578,2056,224,166,519,552,195,270,1030,641,1041,523,275,580,291,5 9,169,560,114,277,156,87,1034,197,116,170,2064,61,1042,531,525,642,281,278,526,177,293,388, 1152,91,584,769,198,2080,172,120,201,336,62,282,143,1036,1057,103,178,294,93,1089,644,202,2 051,592,323,392,2053,297,770,107,180,1044,151,209,284,1280,648,94,204,298,400,608,2112,105 8,352,325,533,155,210,305,2057,547,300,109,1048,184,534,1060,537,115,1031,167,225,326,2054, 306,772,157,2065,656,329,110,117,212,171,1153,776,1090,330,1536,2058,226,549,1035,538,387,3 08,216,416,271,279,158,337,2066,550,672,1064,118,332,579,540,1092,2176,389,173,1154,121,55 3,199,784,179,228,338,312,1043,704,1037,390,174,554,581,1072,393,2060,283,2081,122,448,353, 2113,561,1038,203,63,340,394,1096,1281,527,582,556,181,295,1045,285,232,124,2068,205,182,6 43,2304,1156,562,286,585,299,354,2082,1059,211,401,1282,185,1050,396,344,586,645,1537,593, 535,240,2072,1104,206,95,327,2084,564,800,402,2055,356,307,301,417,1061,213,1049,568,1046, 832,588,1160,1284,186,2177,646,404,2114,1288,227,896,594,418,2560,302,649,771,360,539,2059, 111,1062,331,1538,214,309,1120,1091,2088,188,449,1065,217,408,609,596,2116,551,650,229,159, 420,2178,310,1168,541,1052,773,610,657,333,1093,119,1066,2067,2061,600,339,1540,218,2096, 368,652,1073,230,391,313,450,542,1098,334,1296,233,555,2062,774,175,123,1184,658,2120,612, 341,2305,777,220,314,2069,1544,424,1312,395,673,583,355,1552,2180,1216,287,183,234,1568,12 5,557,1094,660,616,342,316,2083,1068,241,778,2306,563,2074,1155,345,452,397,2561,403,1105, 207,2128,1074,674,558,785,1097,432,1039,357,187,1344,236,664,1157,624,587,780,1076,2085,10 47,705,2073,126,242,2070,1158,565,398,2184,346,456,2308,358,405,303,569,2312,1408,244,1100, 1161,595,1106,189,566,676,1080,1051,1121,361,2086,706,589,2562,1063,215,786,647,348,2144,2 115,419,406,464,680,801,2089,1283,362,1108,590,409,1162,570,1169,788,1285,2192,1053,2076,5 97,1067,572,1122,219,311,2117,708,598,2090,1539,601,651,421,792,802,2564,611,1112,602,1164, 410,231,2097,688,653,1054,248,1170,2122,369,2320,190,364,1095,654,2208,1286,659,1289,335,4 80,315,221,3072,370,1185,613,2568,1600,422,425,2336,451,1069,614,543,1124,235,412,2576,343, 372,2240,1664,775,317,2592,2118,1075,222,1172,426,2092,453,237,1070,559,1099,2179,1290,83 3,804,712,1297,834,661,1541,808,779,2129,1128,617,604,2098,1186,433,720,2121,816,1077,2063, 1217,836,2368,347,897,2181,1176,243,1101,2100,662,2071,1188,454,318,675,1792,618,2182,129 2,898,781,1298,1542,376,428,1078,665,736,567,1107,2432,1081,1545,840,2124,2185,625,238,213 0,1136,359,457,2104,399,787,2075,2145,591,678,434,677,2087,1159,1102,349,1313,1218,245,110 9,458,666,1300,620,1546,1082,2307,1192,363,2132,127,1163,191,2186,1123,782,407,2193,436,62 