CN113810060A - 一种Polar码速率匹配方法及装置 - Google Patents

Abstract

本申请公开了用于卫星通信中的一种Polar码速率匹配的方法、装置和介质，能够提高系统的可靠性。该方法包括：获取K个待编码比特，获取母码长度N，N＝2ⁿ，K、n和N为正整数，根据所述母码长度N对所述K个待编码比特进行极化编码，根据速率匹配序列对极化编码后的比特序列进行速率匹配后输出。根据给定的速率匹配序列，可以简化速率匹配的操作。

Description

一种Polar码速率匹配方法及装置

技术领域

本申请实施例涉及通信技术领域，尤其涉及一种Polar码速率方法及装置。

背景技术

信道编码作为最基本的无线接入技术，在保证数据的可靠性传输方面起到至关重要的作用。在现有的无线通信系统中，一般采用Turbo码、低密度奇偶校验码(low densityparity check，LDPC)和极化(Polar)码进行信道编码。Turbo码不能够支持过低或过高码率的信息传输。而对于中短包传输，Turbo码和LDPC码也由于自身编译码的特点，在有限码长下很难达到理想的性能。在实现方面，Turbo码和LDPC码在编译码实现过程中具有较高的计算复杂度。Polar码是理论上证明可以取得香农容量，且具有相对简单的编译码复杂度的好码，因而得到了越来越广泛的应用。在第五代(5th generation，5G)通信系统中，将Polar码确定为控制信道的编码方式。

但在卫星通信中，尚未明确到底采用何种信道编码方式，如果要将Polar码引入卫星通信系统，需要进行怎样的设计才能满足需求，就成为一个需要解决的问题。

发明内容

本申请实施例提供一种应用于卫星通信的Polar码编码的速率匹配方法及装置，具有实现简单的优点。

本申请实施例提供的具体技术方案如下：

第一方面，提供一种Polar码编码的速率匹配方法，

获取K个待编码比特、目标码长M、母码长度N，N＝2ⁿ，M、K、n和N为正整数；

根据所述母码长度N对所述K个待编码比特进行极化编码，得到编码后的比特序列；

根据速率匹配序列对所述编码后的比特序列进行速率匹配，获取速率匹配后的序列；

输出所述速率匹配后的序列。

这种设计切合了卫星通信的特点，速率匹配序列的嵌套特性也为具体实现提供了多种可能的方式，易于实现，简化了速率匹配的操作，减小了实现难度。

在一个可能的设计中，所述速率匹配序列为第一序列的子序列，所述第一序列为附录一中的序列1或序列2或序列3，其中所述序列1包括N2个极化子信道号，所述序列2包括N2/2个极化子信道号，所述序列3包括N2个大小不同的值，所述极化子信道号由0开始，N2大于或等于N。

在一个可能的设计中，当N＝8192，所述速率匹配序列为说明书中的序列1a或序列2a或序列3a；或者

当N＝4096，所述速率匹配序列为说明书中的序列1b或2b或3b；或者

当N＝2048，所述速率匹配序列为说明书中的序列1c或2c或3c；或者

当N＝1024，所述速率匹配序列为说明书中的序列1d或2d或3d；或者

当N＝512，所述速率匹配序列为说明书中的序列1e或2e或3e；

其中所述序列1a、所述序列1b、所述序列1c、所述序列1d、所述序列1e为所述序列1的子序列；

所述序列2a、所述序列2b、所述序列2c、所述序列2d、所述序列2e为所述序列2的子序列；

所述序列3a、所述序列3b、所述序列3c、所述序列3d、所述序列3e为所述序列3的子序列。

在一个可能的设计中，所述速率匹配的方式为打孔操作，

若所述第一序列为所述序列1，所述打孔操作为：根据所述目标码长M取所述速率匹配序列中后M个极化子信道号对应子信道承载的比特或根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列2，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列3，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中取值最小的N-M个值所在的极化子信道承载的比特或根据所述目标码长M取所述速率匹配序列中取值最大的M个值所在的极化子信道承载的比特。

在一个可能的设计中，所述根据所述母码长度N对所述K个待编码比特进行极化编码为：所述K个待编码比特映射到M-P个非打孔的极化子信道中可靠度较高的K个极化子信道，使得K个待编码比特所在的极化子信道的可靠度高于其余M-P-K个极化子信道的可靠度，P为预冻结的极化子信道的数目，P大于或等于0。

在一个可能的设计中，所述根据速率匹配序列对所述编码后的比特序列进行速率匹配获取速率匹配后的序列之前，对所述编码后的比特序列进行交织。

在一个可能的设计中，所述K个待编码比特中，包括循环冗余校验比特。

在一个可能的设计中，所述K个待编码比特中，包括奇偶校验比特。

在一个可能的设计中，所述速率匹配方法由网络设备或终端执行。

第二方面，提供一种Polar码速率匹配装置，该装置具有实现上述第一方面和第一方面的任一种可能的设计中所述的方法的功能。所述功能可以通过硬件实现，也可以通过硬件执行相应的软件实现。所述硬件或软件包括一个或多个与上述功能相对应的模块。

在一个可能的设计中，当所述功能的部分或全部通过硬件实现时，所述Polar码速率匹配装置包括：输入接口电路，用于获取待编码比特；逻辑电路，用于执行上述第一方面和第一方面的任一种可能的设计中所述的行为；输出接口电路，用于输出速率匹配后的序列。

可选的，所述Polar码速率匹配装置可以是芯片或者集成电路。

在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述Polar码速率匹配装置包括：存储器，用于存储程序；处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，所述Polar码速率匹配装置可以实现如上述第一方面和第一方面的任一种可能的设计中所述的方法。

可选的，上述存储器可以是物理上独立的单元，也可以与处理器集成在一起。

在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述Polar码速率匹配装置包括处理器。用于存储程序的存储器位于所述速率匹配装置之外，处理器通过电路/电线与存储器连接，用于读取并执行所述存储器中存储的程序。

在一个可能的设计中，所述装置为网络设备或终端。

第三方面，提供了一种通信系统，该通信系统包网络设备和终端，所述网络设备或终端可以执行如上述第一方面及其可能的设计所述的方法。

第四方面，提供了一种计算机存储介质，存储有计算机程序，该计算机程序包括用于执行第一方面和第一方面的任一可能设计中任一种所述的方法的指令。

第五方面，本申请实施例提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述各方面所述的方法。

第六方面，提供了一种无线设备，包括用于实施第一方面和第一方面的任一可能设计的速率匹配装置和收发器，

所述收发器用于接收或发送信号。

在一个可能的设计中，所述无线设备为终端或者网络设备。

附图说明

图1为本申请实施例中应用的通信系统架构示意图；

图2为本申请实施例中Polar码速率匹配方法的流程示意图；

图3为本申请实施例中Polar码速率匹配装置结构示意图之一；

图4为本申请实施例中Polar码速率匹配装置结构示意图之二；

图5为本申请实施例中Polar码速率匹配装置结构示意图之三；

图6为本申请实施例中Polar码速率匹配装置结构示意图之四；

图7为本申请实施例中Polar码解速率匹配装置结构示意图之一；

图8为本申请实施例中Polar码解速率匹配装置结构示意图之二；

图9为本申请实施例中Polar码解速率匹配装置结构示意图之三；

图10为本申请实施例中Polar码解速率匹配装置结构示意图之四。

具体实施方式

下面将结合附图，对本申请实施例进行详细描述。

如果不考虑卫星通信的特点，直接将现有5G标准中的Polar码编码方式照搬到卫星通信中，会有至少以下几个问题：1)目前的5G标准中Polar码只用于控制信道，所以不一定能完全适用于数据信道；2)目前的5G标准中，Polar码的母码长度最长为1024，所以能支持的数据包长度有限。因此有必要重新设计Polar码的编码方式，以便更适应于卫星通信，同时兼顾适用于地面通信。

本申请实施例提供一种Polar码速率匹配方法及装置，根据极化子信道的可靠度，在线计算或者预先存储可靠度排序，按照可靠度排序选择用于发送信息比特的极化子信道的序号，按照所选择的信息比特序号进行Polar码编码，然后根据速率匹配序列对编码后的序列进行速率匹配操作，并输出速率匹配后的序列。本申请实施例更适用于卫星通信，尤其是卫星通信中的短消息业务。下面结合附图详细说明本发明实施例提供的速率匹配方法和装置。

为方便对本申请实施例的理解，下面对Polar码作简单介绍。

Polar码的编码策略利用无噪信道传输用户有用的信息，全噪信道传输约定的信息或者不传信息。Polar码也是一种线性块码，其编码矩阵为G_N，编码过程为

其中

是一个二进制的行矢量，长度为N(即码长，可以看到，编码前后的序列x和u的长度均为N，N也称为母码码长)；G_N是一个N×N的矩阵，且

定义为log₂N个矩阵F₂的克罗内克(Kronecker)乘积。上述矩阵

Polar码的编码过程中，

中的一部分比特用来携带信息，称为信息比特集合，这些比特的索引的集合记作

另外的一部分比特设置为接收端和发送端预先约定的固定值，称之为冻结比特集合或冻结比特集合(frozen bits)，其索引的集合用

的补集

表示。Polar码的编码过程相当于：

这里，G_N(A)是G_N中由集合

中的索引对应的那些行得到的子矩阵，G_N(A^C)是G_N中由集合

中的索引对应的那些行得到的子矩阵。

为

中的信息比特集合，数量为K，一般地，包括但不限于循环冗余校验(CyclicRedundancy Check，简称CRC)比特和奇偶校验(Parity Check，简称PC)比特在内的各类校验比特也可以都包括在信息比特集合中；

为

中的冻结比特集合，其数量为(N-K)，是已知比特。这些冻结比特通常被设置为0，但是只要接收端和发送端预先约定，冻结比特可以被任意设置。从而，Polar码的编码输出可简化为：

这里

为

中的信息比特集合，

为长度K的行矢量，即

|·|表示集合中元素的个数，K为信息块大小，

是矩阵G_N中由集合

中的索引对应的那些行得到的子矩阵，

是一个K×N的矩阵。

在确定母码码长N后，Polar码的构造过程即集合

的选取过程，决定了Polar码的性能。Polar码的构造过程通常是，根据母码码长N确定共存在N个极化子信道，分别对应编码矩阵的N个行，在不考虑速率匹配的情况下，将可靠度较高的前K个极化子信道的索引作为集合

的元素，剩余(N-K)个极化子信道对应的索引作为冻结比特的索引集合

的元素。集合

决定了信息比特的位置，集合

决定了冻结比特的位置。极化子信道的序号即为信息比特或者冻结比特的位置索引，也即在

中的位置索引。

当考虑速率匹配的时候，主要是考虑打孔(puncture)或缩短(shorten)的时候，一般是先确定需要打孔或缩短(即删除)的N-M个极化子信道，这里M是目标码长，即速率匹配后的比特序列长度，这里选出的N-M个极化子信道用于放置冻结比特，在5G NR标准中，针对打孔的情形，还额外确定了一些称为预冻结的极化子信道，也用于放置冻结比特，这里不妨将预冻结的极化子信道数量定义为P，P大于或者等于0(对于缩短的情形，P显然为0，这时候是可以不需要考虑P的)，然后在剩下的M-P个极化子信道中按照可靠度挑选其中可靠度较高的K个极化子信道用于放置K个信息比特。当然，也可以先选择可靠度较低的M-P-K个子信道用于放置冻结比特，而余下的K个子信道则用于放置信息比特。放置K个信息比特的K个极化子信道中的任意一个极化子信道的可靠度都高于用于放置冻结比特的M-P-K个子信道中的任意一个子信道的可靠度。在本申请中，对P的取值不做限制，即使对于打孔的情形，P也可以为0，即使对于缩短的情形，P也可以取为大于0，并不影响本申请技术方案的实施，无论是编码端还是解码端，确认K个子信道用于放置K个信息比特的原则和方法是一致的。同时，5G NR标准中，对于N-M个极化子信道的选取，是将子块交织(分成32个子块)后的序列放到循环缓存(英文为circular buffer，相当于速率匹配序列)上，如果是打孔，则在循环缓存上从第N-M个位置开始读取，丢弃从0到N-M-1位置上的比特，如果是缩短，则在循环缓存上从第0个位置开始读取直至第M-1个位置，而丢弃从第M到N-1位置上的比特。这种方式并未考虑不同母码长度之间的速率匹配序列之间的关系。

需要说明的是，这里说的可靠度的相对关系是基于一个给定的可靠度的计算方式，不同的可靠度计算方式可能会导致极化子信道的可靠度相对关系发生变化，但选择放置信息比特的极化子信道的方法是一样的。在5G NR标准之外，信息比特也可以考虑放置于最后被打孔或者缩短的极化子信道。本申请并不限制必须按照5G NR的标准选择放置信息比特的极化子信道。

在当前的卫星通信中，例如北斗卫星通信系统中，有个短报文通信模式。可以看作是现在常用的“短信息”，但又有不同，具体体现在这类发布的信息除了显示信息本身外，既能够定位，又能显示发布者的位置。但是，当前北斗二代短报文系统采用的Turbo码，可以采用Polar码来提升性能和降低复杂度。北斗短报文发送信息比特到地面中心站时，先对信息进行分段，分段后每段的信息比特长度为89到994(包含CRC比特)，采用的码率为1/2。后续消费类终端若要接入短报文系统，需要采用更低的码率，比如1/8。

本申请实施例中，通过预先给定速率匹配序列的方式，不同母码长度对应的速率匹配序列之间也满足嵌套关系，这样可以简化操作流程，提高处理效率。这个嵌套特性，类似于5G NR标准不同母码长度对应的可靠度排序序列类似，即母码长度Na小于或等于母码长度Nb时，Na对应的可靠度序列中的各极化子信道(极化子信道0，…，Na-1)的可靠度相对关系与这些极化子信道(极化子信道0，…，Na-1)在Nb对应的可靠度序列中的可靠度相对关系一致，换言之，在Nb对应的可靠度序列中，只保留小于Na的极化子信道号且不改变该Na个极化子信道号位置的前后相对关系，就可以得到Na对应的可靠度序列了。因此具体实现中，既可以把不同母码长度的可靠度序列都预先存储下来，也可以只预先存储最大母码长度N_max对应的可靠度序列，然后其他母码长度Na对应的可靠度序列就从最大母码长度对应的可靠度序列中只保留小于N_max的极化子信道的序号而得到，这样一方面可以节省一点存储开销，另一方面也便于实施，无需再考虑子块交织等操作。特别地，Na最大也可以等于N_max。

类似地，母码长度Na小于或等于母码长度Nb时，Na对应的速率匹配序列中的各极化子信道(极化子信道0，…，Na-1)的速率匹配(打孔或缩短)顺序的相对关系与这些极化子信道(极化子信道0，…，Na-1)在Nb对应的速率匹配序列中的速率匹配顺序的相对关系一致，换言之，在Nb对应的速率匹配序列中，只保留小于Na的极化子信道号且不改变该Na个极化子信道号位置的前后相对关系，就可以得到Na对应的速率匹配序列了。因此具体实现中，既可以把不同母码长度的速率匹配序列都预先存储下来，也可以只预先存储最大母码长度N_max对应的速率匹配序列，然后其他母码长度Na对应的速率匹配序列就从最大母码长度对应的速率匹配序列中只保留小于N_max的极化子信道的序号而得到，特别地，Na最大也可以等于N_max。

图1为本发明实施例无线通信网络的结构示意图。图1只是一种示例，其它能用到本发明实施例的速率匹配方法或装置的无线网络也都在本发明的保护范围内。

如图1所示，无线通信网络100包括网络设备110，和终端112。当无线通信网络100包括核心网102时，该网络设备110还可以与核心网102相连。网络设备110还可以与IP网络104进行通信，例如，因特网(internet)，私有的IP网，或其它数据网等。网络设备为覆盖范围内的终端提供服务。例如，参见图1所示，网络设备110为网络设备110覆盖范围内的一个或多个终端112提供无线接入。除此之外，网络设备之间的覆盖范围可以存在重叠的区域，例如网络设备110和120。网络设备之间还可以可以互相通信，例如，网络设备110可以与网络设备120之间进行通信。

上述网络设备可以是用于与终端设备进行通信的设备。例如，可以是LTE系统中的演进型基站(Evolved Node B，eNB或eNodeB)，还可以是5G网络中的gNB，还可以是卫星通信中的卫星，或者未来通信系统中的网络侧设备等。或者该网络设备还可以是中继站、接入点、车载设备等。在设备对设备(Device to Device，D2D)通信系统、机器对机器(Machineto Machine，M2M)通信系统和车联网系统中，该网络设备还可以是担任基站功能的终端。

上述终端可以指用户设备(User Equipment，UE)、接入终端、用户单元、移动站、远方站、远程终端、移动设备、用户终端、无线通信设备、用户代理或用户装置。接入终端可以是蜂窝电话、无绳电话、会话启动协议(Session Initiation Protocol，SIP)电话、无线本地环路(Wireless Local Loop，WLL)站、个人数字处理(Personal Digital Assistant，PDA)、具有无线通信功能的手持设备、计算设备或连接到无线调制解调器的其它处理设备、车载设备、可穿戴设备，未来通信网络中的终端设备等。

基于图1所示的通信系统架构，本申请实施例中，执行Polar码速率匹配方法的执行主体可以为上述网络设备或终端，当网络设备或终端作为发送端发送数据或信息时，均可以采用此Polar码速率匹配方法。相应的，当网络设备或终端作为接收端接收数据或信息时，也需要根据本发明所述的方法先确认速率匹配序列。下面将对本申请实施例提供的Polar码速率匹配方法做详细介绍。

基于图1所示的通信系统架构，如图2所示，本申请实施例提供的Polar码速率匹配方法具体流程如下所述。

操作210：获取K个待编码比特、目标码长M、母码长度N，N＝2ⁿ，M、K、n和N为正整数；

这里的K个待编码比特中，除了载荷比特外，还可以包括但不限于CRC比特、PC比特等等其他各种类型的非冻结比特中的一类或者多类。

为了系统简单起见，本发明不考虑重复这种速率匹配方式，因此母码长度N可以根据目标码长获取：N＝2^ceil(log₂(M))，即n＝ceil(log₂(M))，这里的ceil操作是指上取整操作，可以看出，N为不小于M的最小的满足2的整数次方的数。

另外，如果采用固定码率，那么在获取K个待编码比特的时候，目标码长M即可换算得到，或者在获取目标码长M后就可以知道该获取多少个待编码比特。例如采用固定码率1/8，则M＝8K，或者K＝M/8。固定码率还可以是1/2、1/3或1/4等常用码率。这种方式是可以进一步减少实现的复杂度。如果采用可变码率，则需要通过信令等方式通知，以使得收发两端保持一致，这种方式的好处是可以更灵活的使用资源。具体应用中，事先可以通过标准协议或者专有协议予以规定即可。

操作220：根据所述母码长度N对所述K个待编码比特进行极化编码，得到编码后的比特序列；

具体的编码操作可以参见前述的描述。如果是按照与5G NR标准类似的操作，先确定打孔或缩短的极化子信道，那么在这一步操作中就需要用到速率匹配序列，确定到底打孔或者缩短掉(即删除掉)哪些极化子信道以及可能的P个预冻结极化子信道(P大于或等于0)，然后在剩下的M-P个极化子信道中按照可靠度挑选其中可靠度较高的K个极化子信道用于放置K个信息比特。解码侧也通过同样的方式确定K个信息比特的位置。为免赘述，速率匹配序列的描述放在操作230中予以说明。需要注意的是，在5G NR系统中，需要在每次速率匹配的时候，确认到底是采用打孔还是缩短的速率匹配方式。在本申请中，为实现简单起见，可以固定采用打孔或者固定采用缩短作为速率匹配方式。

可选的，对编码后的比特序列，还进行交织。这个交织操作与5G NR中的子块交织略有不同，无需分成32个子块(或者其他数目的子块)，而是根据速率匹配序列将编码后的比特序列映射到循环缓存上以进行后续的打孔操作(当然缩短操作也是类似的)。

操作230：根据速率匹配序列对所述编码后的比特序列进行速率匹配操作获取长度为M的速率匹配后的比特序列；

对于打孔操作，在附录一中，提供了示例性的第一序列，第一序列为序列1或序列2或序列3，其中序列1包括N₂个极化子信道号，序列2包括N₂/2个极化子信道号，极化子信道号的最小值为0、最大值为N₂-1，N₂＝8192，N₂大于或等于N。当然，也可以是极化子信道号的最小值为1、最大值为N₂，这时候涉及的极化子信道号都相应加1即可。第一序列还可以是序列3，序列3中包括N₂个大小不同的值，每个值所在位置的序号就是极化子信道号，其中值的大小就是该值所在极化子信道被速率匹配的优先级。