6,2309,2077,1110,571,465,681,2091,246,707,2146,1084,350,1304,599,668,2563,1113,790,1314,15 53,460,1548,2136,1220,249,2188,682,1165,573,1125,411,803,2078,1171,789,2194,1200,709,365,4 40,628,689,3073,2119,374,1166,423,2310,1554,466,793,2313,1345,250,371,1055,481,574,1224,22 09,413,2624,1114,603,366,2093,1569,2148,1316,1346,468,1556,655,900,2688,805,615,3074,1287, 684,1173,710,2099,1126,429,794,2196,252,1129,373,605,1328,848,690,2094,2123,713,632,2314,1 320,482,806,2321,1187,2565,1116,427,2152,1071,904,2210,1291,414,1409,2101,223,1570,2241,13 48,663,3076,692,835,1232,619,472,2200,1410,455,796,2125,1174,1177,809,714,2212,1189,721,83 7,2816,716,1130,2316,1079,1352,864,2322,2566,810,2102,1560,606,1601,2131,912,2105,2569,15 72,722,696,377,1137,435,2160,1178,1103,817,1293,1132,319,621,1602,812,484,3080,1248,430,11 90,2183,1543,2126,1576,838,2337,2242,667,1219,488,2133,1294,239,378,2324,2570,459,622,210 6,2216,1665,627,437,2187,380,2147,1547,1299,818,1604,1315,461,2134,1083,496,669,1193,1584, 679,1138,1301,2108,1180,724,2328,841,1111,629,2137,1221,351,467,2338,2577,1140,438,2572,22 44,1194,737,251,462,2189,442,441,3088,2149,1085,469,2195,1555,247,683,2224,1549,1666,842,1 305,1302,738,1550,2190,1201,899,2578,1317,670,1412,783,2369,1115,849,2079,1608,1793,820,2 248,1222,728,928,2138,791,367,3104,2593,1196,901,1144,630,2340,2370,1225,685,844,2580,136 0,633,711,1086,253,691,2311,1306,2197,824,2150,1167,902,686,2153,1127,1202,2352,1318,1117, 740,1668,850,375,2344,1226,444,3075,1616,2211,470,1347,483,2140,1416,415,3077,485,2095,90 5,1321,795,473,2315,1794,634,744,2433,2594,1131,852,960,2372,1204,865,693,2256,1175,2434,1 233,1308,797,2198,2201,1672,2213,1118,1228,906,1322,2154,715,1424,2103,2376,1632,807,3136, 474,636,1376,694,254,2584,1349,1557,717,2625,1179,1234,575,913,2596,1329,798,811,3081,216 1,379,1571,2202,1324,2127,1133,697,2317,2156,1208,431,2626,1558,607,2272,1561,2214,489,25 67,2600,1139,866,723,2243,486,1191,2318,1249,1350,3078,908,1330,1796,718,813,2689,1181,476, 856,3089,1680,1353,839,1134,2571,1141,2323,1236,725,2628,2339,698,1195,914,2107,1800,752, 868,2217,2608,2162,819,2325,2204,1354,814,439,2135,929,3082,2245,1250,1573,490,2164,1562, 1411,623,2218,1332,1240,671,1440,1295,739,1303,1182,2109,1361,916,3090,2579,1574,463,1696, 843,2573,2690,1142,381,2329,2326,1356,1603,497,2574,2225,1564,930,821,2341,2436,726,961,3 200,2139,1413,1197,872,2632,2817,1145,492,2246,1577,1223,631,1808,1203,729,2220,1252,2168, 1362,700,2249,1336,443,1728,741,2384,1414,1198,2110,1578,1605,845,2330,1417,920,382,2191, 3084,1307,822,3105,2151,1146,2226,851,1472,730,2342,2141,1377,498,3137,880,2692,1585,742, 445,2250,1227,471,635,2640,1087,2371,1364,932,2440,1418,687,2345,1551,1606,2818,1580,1205, 1319,903,2155,1309,825,2228,1256,1148,500,3092,1229,2199,846,1206,2257,2332,1667,745,332 