需要注意的是，序列1、2、3实质上是等价的。对于打孔操作，序列2实质上就是序列1的子序列，直接取了序列1的前一半，而序列3中的各元素的取值表示该元素所在位置(即极化子信道)的被打孔的优先级，值越小，被打孔的优先级越高。根据序列1或序列2，如果目标码长为M，那么需要打孔(或者说删除)的就是序列1或者序列2中前N-M个极化子信道号对应的极化子信道上承载的比特，对于序列3而言，需要打孔的就是打孔序列3中最小的N-M个值所在的极化子信道承载的比特，或者说保留最大的M个值所在的极化子信道承载的比特。

通信系统通常会定义一个最大母码长度N_max，假如N_max＝8，序列1为[0,4,6,2,3,1,7,5]，相应地，序列2为[0,4,6,2]，即为序列1的前半段，序列3为[0,5,3,4,1,7,2,6]，序列1中的‘5’表示极化子信道5，它被打孔的优先级为7，是最迟被打孔的，也就是对应于序列3中的‘7’，即序列3中极化子信道5(从第0个元素开始排的第5个元素)的打孔优先级为‘7’。假如M＝6，则在序列1或序列2中，打孔的就是序列最前N-M＝2个极化子信道(极化子信道0和4)承载的比特，则打孔的就是小于或等于N-M＝2的值(即为0和1)所在的极化子信道(极化子信道0和4)。根据嵌套的特性，当N＝4的时候，序列1对应的序列为[0,2,3,1]，序列2对应的序列为[0,2]，注意在序列3中，由于其中的值的大小仅代表优先级，因此取值不一定非得受限于最大的极化子信道号，在不同的取值方法下，只需要确认不同的极化子信道对应的优先级的先后关系一致即可，因此在N＝4时，对序列3而言，可以简单的取N_max＝8的序列的前一半，即此时序列3对应的序列为[0,5,3,4]，其中的5已经比N大了，但这个取法和根据N＝4时的序列1(即[0,2,3,1])推导得到的序列3(即[0,3,1,2])是等价的，即当速率匹配方式为打孔时，两种方式都表示第0个极化子信道被打孔的优先级为第0个(即最高)，第1个极化子信道被打孔的优先级为第3(即最低)，第2个极化子信道被打孔的优先级位为第1，第3个极化子信道被打孔的优先级为第2，类似的，当速率匹配方式为缩短时，两种方式都表示第0个极化子信道被缩短的优先级为第0个(即最高)，第1个极化子信道被缩短的优先级为第3(即最高)，第2个极化子信道被缩短的优先级位为第1，第3个极化子信道被缩短的优先级为第2，因此序列3的嵌套方式一方面可以类似于序列1的嵌套方式从大于N的序列中挑选小于或等于N的值，另一方面也可以更简单的从长度为大于N的第3序列中取前N个位置的值即可。事实上，由于序列1、序列2、序列3都要满足嵌套特性，而序列2又是序列1的前一半，序列3则是序列1的以打孔优先级表达的方式，所以并非所有的序列都能满足这样的要求的，仍以N_max＝8为例，假如序列1为[0,2,4,3,6,1,7,5]时就无法满足序列2在N＝4时的嵌套，因此在N₂较大时，嵌套的速率匹配序列的设计是非常有难度的。

当速率匹配方式是缩短时，序列1和序列3可以取为与打孔操作的序列1和序列3相同的序列(因此附录一中的序列1和序列3可以直接采用)，而序列2就可以取序列1的后一半序列，它们也同样都满足嵌套特性，序列3中的各元素的取值表示该元素所在位置(即极化子信道)的被缩短的优先级，值越大，被缩短的优先级越高。根据序列1或序列2，如果目标码长为M，那么需要缩短的就是序列1或者序列2最后的N-M个极化子信道号对应的极化子信道上承载的比特，对于序列3而言，需要缩短的就是缩短序列3中所有大于或等于M的值所在的极化子信道承载的比特。还以上面的序列[0,4,6,2,3,1,7,5]作为序列1的话，相应的序列2则为[3,1,7,5]，具体进行缩短操作时，需要缩短的就是序列1或者序列2最后的N-M个极化子信道号对应的极化子信道上承载的比特，对于序列3而言，需要缩短的就是缩短序列3中取值最大的N-M个值所在的极化子信道承载的比特，或者说，是保留缩短序列3中取值最小的M个值所在的极化子信道承载的比特。为避免混淆，本申请其他部分均以打孔为例，但整体的原则也适用于缩短的操作，不再赘述。

实际应用中，速率匹配序列可以为该第一序列的子序列，注意在本申请中，一个序列的子序列也可以包括该序列本身，同时，所谓序列A为序列B的子序列，指的是序列A中所有元素均取自于序列B，而且这些元素之间的先后相对顺序与它们在序列B中的先后相对顺序完全一致。当N＝8192时，速率匹配序列为1a或2a或3a，序列1a与序列1相同，序列2a与序列2相同，序列3a与序列3相同，因此不再重复给出序列1a、2a和3a。附录一中，还提供了母码长度为N＝4096的速率匹配序列1b、2b和3b(序列2b长为2048)，母码长度为N＝2048的速率匹配序列1c、2c和3c(序列2c长为1024)，母码长度为1024的速率匹配序列1d、2d和3d(序列2d长为512)，母码长度为512的速率匹配序列1e、2e和3e(序列2e长为256)。其中序列1a、序列1b、序列1c、序列1d、序列1e为序列1的子序列，都满足前文所述的嵌套特性；序列2a、序列2b、序列2c、序列2d、序列2e为序列2的子序列，也都满足前文所述的嵌套特性；序列3a、序列3b、序列3c、序列3d、序列3e为所述序列3的子序列，且序列3b即为序列3a的前一半序列，序列3c为序列3b的前一半序列(也即序列3a的前1/4序列)，序列3d为序列3c的前一半序列(也即序列3a的前1/8序列)，序列3e为序列3d的前一半序列(也即序列3a的前1/16序列)，同样也都满足前文所述的嵌套特性。

一般地，通信系统会定义一个最大母码长度N_max，一般地，N_max小于或等于N₂，也即满足N<＝N_max<＝N₂。发送端和接收端可以只存储N_max对应的打孔序列(即速率匹配序列)，也可以存储小于或等于N_max的不同母码长度对应的打孔序列，还可以存储N_max和常用的几个不同母码长度对应的打孔序列。

除了附录一中的例子，附录二给出了另一个第一序列的例子，相应的，也就有两套可能的速率匹配序列可用，实际应用中取其中一套应用即可，如无特别说明，本申请均以附录一为例。

操作240：输出速率匹配后的序列。

注意如果考虑调制操作，这里输出的就应是基于速率匹配后的比特序列进行调制后的序列，该序列为符号序列，此时序列的长度也就不一定还是M了。如果不考虑调制，则速率匹配后的序列即为速率匹配后的比特序列。由于调制本身并非实现本申请实施例方案必不可少的技术，在不影响理解的情况下，在本申请中对“速率匹配后的序列”和“速率匹配后的比特序列”这两个术语并不加以严格区分。

上述图2所示的实施例是发送端的操作，接收端的操作也是类似的，接收机(或者接收装置)在接收到待解码信息序列后，也需要根据类似的方法，具体而言，获取包括K个待解码比特的待解码信息序列、目标码长M和母码长度N，确定速率匹配序列从而对待解码信息序列序列进行解速率匹配的操作和解码解调操作，从而得到并输出解码结果，其中解速率匹配为恢复打孔的位置或缩短的位置，对于打孔位置，解码时可以认为似然比(likelihood，LLR)为0，对于缩短位置，解码时可以认为LLR为无穷大，详细的解码算法这里不做限定。

需要说明的是，附录一和附录二中的第一序列是优选的两个例子，其应用到Polar编码过程中会有助于提高Poalr码编译码性能。任一种举例的序列中，在不影响其整体效果的前提下，可以做包括但不限于如下几方面的调整或者等同替换：

1、序列中少数元素之间的位置互换。例如，序号位置可以在设定幅度内调整，例如，设定幅度为5，将序号为10的元素位置在左右5个位置内调整均可；

2、序列中的部分元素进行调整，但是根据该序列选择出用于传输T比特信息的信道集合是一致或相似的。

3、序列中包含从0开始到N-1结束的N个元素，从0开始到N-1结束的N个元素代表N个极化子信道的序号。实际上，N个极化子信道的序号也可以从1开始到N结束，将上述序列中各序号均加1即可，这也是上述各计算方式中的序号形式。当然，也可以采取其他方式表示上述极化子信道的序号或者标识，该具体表达方式不影响序列中所表示的极化子信道的具体位置。特别是序列3b、3c、3d和3e，如前所述，其中的元素未必都在0～N-1之间，但并不影响各个极化子信道的优先级先后排序。

4、上述序列中的N个极化子信道的序号是按照N个极化子信道速率匹配的优先级从小到大排列的，实际上，N个极化子信道的序号也可以按照N个极化子信道的速率匹配优先级从大到小排列，将上述序列中的元素反序排列即可。

如图3所示，本申请实施例中还提供一种Polar码速率匹配装置300或者Polar码解速率匹配装置300。图3所示的Polar码速率匹配方法中的部分或全部可以通过硬件来实现也可以通过软件来实现。

对于Polar码速率匹配装置300，基于图2所示的Polar码速率匹配方法的同一发明构思，该Polar码速率匹配装置300用于执行图2所示的Polar码速率匹配方法。当通过硬件实现时，Polar码速率匹配装置300包括：输入接口电路301，用于获取待编码比特；逻辑电路302，用于执行上述图2所示的Polar码速率匹配方法，具体请见前面方法实施例中的描述，此处不再赘述；输出接口电路303，用于输出速率匹配后的序列。进一步地，速率匹配后的序列还是经过调制的序列，这个序列是调制后的符号序列，它们输出给收发器320，收发器320对调制后的序列进行相应处理(包括但不限于数模变换和/或变频等处理)后通过天线330发送出去。可选的，Polar码速率匹配装置300在具体实现时可以是芯片或者集成电路。

可选的，当上述实施例的Polar码速率匹配方法中的部分或全部通过软件来实现时，如图4所示，Polar码解速率匹配装置400包括：存储器401，用于存储程序；处理器402，用于执行存储器401存储的程序，当程序被执行时，使得Polar码速率匹配装置400可以实现上述实施例提供的Polar码解速率匹配方法。

可选的，上述存储器401可以是物理上独立的单元，也可以如图5所示，存储器501与处理器502集成在一起。

可选的，当上述实施例的速率匹配方法中的部分或全部通过软件实现时，Polar码速率匹配装置400也可以只包括处理器402。用于存储程序的存储器401位于Polar码速率匹配装置400之外，处理器402通过电路/电线与存储器401连接，用于读取并执行存储器401中存储的程序。

基于图2所示的Polar码速率匹配方法，如图6所示，本申请实施例还提供了一种Polar码速率匹配装置600，Polar码速率匹配装置600用于执行图2所示的Polar码速率匹配方法，Polar码速率匹配装置600包括：

获取单元601，用于获取K个待编码比特、目标码长M；

编码单元602，用于确定母码长度N，根据母码长度N对该K个待编码比特进行极化编码，得到编码后的比特序列，具体编码过程可参见前述实施例的操作220；

速率匹配单元603，用于根据速率匹配序列对编码后的比特序列进行速率匹配操作获取长度为M的速率匹配后的比特序列(或者是对该比特序列进一步通过调制的序列，也称为速率匹配后的序列)，具体的速率匹配方法可参见前述实施例的操作230。

与发送端相对应，接收端的装置也可以进行类似的设计。

对于Polar码解速率匹配装置700包括：输入接口电路701用于获取待解码信息序列，逻辑电路702用于执行前述的Polar码解速率匹配的方法，以获取解码后的信息比特；输出接口电路703用于输出解码后的信息比特。Polar码解速率匹配装置700还可以包括收发器720通过天线730获取待解码信息序列。在具体实现时可以是芯片或者集成电路。

可选的，当上述实施例的Polar码解速率匹配方法中的部分或全部通过软件来实现时，如图8所示，Polar码解速率匹配装置800包括：存储器801，用于存储程序；处理器802，用于执行存储器801存储的程序，当程序被执行时，使得Polar码速率匹配装置800可以实现上述实施例提供的Polar码解速率匹配方法。

可选的，上述存储器801可以是物理上独立的单元，也可以如图9所示，存储器901与处理器902集成在一起。

可选的，当上述实施例的速率匹配方法中的部分或全部通过软件实现时，Polar码解速率匹配装置800也可以只包括处理器802。用于存储程序的存储器01位于Polar码速率匹配装置800之外，处理器802通过电路/电线与存储器801连接，用于读取并执行存储器801中存储的程序。

处理器402和/或处理器802可以是中央处理器(central processing unit，CPU)，网络处理器(network processor，NP)或者CPU和NP的组合。

处理器402和/或处理器802还可以进一步包括硬件芯片。上述硬件芯片可以是专用集成电路(application-specific integrated circuit，ASIC)，可编程逻辑器件(programmable logic device，PLD)或其组合。上述PLD可以是复杂可编程逻辑器件(complex programmable logic device，CPLD)，现场可编程逻辑门阵列(field-programmable gate array，FPGA)，通用阵列逻辑(generic array logic,GAL)或其任意组合。

上述实施例中的存储器可以包括易失性存储器(volatile memory)，例如随机存取存储器(random-access memory，RAM)；存储器也可以包括非易失性存储器(non-volatile memory)，例如快闪存储器(flash memory)，硬盘(hard disk drive，HDD)或固态硬盘(solid-state drive，SSD)；存储器还可以包括上述种类的存储器的组合。

基于上述的Polar码解速率匹配方法，如图10所示，本申请实施例还提供了一种Polar码速率匹配装置1000，Polar码速率匹配装置1000用于执行前述的Polar码解速率匹配方法，Polar码解速率匹配装置1000包括：

获取单元1001，用于获取待解码信息序列；

处理单元1002，用于确定母码长度N，根据母码长度N和速率匹配序列对待解码信息序列序列进行解速率匹配的操作和解码解调操作，从而得到并输出解码结果；

本申请实施例还提供了一种计算机存储介质，存储有计算机程序指令，该计算机程序指令由计算机执行时，使得前述的Polar码速率匹配方法或者Polar码解速率匹配方法被执行。

本申请实施例还提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得前述的Polar码速率匹配方法或者Polar码解速率匹配方法被执行。

本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。

本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。

这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。

这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。

尽管已描述了本申请的优选实施例，但本领域内的技术人员一旦得知了基本创造性概念，则可对这些实施例作出另外的变更和修改。所以，所附权利要求意欲解释为包括优选实施例以及落入本申请范围的所有变更和修改。

显然，本领域的技术人员可以对本申请实施例进行各种改动和变型而不脱离本申请实施例的精神和范围。这样，倘若本申请实施例的这些修改和变型属于本申请权利要求及其等同技术的范围之内，则本申请也意图包含这些改动和变型在内。

附录一：第一序列的一个例子：

序列1：

Punc_Q＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,4096,4097,4098,4099,4100,4101,4102,4103,4104,4105,4106,4107,4108,4109,4110,4111,4112,4113,4114,4115,4116,4117,4118,4119,4120,4121,4122,4123,4124,4125,4126,4127,4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,4138,4139,4140,4141,4142,4143,4144,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,4158,4159,4160,4161,4162,4163,4164,4165,4166,4167,4168,4169,4170,4171,4172,4173,4174,4175,4176,4177,4178,4179,4180,4181,4182,4183,4184,4185,4186,4187,4188,4189,4190,4191,4192,4193,4194,4195,4196,4197,4198,4199,4200,4201,4202,4203,4204,4205,4206,4207,4208,4209,4210,4211,4212,4213,4214,4215,4216,4217,4218,4219,4220,4221,4222,4223,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,79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序列2：

Punc_Q_half＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,4096,4097,4098,4099,4100,4101,4102,4103,4104,4105,4106,4107,4108,4109,4110,4111,4112,4113,4114,4115,4116,4117,4118,4119,4120,4121,4122,4123,4124,4125,4126,4127,4128,4129,4130,4131,4132,4133,4134,4135,4136,4137,4138,4139,4140,4141,4142,4143,4144,4145,4146,4147,4148,4149,4150,4151,4152,4153,4154,4155,4156,4157,4158,4159,4160,4161,4162,4163,4164,4165,4166,4167,4168,4169,4170,4171,4172,4173,4174,4175,4176,4177,4178,4179,4180,4181,4182,4183,4184,4185,4186,4187,4188,4189,4190,4191,4192,4193,4194,4195,4196,4197,4198,4199,4200,4201,4202,4203,4204,4205,4206,4207,4208,4209,4210,4211,4212,4213,4214,4215,4216,4217,4218,4219,4220,4221,4222,4223,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,7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序列3：

Punc_Z＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,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12,5813,5814,5815,5816,5817,5818,5819,5820,5821,5822,5823,5824,5825,5826,5827,5828,5829,5830,5831,5832,5833,5834,5835,5836,5837,5838,5839,5840,5841,5842,5843,5844,5845,5846,5847,5848,5849,5850,5851,5852,5853,5854,5855,5856,5857,5858,5859,5860,5861,5862,5863,5864,5865,5866,5867,5868,5869,5870,5871,5872,5873,5874,5875,5876,5877,5878,5879,5880,5881,5882,5883,5884,5885,5886,5887,6912,6913,6914,6915,6916,6917,6918,6919,6920,6921,6922,6923,6924,6925,6926,6927,6928,6929,6930,6931,6932,6933,6934,6935,6936,6937,6938,6939,6940,6941,6942,6943,6944,6945,6946,6947,6948,6949,6950,6951,6952,6953,6954,6955,6956,6957,6958,6959,6960,6961,6962,6963,6964,6965,6966,6967,6968,6969,6970,6971,6972,6973,6974,6975,6976,6977,6978,6979,6980,6981,6982,6983,6984,6985,6986,6987,6988,6989,6990,6991,6992,6993,6994,6995,6996,6997,6998,6999,7000,7001,7002,7003,7004,7005,7006,7007,7008,7009,7010,7011,7012,7013,7014,7015,7016,7017,7018,7019,7020,7021,7022,7023,7024,7025,7026,7027,7028,7029,7030,7031,7032,7033,7034,7035,7036,7037,7038,7039,7040,7041,7042,7043,7044,7045,7046,7047,7048,7049,7050,7051,7052,7053,7054,7055,7056,7057,7058,7059,7060,7061,7062,7063,7064,7065,7066,7067,7068,7069,7070,7071,7072,7073,7074,7075,7076,7077,7078,7079,7080,7081,7082,7083,7084,7085,7086,7087,7088,7089,7090,7091,7092,7093,7094,7095,7096,7097,7098,7099,7100,7101,7102,7103,7104,7105,7106,7107,7108,7109,7110,7111,7112,7113,7114,7115,7116,7117,7118,7119,7120,7121,7122,7123,7124,7125,7126,7127,7128,7129,7130,7131,7132,7133,7134,7135,7136,7137,7138,7139,7140,7141,7142,7143,7144,7145,7146,7147,7148,7149,7150,7151,7152,7153,7154,7155,7156,7157,7158,7159,7160,7161,7162,7163,7164,7165,7166,7167,7680,7681,7682,7683,7684,7685,7686,7687,7688,7689,7690,7691,7692,7693,7694,7695,7696,7697,7698,7699,7700,7701,7702,7703,7704,7705,7706,7707,7708,7709,7710,7711,7712,7713,7714,7715,7716,7717,7718,7719,7720,7721,7722,7723,7724,7725,7726,7727,7728,7729,7730,7731,7732,7733,7734,7735,7736,7737,7738,7739,7740,7741,7742,7743,7744,7745,7746,7747,7748,7749,7750,7751,7752,7753,7754,7755,7756,7757,7758,7759,7760,7761,7762,7763,7764,7765,7766,7767,7768,7769,7770,7771,7772,7773,7774,7775,7776,7777,7778,7779,7780,7781,7782,7783,7784,7785,7786,7787,7788,7789,7790,7791,7792,7793,7794,7795,7796,7797,7798,7799,7800,7801,7802,7803,7804,7805,7806,7807,7296,7297,7298,7299,7300,7301,7302,7303,7304,7305,7306,7307,7308,7309,7310,7311,7312,7313,7314,7315,7316,7317,7318,7319,7320,7321,7322,7323,7324,7325,7326,7327,7328,7329,7330,7331,7332,7333,7334,7335,7336,7337,7338,7339,7340,7341,7342,7343,7344,7345,7346,7347,7348,7349,7350,7351,7352,7353,7354,7355,7356,7357,7358,7359,7360,7361,7362,7363,7364,7365,7366,7367,7368,7369,7370,7371,7372,7373,7374,7375,7376,7377,7378,7379,7380,7381,7382,7383,7384,7385,7386,7387,7388,7389,7390,7391,7392,7393,7394,7395,7396,7397,7398,7399,7400,7401,7402,7403,7404,7405,7406,7407,7408,7409,7410,7411,7412,7413,7414,7415,7416,7417,7418,7419,7420,7421,7422,7423,7808,7809,7810,7811,7812,7813,7814,7815,7816,7817,7818,7819,7820,7821,7822,7823,7824,7825,7826,7827,7828,7829,7830,7831,7832,7833,7834,7835,7836,7837,7838,7839,7840,7841,7842,7843,7844,7845,7846,7847,7848,7849,7850,7851,7852,7853,7854,7855,7856,7857,7858,7859,7860,7861,7862,7863,7864,7865,7866,7867,7868,7869,7870,7871,7872,7873,7874,7875,7876,7877,7878,7879,7880,7881,7882,7883,7884,7885,7886,7887,7888,7889,7890,7891,7892,7893,7894,7895,7896,7897,7898,7899,7900,7901,7902,7903,7904,7905,7906,7907,7908,7909,7910,7911,7912,7913,7914,7915,7916,7917,7918,7919,7920,7921,7922,7923,7924,7925,7926,7927,7928,7929,7930,7931,7932,7933,7934,7935,7936,7937,7938,7939,7940,7941,7942,7943,7944,7945,7946,7947,7948,7949,7950,7951,7952,7953,7954,7955,7956,7957,7958,7959,7960,7961,7962,7963,7964,7965,7966,7967,7968,7969,7970,7971,7972,7973,7974,7975,7976,7977,7978,7979,7980,7981,7982,7983,7984,7985,7986,7987,7988,7989,7990,7991,7992,7993,7994,7995,7996,7997,7998,7999,8000,8001,8002,8003,8004,8005,8006,8007,8008,8009,8010,8011,8012,8013,8014,8015,8016,8017,8018,8019,8020,8021,8022,8023,8024,8025,8026,8027,8028,8029,8030,8031,8032,8033,8034,8035,8036,8037,8038,8039,8040,8041,8042,8043,8044,8045,8046,8047,8048,8049,8050,8051,8052,8053,8054,8055,8056,8057,8058,8059,8060,8061,8062,8063,8064,8065,8066,8067,8068,8069,8070,8071,8072,8073,8074,8075,8076,8077,8078,8079,8080,8081,8082,8083,8084,8085,8086,8087,8088,8089,8090,8091,8092,8093,8094,8095,8096,8097,8098,8099,8100,8101,8102,8103,8104,8105,8106,8107,8108,8109,8110,8111,8112,8113,8114,8115,8116,8117,8118,8119,8120,8121,8122,8123,8124,8125,8126,8127,8128,8129,8130,8131,8132,8133,8134,8135,8136,8137,8138,8139,8140,8141,8142,8143,8144,8145,8146,8147,8148,8149,8150,8151,8152,8153,8154,8155,8156,8157,8158,8159,8160,8161,8162,8163,8164,8165,8166,8167,8168,8169,8170,8171,8172,8173,8174,8175,8176,8177,8178,8179,8180,8181,8182,8183,8184,8185,8186,8187,8188,8189,8190,8191]。