8,826,2696,732,1586,446,962,2142,2252,1310,1609,936,2346,2448,1323,475,853,2656,1378,867,6 37,3106,2400,1235,2373,1425,2581,1209,907,2203,2258,1420,1368,2353,1610,1669,487,1617,259 5,695,1559,2348,2157,1264,746,3096,828,2232,753,1230,854,2582,1119,1351,3108,857,2585,158 8,1824,504,799,2163,1426,255,964,3079,2215,1380,909,1331,2273,1325,2374,1441,719,2354,282 0,1237,477,2205,1592,915,2704,2377,1856,2158,2165,2260,1612,638,748,2219,944,1210,3201,28 24,1670,1428,3138,869,1251,1920,491,699,2378,1618,1442,754,3584,1326,1673,858,1795,2274,1 384,2597,1563,478,3083,2586,2435,968,1135,383,2356,2264,1355,910,2464,2319,2327,1238,815, 2206,2385,1333,976,2598,2720,870,3112,2166,1212,1473,917,2380,2627,1241,1432,2588,1633,16 20,3140,727,1575,1674,493,1253,2437,1183,2221,1444,873,3202,2169,1334,701,1565,931,2601,2 247,1797,1634,2832,2227,1681,1357,756,2276,2386,1143,860,499,2360,3091,2752,731,3085,2438, 1624,2222,1363,823,2602,2629,1242,3120,922,2441,1392,1676,874,2331,1254,1415,918,2170,13 37,2496,1474,502,2401,1566,933,1358,2609,1257,1579,3086,2251,1798,1199,1147,743,2111,2388, 1682,760,2442,3144,1636,1365,881,3329,2575,1801,2630,494,1244,2604,2229,2343,1338,702,309 3,921,2333,1448,501,876,2280,2172,1419,847,2253,1697,2230,1607,992,2691,1379,447,3204,261 0,1311,1207,2334,1258,2633,1149,1581,733,2347,1684,1640,2402,1366,1340,827,3107,1265,2259, 934,1802,2449,3330,2233,1587,882,3098,937,2444,2392,963,1369,747,2634,2693,1476,1421,358 5,505,2641,2583,1427,855,924,2288,1231,734,829,3152,2254,1698,1582,2143,1809,2375,1456,26 12,2848,1381,1211,2450,1260,1688,965,2404,1648,2355,1611,2349,2465,1804,938,3109,884,2261, 506,1729,3097,2616,1150,1266,3094,749,2880,1589,1422,945,966,2636,3208,1370,1480,755,333 2,2234,1382,859,1429,2694,1327,2452,1593,940,3336,2275,2944,1268,830,2642,2466,1619,911,2 350,2697,1213,2819,1590,2408,2587,1700,871,2159,639,1385,3110,2379,1730,1613,3586,888,226 2,1239,1810,479,2357,1671,1372,3168,946,3139,1443,1430,750,1488,2236,1704,2497,1825,969,3 113,2265,2456,508,1386,861,2657,2644,1614,1433,2599,2698,2277,1594,757,2207,2468,1812,970, 2358,3216,2589,3100,2821,1621,2658,1596,919,2705,2381,1243,1335,3141,2167,1732,1622,3114, 875,1625,1675,862,1445,2648,1816,2387,1826,758,3588,2266,1635,948,1626,2416,2700,1434,12 55,3121,2278,2439,1712,1677,977,2361,2498,1272,923,2590,3146,2382,1393,972,3344,2281,1214, 2603,1388,2822,2223,2171,1678,3232,761,2706,1683,877,2660,2389,1359,1504,2825,1339,2268, 1245,952,2362,1394,495,1637,3592,2472,1446,1449,3360,2443,1475,1638,1567,703,2721,2631,12 59,1436,2403,3600,1367,1396,935,3264,2335,1799,2231,978,1341,2282,3616,2173,2605,883,3142, 762,2708,2664,1246,503,2390,2364,1450,3116,925,2289,1477,2826,1261,878,2611,1583,735,320 