当N＝8192，序列1a即为序列1，序列2a即为序列2，序列3a即为序列3；

当N＝4096，

序列1b为：

Punc_Q＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,119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04,3605,3606,3607,3608,3609,3610,3611,3612,3613,3614,3615,3616,3617,3618,3619,3620,3621,3622,3623,3624,3625,3626,3627,3628,3629,3630,3631,3632,3633,3634,3635,3636,3637,3638,3639,3640,3641,3642,3643,3644,3645,3646,3647,3648,3649,3650,3651,3652,3653,3654,3655,3656,3657,3658,3659,3660,3661,3662,3663,3664,3665,3666,3667,3668,3669,3670,3671,3672,3673,3674,3675,3676,3677,3678,3679,3680,3681,3682,3683,3684,3685,3686,3687,3688,3689,3690,3691,3692,3693,3694,3695,3696,3697,3698,3699,3700,3701,3702,3703,3704,3705,3706,3707,3708,3709,3710,3711,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3456,3457,3458,3459,3460,3461,3462,3463,3464,3465,3466,3467,3468,3469,3470,3471,3472,3473,3474,3475,3476,3477,3478,3479,3480,3481,3482,3483,3484,3485,3486,3487,3488,3489,3490,3491,3492,3493,3494,3495,3496,3497,3498,3499,3500,3501,3502,3503,3504,3505,3506,3507,3508,3509,3510,3511,3512,3513,3514,3515,3516,3517,3518,3519,3520,3521,3522,3523,3524,3525,3526,3527,3528,3529,3530,3531,3532,3533,3534,3535,3536,3537,3538,3539,3540,3541,3542,3543,3544,3545,3546,3547,3548,3549,3550,3551,3552,3553,3554,3555,3556,3557,3558,3559,3560,3561,3562,3563,3564,3565,3566,3567,3568,3569,3570,3571,3572,3573,3574,3575,3576,3577,3578,3579,3580,3581,3582,3583,3712,3713,3714,3715,3716,3717,3718,3719,3720,3721,3722,3723,3724,3725,3726,3727,3728,3729,3730,3731,3732,3733,3734,3735,3736,3737,3738,3739,3740,3741,3742,3743,3744,3745,3746,3747,3748,3749,3750,3751,3752,3753,3754,3755,3756,3757,3758,3759,3760,3761,3762,3763,3764,3765,3766,3767,3768,3769,3770,3771,3772,3773,3774,3775,3776,3777,3778,3779,3780,3781,3782,3783,3784,3785,3786,3787,3788,3789,3790,3791,3792,3793,3794,3795,3796,3797,3798,3799,3800,3801,3802,3803,3804,3805,3806,3807,3808,3809,3810,3811,3812,3813,3814,3815,3816,3817,3818,3819,3820,3821,3822,3823,3824,3825,3826,3827,3828,3829,3830,3831,3832,3833,3834,3835,3836,3837,3838,3839,3840,3841,3842,3843,3844,3845,3846,3847,3848,3849,3850,3851,3852,3853,3854,3855,3856,3857,3858,3859,3860,3861,3862,3863,3864,3865,3866,3867,3868,3869,3870,3871,3872,3873,3874,3875,3876,3877,3878,3879,3880,3881,3882,3883,3884,3885,3886,3887,3888,3889,3890,3891,3892,3893,3894,3895,3896,3897,3898,3899,3900,3901,3902,3903,3904,3905,3906,3907,3908,3909,3910,3911,3912,3913,3914,3915,3916,3917,3918,3919,3920,3921,3922,3923,3924,3925,3926,3927,3928,3929,3930,3931,3932,3933,3934,3935,3936,3937,3938,3939,3940,3941,3942,3943,3944,3945,3946,3947,3948,3949,3950,3951,3952,3953,3954,3955,3956,3957,3958,3959,3960,3961,3962,3963,3964,3965,3966,3967,3968,3969,3970,3971,3972,3973,3974,3975,3976,3977,3978,3979,3980,3981,3982,3983,3984,3985,3986,3987,3988,3989,3990,3991,3992,3993,3994,3995,3996,3997,3998,3999,4000,4001,4002,4003,4004,4005,4006,4007,4008,4009,4010,4011,4012,4013,4014,4015,4016,4017,4018,4019,4020,4021,4022,4023,4024,4025,4026,4027,4028,4029,4030,4031,4032,4033,4034,4035,4036,4037,4038,4039,4040,4041,4042,4043,4044,4045,4046,4047,4048,4049,4050,4051,4052,4053,4054,4055,4056,4057,4058,4059,4060,4061,4062,4063,4064,4065,4066,4067,4068,4069,4070,4071,4072,4073,4074,4075,4076,4077,4078,4079,4080,4081,4082,4083,4084,4085,4086,4087,4088,4089,4090,4091,4092,4093,4094,4095]。

序列2b为：

Punc_Q_half＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,2048,2049,2050,2051,2052,2053,2054,2055,2056,2057,2058,2059,2060,2061,2062,2063,2064,2065,2066,2067,2068,2069,2070,2071,2072,2073,2074,2075,2076,2077,2078,2079,2080,2081,2082,2083,2084,2085,2086,2087,2088,2089,2090,2091,2092,2093,2094,2095,2096,2097,2098,2099,2100,2101,2102,2103,2104,2105,2106,2107,2108,2109,2110,2111,2112,2113,2114,2115,2116,2117,2118,2119,2120,2121,2122,2123,2124,2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135,2136,2137,2138,2139,2140,2141,2142,2143,2144,2145,2146,2147,2148,2149,2150,2151,2152,2153,2154,2155,2156,2157,2158,2159,2160,2161,2162,2163,2164,2165,2166,2167,2168,2169,2170,2171,2172,2173,2174,2175,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,2176,2177,2178,2179,2180,2181,2182,2183,2184,2185,2186,2187,2188,2189,2190,2191,2192,2193,2194,2195,2196,2197,2198,2199,2200,2201,2202,2203,2204,2205,2206,2207,2208,2209,2210,2211,2212,2213,2214,2215,2216,2217,2218,2219,2220,2221,2222,2223,2224,2225,2226,2227,2228,2229,2230,2231,2232,2233,2234,2235,2236,2237,2238,2239,2240,2241,2242,2243,2244,2245,2246,2247,2248,2249,2250,2251,2252,2253,2254,2255,2256,2257,2258,2259,2260,2261,2262,2263,2264,2265,2266,2267,2268,2269,2270,2271,2272,2273,2274,2275,2276,2277,2278,2279,2280,2281,2282,2283,2284,2285,2286,2287,2288,2289,2290,2291,2292,2293,2294,2295,2296,2297,2298,2299,2300,2301,2302,2303,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,2560,2561,2562,2563,2564,2565,2566,2567,2568,2569,2570,2571,2572,2573,2574,2575,2576,2577,2578,2579,2580,2581,2582,2583,2584,2585,2586,2587,2588,2589,2590,2591,2592,2593,2594,2595,2596,2597,2598,2599,2600,2601,2602,2603,2604,2605,2606,2607,2608,2609,2610,2611,2612,2613,2614,2615,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2626,2627,2628,2629,2630,2631,2632,2633,2634,2635,2636,2637,2638,2639,2640,2641,2642,2643,2644,2645,2646,2647,2648,2649,2650,2651,2652,2653,2654,2655,2656,2657,2658,2659,2660,2661,2662,2663,2664,2665,2666,2667,2668,2669,2670,2671,2672,2673,2674,2675,2676,2677,2678,2679,2680,2681,2682,2683,2684,2685,2686,2687,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023]。

序列3b为：

Punc_Z＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,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当N＝2048，

序列1c为：

Punc_Q＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,1792,1793,1794,1795,1796,1797,1798,1799,1800,1801,1802,1803,1804,1805,1806,1807,1808,1809,1810,1811,1812,1813,1814,1815,1816,1817,1818,1819,1820,1821,1822,1823,1824,1825,1826,1827,1828,1829,1830,1831,1832,1833,1834,1835,1836,1837,1838,1839,1840,1841,1842,1843,1844,1845,1846,1847,1848,1849,1850,1851,1852,1853,1854,1855,1856,1857,1858,1859,1860,1861,1862,1863,1864,1865,1866,1867,1868,1869,1870,1871,1872,1873,1874,1875,1876,1877,1878,1879,1880,1881,1882,1883,1884,1885,1886,1887,1888,1889,1890,1891,1892,1893,1894,1895,1896,1897,1898,1899,1900,1901,1902,1903,1904,1905,1906,1907,1908,1909,1910,1911,1912,1913,1914,1915,1916,1917,1918,1919,1920,1921,1922,1923,1924,1925,1926,1927,1928,1929,1930,1931,1932,1933,1934,1935,1936,1937,1938,1939,1940,1941,1942,1943,1944,1945,1946,1947,1948,1949,1950,1951,1952,1953,1954,1955,1956,1957,1958,1959,1960,1961,1962,1963,1964,1965,1966,1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020,2021,2022,2023,2024,2025,2026,2027,2028,2029,2030,2031,2032,2033,2034,2035,2036,2037,2038,2039,2040,2041,2042,2043,2044,2045,2046,2047]。

序列2c为：

Punc_Q_half＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895]。

序列3c为；

Punc_Z＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,2688,2689,2690,2691,2692,2693,2694,2695,2696,2697,2698,2699,2700,2701,2702,2703,2704,2705,2706,2707,2708,2709,2710,2711,2712,2713,2714,2715,2716,2717,2718,2719,2720,2721,2722,2723,2724,2725,2726,2727,2728,2729,2730,2731,2732,2733,2734,2735,2736,2737,2738,2739,2740,2741,2742,2743,2744,2745,2746,2747,2748,2749,2750,2751,2752,2753,2754,2755,2756,2757,2758,2759,2760,2761,2762,2763,2764,2765,2766,2767,2768,2769,2770,2771,2772,2773,2774,2775,2776,2777,2778,2779,2780,2781,2782,2783,2784,2785,2786,2787,2788,2789,2790,2791,2792,2793,2794,2795,2796,2797,2798,2799,2800,2801,2802,2803,2804,2805,2806,2807,2808,2809,2810,2811,2812,2813,2814,2815,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,1764,1765,1766,1767,1768,1769,1770,1771,1772,1773,1774,1775,1776,1777,1778,1779,1780,1781,1782,1783,1784,1785,1786,1787,1788,1789,1790,1791,2944,2945,2946,2947,2948,2949,2950,2951,2952,2953,2954,2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977,2978,2979,2980,2981,2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003,3004,3005,3006,3007,3008,3009,3010,3011,3012,3013,3014,3015,3016,3017,3018,3019,3020,3021,3022,3023,3024,3025,3026,3027,3028,3029,3030,3031,3032,3033,3034,3035,3036,3037,3038,3039,3040,3041,3042,3043,3044,3045,3046,3047,3048,3049,3050,3051,3052,3053,3054,3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3200,3201,3202,3203,3204,3205,3206,3207,3208,3209,3210,3211,3212,3213,3214,3215,3216,3217,3218,3219,3220,3221,3222,3223,3224,3225,3226,3227,3228,3229,3230,3231,3232,3233,3234,3235,3236,3237,3238,3239,3240,3241,3242,3243,3244,3245,3246,3247,3248,3249,3250,3251,3252,3253,3254,3255,3256,3257,3258,3259,3260,3261,3262,3263,3264,3265,3266,3267,3268,3269,3270,3271,3272,3273,3274,3275,3276,3277,3278,3279,3280,3281,3282,3283,3284,3285,3286,3287,3288,3289,3290,3291,3292,3293,3294,3295,3296,3297,3298,3299,3300,3301,3302,3303,3304,3305,3306,3307,3308,3309,3310,3311,3312,3313,3314,3315,3316,3317,3318,3319,3320,3321,3322,3323,3324,3325,3326,3327,4736,4737,4738,4739,4740,4741,4742,4743,4744,4745,4746,4747,4748,4749,4750,4751,4752,4753,4754,4755,4756,4757,4758,4759,4760,4761,4762,4763,4764,4765,4766,4767,4768,4769,4770,4771,4772,4773,4774,4775,4776,4777,4778,4779,4780,4781,4782,4783,4784,4785,4786,4787,4788,4789,4790,4791,4792,4793,4794,4795,4796,4797,4798,4799,4800,4801,4802,4803,4804,4805,4806,4807,4808,4809,4810,4811,4812,4813,4814,4815,4816,4817,4818,4819,4820,4821,4822,4823,4824,4825,4826,4827,4828,4829,4830,4831,4832,4833,4834,4835,4836,4837,4838,4839,4840,4841,4842,4843,4844,4845,4846,4847,4848,4849,4850,4851,4852,4853,4854,4855,4856,4857,4858,4859,4860,4861,4862,4863]。

当N＝1024，

序列1d为：

Punc_Q＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023]。

序列2d为：

Punc_Q_half＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639]。

序列3d为；

Punc_Z＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,2304,2305,2306,2307,2308,2309,2310,2311,2312,2313,2314,2315,2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330,2331,2332,2333,2334,2335,2336,2337,2338,2339,2340,2341,2342,2343,2344,2345,2346,2347,2348,2349,2350,2351,2352,2353,2354,2355,2356,2357,2358,2359,2360,2361,2362,2363,2364,2365,2366,2367,2368,2369,2370,2371,2372,2373,2374,2375,2376,2377,2378,2379,2380,2381,2382,2383,2384,2385,2386,2387,2388,2389,2390,2391,2392,2393,2394,2395,2396,2397,2398,2399,2400,2401,2402,2403,2404,2405,2406,2407,2408,2409,2410,2411,2412,2413,2414,2415,2416,2417,2418,2419,2420,2421,2422,2423,2424,2425,2426,2427,2428,2429,2430,2431]。