3,2393,1857,1828,2500,1736,2445,1858,1685,2451,1832,1803,3153,2255,1641,1628,993,3122,272 2,1457,2606,1744,2833,3145,2480,1840,885,3087,939,2405,2235,994,1860,3392,2284,2712,1371, 1921,3205,980,2672,2635,1267,926,764,2828,3124,1686,941,3095,2753,1478,1342,2174,1699,229 0,1642,3206,2613,2446,1922,1805,2394,2504,1400,1452,967,2406,1689,2453,1760,2351,2617,159 1,886,3456,2292,831,1864,3148,3209,2643,1649,1262,3154,947,2237,2614,1383,1481,507,2724,3 128,1423,1811,3099,889,3169,2409,1615,984,1702,2754,1458,2637,1701,751,3111,2263,2834,137 3,942,2695,2396,1269,2467,2454,1482,2512,1690,2728,2849,1644,996,3331,2410,1387,3156,2638, 1151,2457,1215,3210,971,2618,1806,1431,3217,2836,1460,1650,3333,890,3101,1595,1489,509,1 705,2645,3115,1270,2620,1731,949,3170,2267,2359,973,1374,2756,2646,1623,1692,3587,2649,26 99,2469,1814,1000,2840,2850,1484,892,2659,3160,2650,1273,3212,2458,1706,2279,1597,2736,27 01,1435,1827,3102,2296,1813,3218,950,2417,1733,1389,1464,2238,1652,2412,1713,863,3143,270 2,1398,759,1447,3334,2707,1490,1817,3337,2383,2528,1274,1395,1008,2363,2269,1505,1598,241 8,3233,2661,1437,510,3648,2470,1627,2473,1390,2499,3117,2662,2591,3172,979,2283,2460,1492, 953,2391,2420,1679,1924,3712,2823,1829,2365,1639,763,1708,974,1734,3123,2270,1453,1818,3 220,2474,1276,1397,1629,2501,2285,1872,1714,3118,2607,3147,1737,1656,954,3338,2881,1506,2 852,1830,2760,3345,2882,2709,879,3589,981,2856,2827,1451,3176,2665,2652,1928,3234,982,248 1,2768,1438,927,2864,3125,1247,3265,2884,1687,1716,2395,1859,2945,1643,1496,3224,2291,147 9,1820,3149,2710,1833,1738,995,3236,2502,1745,2366,1861,2723,3840,2666,1740,765,3340,2946, 2829,956,1888,3346,3590,2424,2476,1834,3126,887,2713,2784,1630,985,2615,3155,1936,3129,9 97,3593,2888,1746,1720,2673,1401,2286,1459,3184,2407,2505,1841,2447,2835,1343,1645,2639,1 836,2726,1508,2482,2725,1454,986,3207,3150,2397,1862,3361,3266,2293,1691,1512,3157,943,25 06,2714,1263,1402,3348,2668,3594,1483,1646,3130,891,3240,2411,1651,998,1461,2175,3211,140 4,2239,766,3171,2830,2455,1842,2484,2674,1485,3158,2619,2513,1520,2729,1693,2294,2755,170 3,511,3132,2398,1748,3352,2647,1865,2716,1653,3161,2838,1375,1491,3362,3601,2508,1462,359 6,988,3268,2297,1761,1275,1486,2730,3213,1466,2621,1465,1001,3173,2459,2851,951,1493,3219, 2837,1271,1707,3248,2757,2413,2488,1866,1002,2676,2737,1762,2422,3214,2471,1923,3602,251 4,1694,2841,1807,3393,2298,2419,1873,3103,2529,2622,1844,3272,893,2461,1752,1952,3162,265 1,1815,2414,1391,975,3617,1925,894,1654,3364,3394,2516,1709,1868,3604,2703,2948,1657,1735, 2853,2663,1277,1715,3335,2732,3221,2758,1848,1009,3174,2477,1926,2842,1710,2300,3177,242 1,2653,3376,955,2896,2738,1764,2761,2680,1874,1399,3368,2530,2854,1468,1004,3235,1494,150 