当N＝512，

序列1e为：

Punc_Q＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511]。

序列2e为：

Punc_Q_half＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255]。

序列3e为：

Punc_Z＝[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895]。

附录二：第一序列的另一个例子：

序列1：

Shorten_Q＝[0,4096,2048,6144,1024,5120,3072,7168,512,4608,2560,6656,1536,5632,3584,7680,256,4352,2304,6400,1280,5376,3328,7424,768,4864,2816,6912,1792,5888,3840,7936,128,4224,2176,6272,1152,5248,3200,7296,640,4736,2688,6784,1664,5760,3712,7808,384,4480,2432,6528,1408,5504,3456,7552,896,4992,2944,7040,1920,6016,3968,8064,64,4160,2112,6208,1088,5184,3136,7232,576,4672,2624,6720,1600,5696,3648,7744,320,4416,2368,6464,1344,5440,3392,7488,832,4928,2880,6976,1856,5952,3904,8000,192,4288,2240,6336,1216,5312,3264,7360,704,4800,2752,6848,1728,5824,3776,7872,448,4544,2496,6592,1472,5568,3520,7616,960,5056,3008,7104,1984,6080,4032,8128,32,4128,2080,6176,1056,5152,3104,7200,544,4640,2592,6688,1568,5664,3616,7712,288,4384,2336,6432,1312,5408,3360,7456,800,4896,2848,6944,1824,5920,3872,7968,160,4256,2208,6304,1184,5280,3232,7328,672,4768,2720,6816,1696,5792,3744,7840,416,4512,2464,6560,1440,5536,3488,7584,928,5024,2976,7072,1952,6048,4000,8096,96,4192,2144,6240,1120,5216,3168,7264,608,4704,2656,6752,1632,5728,3680,7776,352,4448,2400,6496,1376,5472,3424,7520,864,4960,2912,7008,1888,5984,3936,8032,224,4320,2272,6368,1248,5344,3296,7392,736,4832,2784,6880,1760,5856,3808,7904,480,4576,2528,6624,1504,5600,3552,7648,992,5088,3040,7136,2016,6112,4064,8160,16,4112,2064,6160,1040,5136,3088,7184,528,4624,2576,6672,1552,5648,3600,7696,272,4368,2320,6416,1296,5392,3344,7440,784,4880,2832,6928,1808,5904,3856,7952,144,4240,2192,6288,1168,5264,3216,7312,656,4752,2704,6800,1680,5776,3728,7824,400,4496,2448,6544,1424,5520,3472,7568,912,5008,2960,7056,1936,6032,3984,8080,80,4176,2128,6224,1104,5200,3152,7248,592,4688,2640,6736,1616,5712,3664,7760,336,4432,2384,6480,1360,5456,3408,7504,848,4944,2896,6992,1872,5968,3920,8016,208,4304,2256,6352,1232,5328,3280,7376,720,4816,2768,6864,1744,5840,3792,7888,464,4560,2512,6608,1488,5584,3536,7632,976,5072,3024,7120,2000,6096,4048,8144,48,4144,2096,6192,1072,5168,3120,7216,560,4656,2608,6704,1584,5680,3632,7728,304,4400,2352,6448,1328,5424,3376,7472,816,4912,2864,6960,1840,5936,3888,7984,176,4272,2224,6320,1200,5296,3248,7344,688,4784,2736,6832,1712,5808,3760,7856,432,4528,2480,6576,1456,5552,3504,7600,944,5040,2992,7088,1968,6064,4016,8112,112,4208,2160,6256,1136,5232,3184,7280,624,4720,2672,6768,1648,5744,3696,7792,368,4464,2416,6512,1392,5488,3440,7536,880,4976,2928,7024,1904,6000,3952,8048,240,4336,2288,6384,1264,5360,3312,7408,752,4848,2800,6896,1776,5872,3824,7920,496,4592,2544,6640,1520,5616,3568,7664,1008,5104,3056,7152,2032,6128,4080,8176,8,4104,2056,6152,1032,5128,3080,7176,520,4616,2568,6664,1544,5640,3592,7688,264,4360,2312,6408,1288,5384,3336,7432,776,4872,2824,6920,1800,5896,3848,7944,136,4232,2184,6280,1160,5256,3208,7304,648,4744,2696,6792,1672,5768,3720,7816,392,4488,2440,6536,1416,5512,3464,7560,904,5000,2952,7048,1928,6024,3976,8072,72,4168,2120,6216,1096,5192,3144,7240,584,4680,2632,6728,1608,5704,3656,7752,328,4424,2376,6472,1352,5448,3400,7496,840,4936,2888,6984,1864,5960,3912,8008,200,4296,2248,6344,1224,5320,3272,7368,712,4808,2760,6856,1736,5832,3784,7880,456,4552,2504,6600,1480,5576,3528,7624,968,5064,3016,7112,1992,6088,4040,8136,40,4136,2088,6184,1064,5160,3112,7208,552,4648,2600,6696,1576,5672,3624,7720,296,4392,2344,6440,1320,5416,3368,7464,808,4904,2856,6952,1832,5928,3880,7976,168,4264,2216,6312,1192,5288,3240,7336,680,4776,2728,6824,1704,5800,3752,7848,424,4520,2472,6568,1448,5544,3496,7592,936,5032,2984,7080,1960,6056,4008,8104,104,4200,2152,6248,1128,5224,3176,7272,616,4712,2664,6760,1640,5736,3688,7784,360,4456,2408,6504,1384,5480,3432,7528,872,4968,2920,7016,1896,5992,3944,8040,232,4328,2280,6376,1256,5352,3304,7400,744,4840,2792,6888,1768,5864,3816,7912,488,4584,2536,6632,1512,5608,3560,7656,1000,5096,3048,7144,2024,6120,4072,8168,24,4120,2072,6168,1048,5144,3096,7192,536,4632,2584,6680,1560,5656,3608,7704,280,4376,2328,6424,1304,5400,3352,7448,792,4888,2840,6936,1816,5912,3864,7960,152,4248,2200,6296,1176,5272,3224,7320,664,4760,2712,6808,1688,5784,3736,7832,408,4504,2456,6552,1432,5528,3480,7576,920,5016,2968,7064,1944,6040,3992,8088,88,4184,2136,6232,1112,5208,3160,7256,600,4696,2648,6744,1624,5720,3672,7768,344,4440,2392,6488,1368,5464,3416,7512,856,4952,2904,7000,1880,5976,3928,8024,216,4312,2264,6360,1240,5336,3288,7384,728,4824,2776,6872,1752,5848,3800,7896,472,4568,2520,6616,1496,5592,3544,7640,984,5080,3032,7128,2008,6104,4056,8152,56,4152,2104,6200,1080,5176,3128,7224,568,4664,2616,6712,1592,5688,3640,7736,312,4408,2360,6456,1336,5432,3384,7480,824,4920,2872,6968,1848,5944,3896,7992,184,4280,2232,6328,1208,5304,3256,7352,696,4792,2744,6840,1720,5816,3768,7864,440,4536,2488,6584,1464,5560,3512,7608,952,5048,3000,7096,1976,6072,4024,8120,120,4216,2168,6264,1144,5240,3192,7288,632,4728,2680,6776,1656,5752,3704,7800,376,4472,2424,6520,1400,5496,3448,7544,888,4984,2936,7032,1912,6008,3960,8056,248,4344,2296,6392,1272,5368,3320,7416,760,4856,2808,6904,1784,5880,3832,7928,504,4600,2552,6648,1528,5624,3576,7672,1016,5112,3064,7160,2040,6136,4088,8184,4,4100,2052,6148,1028,5124,3076,7172,516,4612,2564,6660,1540,5636,3588,7684,260,4356,2308,6404,1284,5380,3332,7428,772,4868,2820,6916,1796,5892,3844,7940,132,4228,2180,6276,1156,5252,3204,7300,644,4740,2692,6788,1668,5764,3716,7812,388,4484,2436,6532,1412,5508,3460,7556,900,4996,2948,7044,1924,6020,3972,8068,68,4164,2116,6212,1092,5188,3140,7236,580,4676,2628,6724,1604,5700,3652,7748,324,4420,2372,6468,1348,5444,3396,7492,836,4932,2884,6980,1860,5956,3908,8004,196,4292,2244,6340,1220,5316,3268,7364,708,4804,2756,6852,1732,5828,3780,7876,452,4548,2500,6596,1476,5572,3524,7620,964,5060,3012,7108,1988,6084,4036,8132,36,4132,2084,6180,1060,5156,3108,7204,548,4644,2596,6692,1572,5668,3620,7716,292,4388,2340,6436,1316,5412,3364,7460,804,4900,2852,6948,1828,5924,3876,7972,164,4260,2212,6308,1188,5284,3236,7332,676,4772,2724,6820,1700,5796,3748,7844,420,4516,2468,6564,1444,5540,3492,7588,932,5028,2980,7076,1956,6052,4004,8100,100,4196,2148,6244,1124,5220,3172,7268,612,4708,2660,6756,1636,5732,3684,7780,356,4452,2404,6500,1380,5476,3428,7524,868,4964,2916,7012,1892,5988,3940,8036,228,4324,2276,6372,1252,5348,3300,7396,740,4836,2788,6884,1764,5860,3812,7908,484,4580,2532,6628,1508,5604,3556,7652,996,5092,3044,7140,2020,6116,4068,8164,20,4116,2068,6164,1044,5140,3092,7188,532,4628,2580,6676,1556,5652,3604,7700,276,4372,2324,6420,1300,5396,3348,7444,788,4884,2836,6932,1812,5908,3860,7956,148,4244,2196,6292,1172,5268,3220,7316,660,4756,2708,6804,1684,5780,3732,7828,404,4500,2452,6548,1428,5524,3476,7572,916,5012,2964,7060,1940,6036,3988,8084,84,4180,2132,6228,1108,5204,3156,7252,596,4692,2644,6740,1620,5716,3668,7764,340,4436,2388,6484,1364,5460,3412,7508,852,4948,2900,6996,1876,5972,3924,8020,212,4308,2260,6356,1236,5332,3284,7380,724,4820,2772,6868,1748,5844,3796,7892,468,4564,2516,6612,1492,5588,3540,7636,980,5076,3028,7124,2004,6100,4052,8148,52,4148,2100,6196,1076,5172,3124,7220,564,4660,2612,6708,1588,5684,3636,7732,308,4404,2356,6452,1332,5428,3380,7476,820,4916,2868,6964,1844,5940,3892,7988,180,4276,2228,6324,1204,5300,3252,7348,692,4788,2740,6836,1716,5812,3764,7860,436,4532,2484,6580,1460,5556,3508,7604,948,5044,2996,7092,1972,6068,4020,8116,116,4212,2164,6260,1140,5236,3188,7284,628,4724,2676,6772,1652,5748,3700,7796,372,4468,2420,6516,1396,5492,3444,7540,884,4980,2932,7028,1908,6004,3956,8052,244,4340,2292,6388,1268,5364,3316,7412,756,4852,2804,6900,1780,5876,3828,7924,500,4596,2548,6644,1524,5620,3572,7668,1012,5108,3060,7156,2036,6132,4084,8180,12,4108,2060,6156,1036,5132,3084,7180,524,4620,2572,6668,1548,5644,3596,7692,268,4364,2316,6412,1292,5388,3340,7436,780,4876,2828,6924,1804,5900,3852,7948,140,4236,2188,6284,1164,5260,3212,7308,652,4748,2700,6796,1676,5772,3724,7820,396,4492,2444,6540,1420,5516,3468,7564,908,5004,2956,7052,1932,6028,3980,8076,76,4172,2124,6220,1100,5196,3148,7244,588,4684,2636,6732,1612,5708,3660,7756,332,4428,2380,6476,1356,5452,3404,7500,844,4940,2892,6988,1868,5964,3916,8012,204,4300,2252,6348,1228,5324,3276,7372,716,4812,2764,6860,1740,5836,3788,7884,460,4556,2508,6604,1484,5580,3532,7628,972,5068,3020,7116,1996,6092,4044,8140,44,4140,2092,6188,1068,5164,3116,7212,556,4652,2604,6700,1580,5676,3628,7724,300,4396,2348,6444,1324,5420,3372,7468,812,4908,2860,6956,1836,5932,3884,7980,172,4268,2220