7,3164,2475,1439,1509,3119,2952,1929,1819,1497,3339,2462,1658,1768,3457,2271,3618,1876,19 84,1010,3396,2711,1889,2740,1717,2883,3280,2667,2520,957,3458,2503,2844,1821,3222,3225,28 57,2762,3237,983,2769,2885,1930,958,2764,3178,1739,3127,3400,2912,1831,1498,1660,2858,171 8,1278,3608,2654,1741,3649,2960,1599,1937,3620,2770,1822,2744,1835,2425,3185,2483,1403,98 7,3226,3151,2865,1721,3341,3180,2367,2669,1455,3650,1012,2860,2532,1631,3296,2478,3238,15 13,3591,999,3624,2886,1890,1747,2715,3267,1510,2536,3342,2287,2426,1932,2507,2670,1742,18 37,3713,2675,1500,2485,1880,2428,1863,1016,3595,3347,2866,1749,3652,3363,2509,1722,1938,3 131,2544,2717,1776,1892,3241,3632,2727,3186,1843,3349,767,3228,2772,1838,1463,2889,3159,1 953,2677,989,3269,2399,2515,1514,3188,2486,1647,3242,2785,2299,2510,1695,2490,2489,1763,3 133,2517,1940,3603,2295,1487,2731,1867,3597,3714,2890,1405,3353,3350,2786,1521,3598,1003, 3249,2947,1954,1845,3365,2718,3460,1750,2831,1985,990,3163,2897,1005,1896,3656,3841,2868, 1516,3270,2776,2976,1655,2839,2415,1753,3244,2949,3192,2678,1724,3273,2733,1467,2892,176 5,3408,2681,2759,3134,2301,2739,1869,3354,2872,1944,1406,3215,2950,2734,1846,959,3175,325 0,1875,1754,3366,3165,2788,1522,1904,3716,2898,2423,1766,1469,3274,2492,1495,1659,3664,25 18,3395,2531,1956,1011,3464,2463,1711,2533,2953,3369,2843,2521,3842,2682,2792,1927,3179,2 900,3008,1849,3252,2913,2741,1524,1013,3223,1870,3281,3356,2845,1769,1850,3720,1756,1470, 1986,3166,3276,2954,1960,3370,2763,3472,1499,1877,3680,2855,1891,2522,1661,2684,3424,274 2,2302,895,3397,3605,2765,1931,3227,3282,2623,2961,3377,1006,2846,2859,1511,2427,3619,171 9,3372,3181,2745,1770,1852,3256,1777,2479,1878,3606,2655,1881,3609,2537,1528,1823,3187,29 14,1279,2771,1988,2534,3239,1933,1014,3297,3398,2956,1743,3378,3844,2766,2861,1501,3229,2 524,2904,1939,3728,3401,2887,3182,3189,1017,3284,2773,1662,1772,2746,3243,1968,2962,3848, 2800,2916,1893,2867,1515,1723,3402,2862,2487,1778,2977,1882,3298,3621,2538,1502,3610,345 9,2671,1992,1407,3380,3288,2719,1934,3488,3343,2787,3351,1839,3230,1018,3409,2964,2000,36 22,2511,3744,1894,2891,991,3190,2429,1941,3404,3651,2545,3612,2978,2869,1751,2774,3009,15 17,3461,3245,2920,1897,3193,1725,2540,1955,3625,3271,2679,3856,3251,2777,1780,3300,3410,2 748,1884,1523,3384,2491,3776,2789,1755,1020,3462,3246,1847,3626,3653,2893,1946,3465,2968, 2430,1898,3355,2870,1942,3194,2899,3520,2778,1526,3425,2546,1957,2928,3633,2790,2493,327 5,2519,2683,1767,3135,3412,2980,1784,3466,2735,1905,1007,3599,3654,1518,3628,3253,3367,29 51,1726,1945,3357,2873,1525,1900,3304,3196,2548,1871,3277,2894,3254,2016,3715,2793,1471,2 874,2780,3634,2494,3010,3358,3657,2984,1757,3371,2523,2901,3426,2915,2685,1851,3283,1958, 3473,3257,2955,1906,1961,3468,3416
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