,6316,1196,5292,3244,7340,684,4780,2732,6828,1708,5804,3756,7852,428,4524,2476,6572,1452,5548,3500,7596,940,5036,2988,7084,1964,6060,4012,8108,108,4204,2156,6252,1132,5228,3180,7276,620,4716,2668,6764,1644,5740,3692,7788,364,4460,2412,6508,1388,5484,3436,7532,876,4972,2924,7020,1900,5996,3948,8044,236,4332,2284,6380,1260,5356,3308,7404,748,4844,2796,6892,1772,5868,3820,7916,492,4588,2540,6636,1516,5612,3564,7660,1004,5100,3052,7148,2028,6124,4076,8172,28,4124,2076,6172,1052,5148,3100,7196,540,4636,2588,6684,1564,5660,3612,7708,284,4380,2332,6428,1308,5404,3356,7452,796,4892,2844,6940,1820,5916,3868,7964,156,4252,2204,6300,1180,5276,3228,7324,668,4764,2716,6812,1692,5788,3740,7836,412,4508,2460,6556,1436,5532,3484,7580,924,5020,2972,7068,1948,6044,3996,8092,92,4188,2140,6236,1116,5212,3164,7260,604,4700,2652,6748,1628,5724,3676,7772,348,4444,2396,6492,1372,5468,3420,7516,860,4956,2908,7004,1884,5980,3932,8028,220,4316,2268,6364,1244,5340,3292,7388,732,4828,2780,6876,1756,5852,3804,7900,476,4572,2524,6620,1500,5596,3548,7644,988,5084,3036,7132,2012,6108,4060,8156,60,4156,2108,6204,1084,5180,3132,7228,572,4668,2620,6716,1596,5692,3644,7740,316,4412,2364,6460,1340,5436,3388,7484,828,4924,2876,6972,1852,5948,3900,7996,188,4284,2236,6332,1212,5308,3260,7356,700,4796,2748,6844,1724,5820,3772,7868,444,4540,2492,6588,1468,5564,3516,7612,956,5052,3004,7100,1980,6076,4028,8124,124,4220,2172,6268,1148,5244,3196,7292,636,4732,2684,6780,1660,5756,3708,7804,380,4476,2428,6524,1404,5500,3452,7548,892,4988,2940,7036,1916,6012,3964,8060,252,4348,2300,6396,1276,5372,3324,7420,764,4860,2812,6908,1788,5884,3836,7932,508,4604,2556,6652,1532,5628,3580,7676,1020,5116,3068,7164,2044,6140,4092,8188,2,4098,2050,6146,1026,5122,3074,7170,514,4610,2562,6658,1538,5634,3586,7682,258,4354,2306,6402,1282,5378,3330,7426,770,4866,2818,6914,1794,5890,3842,7938,130,4226,2178,6274,1154,5250,3202,7298,642,4738,2690,6786,1666,5762,3714,7810,386,4482,2434,6530,1410,5506,3458,7554,898,4994,2946,7042,1922,6018,3970,8066,66,4162,2114,6210,1090,5186,3138,7234,578,4674,2626,6722,1602,5698,3650,7746,322,4418,2370,6466,1346,5442,3394,7490,834,4930,2882,6978,1858,5954,3906,8002,194,4290,2242,6338,1218,5314,3266,7362,706,4802,2754,6850,1730,5826,3778,7874,450,4546,2498,6594,1474,5570,3522,7618,962,5058,3010,7106,1986,6082,4034,8130,34,4130,2082,6178,1058,5154,3106,7202,546,4642,2594,6690,1570,5666,3618,7714,290,4386,2338,6434,1314,5410,3362,7458,802,4898,2850,6946,1826,5922,3874,7970,162,4258,2210,6306,1186,5282,3234,7330,674,4770,2722,6818,1698,5794,3746,7842,418,4514,2466,6562,1442,5538,3490,7586,930,5026,2978,7074,1954,6050,4002,8098,98,4194,2146,6242,1122,5218,3170,7266,610,4706,2658,6754,1634,5730,3682,7778,354,4450,2402,6498,1378,5474,3426,7522,866,4962,2914,7010,1890,5986,3938,8034,226,4322,2274,6370,1250,5346,3298,7394,738,4834,2786,6882,1762,5858,3810,7906,482,4578,2530,6626,1506,5602,3554,7650,994,5090,3042,7138,2018,6114,4066,8162,18,4114,2066,6162,1042,5138,3090,7186,530,4626,2578,6674,1554,5650,3602,7698,274,4370,2322,6418,1298,5394,3346,7442,786,4882,2834,6930,1810,5906,3858,7954,146,4242,2194,6290,1170,5266,3218,7314,658,4754,2706,6802,1682,5778,3730,7826,402,4498,2450,6546,1426,5522,3474,7570,914,5010,2962,7058,1938,6034,3986,8082,82,4178,2130,6226,1106,5202,3154,7250,594,4690,2642,6738,1618,5714,3666,7762,338,4434,2386,6482,1362,5458,3410,7506,850,4946,2898,6994,1874,5970,3922,8018,210,4306,2258,6354,1234,5330,3282,7378,722,4818,2770,6866,1746,5842,3794,7890,466,4562,2514,6610,1490,5586,3538,7634,978,5074,3026,7122,2002,6098,4050,8146,50,4146,2098,6194,1074,5170,3122,7218,562,4658,2610,6706,1586,5682,3634,7730,306,4402,2354,6450,1330,5426,3378,7474,818,4914,2866,6962,1842,5938,3890,7986,178,4274,2226,6322,1202,5298,3250,7346,690,4786,2738,6834,1714,5810,3762,7858,434,4530,2482,6578,1458,5554,3506,7602,946,5042,2994,7090,1970,6066,4018,8114,114,4210,2162,6258,1138,5234,3186,7282,626,4722,2674,6770,1650,5746,3698,7794,370,4466,2418,6514,1394,5490,3442,7538,882,4978,2930,7026,1906,6002,3954,8050,242,4338,2290,6386,1266,5362,3314,7410,754,4850,2802,6898,1778,5874,3826,7922,498,4594,2546,6642,1522,5618,3570,7666,1010,5106,3058,7154,2034,6130,4082,8178,10,4106,2058,6154,1034,5130,3082,7178,522,4618,2570,6666,1546,5642,3594,7690,266,4362,2314,6410,1290,5386,3338,7434,778,4874,2826,6922,1802,5898,3850,7946,138,4234,2186,6282,1162,5258,3210,7306,650,4746,2698,6794,1674,5770,3722,7818,394,4490,2442,6538,1418,5514,3466,7562,906,5002,2954,7050,1930,6026,3978,8074,74,4170,2122,6218,1098,5194,3146,7242,586,4682,2634,6730,1610,5706,3658,7754,330,4426,2378,6474,1354,5450,3402,7498,842,4938,2890,6986,1866,5962,3914,8010,202,4298,2250,6346,1226,5322,3274,7370,714,4810,2762,6858,1738,5834,3786,7882,458,4554,2506,6602,1482,5578,3530,7626,970,5066,3018,7114,1994,6090,4042,8138,42,4138,2090,6186,1066,5162,3114,7210,554,4650,2602,6698,1578,5674,3626,7722,298,4394,2346,6442,1322,5418,3370,7466,810,4906,2858,6954,1834,5930,3882,7978,170,4266,2218,6314,1194,5290,3242,7338,682,4778,2730,6826,1706,5802,3754,7850,426,4522,2474,6570,1450,5546,3498,7594,938,5034,2986,7082,1962,6058,4010,8106,106,4202,2154,6250,1130,5226,3178,7274,618,4714,2666,6762,1642,5738,3690,7786,362,4458,2410,6506,1386,5482,3434,7530,874,4970,2922,7018,1898,5994,3946,8042,234,4330,2282,6378,1258,5354,3306,7402,746,4842,2794,6890,1770,5866,3818,7914,490,4586,2538,6634,1514,5610,3562,7658,1002,5098,3050,7146,2026,6122,4074,8170,26,4122,2074,6170,1050,5146,3098,7194,538,4634,2586,6682,1562,5658,3610,7706,282,4378,2330,6426,1306,5402,3354,7450,794,4890,2842,6938,1818,5914,3866,7962,154,4250,2202,6298,1178,5274,3226,7322,666,4762,2714,6810,1690,5786,3738,7834,410,4506,2458,6554,1434,5530,3482,7578,922,5018,2970,7066,1946,6042,3994,8090,90,4186,2138,6234,1114,5210,3162,7258,602,4698,2650,6746,1626,5722,3674,7770,346,4442,2394,6490,1370,5466,3418,7514,858,4954,2906,7002,1882,5978,3930,8026,218,4314,2266,6362,1242,5338,3290,7386,730,4826,2778,6874,1754,5850,3802,7898,474,4570,2522,6618,1498,5594,3546,7642,986,5082,3034,7130,2010,6106,4058,8154,58,4154,2106,6202,1082,5178,3130,7226,570,4666,2618,6714,1594,5690,3642,7738,314,4410,2362,6458,1338,5434,3386,7482,826,4922,2874,6970,1850,5946,3898,7994,186,4282,2234,6330,1210,5306,3258,7354,698,4794,2746,6842,1722,5818,3770,7866,442,4538,2490,6586,1466,5562,3514,7610,954,5050,3002,7098,1978,6074,4026,8122,122,4218,2170,6266,1146,5242,3194,7290,634,4730,2682,6778,1658,5754,3706,7802,378,4474,2426,6522,1402,5498,3450,7546,890,4986,2938,7034,1914,6010,3962,8058,250,4346,2298,6394,1274,5370,3322,7418,762,4858,2810,6906,1786,5882,3834,7930,506,4602,2554,6650,1530,5626,3578,7674,1018,5114,3066,7162,2042,6138,4090,8186,6,4102,2054,6150,1030,5126,3078,7174,518,4614,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79,3331,7427,771,4867,2819,6915,1795,5891,3843,7939,131,4227,2179,6275,1155,5251,3203,7299,643,4739,2691,6787,1667,5763,3715,7811,387,4483,2435,6531,1411,5507,3459,7555,899,4995,2947,7043,1923,6019,3971,8067,67,4163,2115,6211,1091,5187,3139,7235,579,4675,2627,6723,1603,5699,3651,7747,323,4419,2371,6467,1347,5443,3395,7491,835,4931,2883,6979,1859,5955,3907,8003,195,4291,2243,6339,1219,5315,3267,7363,707,4803,2755,6851,1731,5827,3779,7875,451,4547,2499,6595,1475,5571,3523,7619,963,5059,3011,7107,1987,6083,4035,8131,35,4131,2083,6179,1059,5155,3107,7203,547,4643,2595,6691,1571,5667,3619,7715,291,4387,2339,6435,1315,5411,3363,7459,803,4899,2851,6947,1827,5923,3875,7971,163,4259,2211,6307,1187,5283,3235,7331,675,4771,2723,6819,1699,5795,3747,7843,419,4515,2467,6563,1443,5539,3491,7587,931,5027,2979,7075,1955,6051,4003,8099,99,4195,2147,6243,1123,5219,3171,7267,611,4707,2659,6755,1635,5731,3683,7779,355,4451,2403,6499,1379,5475,3427,7523,867,4963,2915,7011,1891,5987,3939,8035,227,4323,2275,6371,1251,5347,3299,7395,739,4835,2787,6883,1763,5859,3811,7907,483,4579,2531,6627,1507,5603,3555,7651,995,5091,3043,7139,2019,6115,4067,8163,19,4115,2067,6163,1043,5139,3091,7187,531,4627,2579,6675,1555,5651,3603,7699,275,4371,2323,6419,1299,5395,3347,7443,787,4883,2835,6931,1811,5907,3859,7955,147,4243,2195,6291,1171,5267,3219,7315,659,4755,2707,6803,1683,5779,3731,7827,403,4499,2451,6547,1427,5523,3475,7571,915,5011,2963,7059,1939,6035,3987,8083,83,4179,2131,6227,1107,5203,3155,7251,595,4691,2643,6739,1619,5715,3667,7763,339,4435,2387,6483,1363,5459,3411,7507,851,4947,2899,6995,1875,5971,3923,8019,211,4307,2259,6355,1235,5331,3283,7379,723,4819,2771,6867,1747,5843,3795,7891,467,4563,2515,6611,1491,5587,3539,7635,979,5075,3027,7123,2003,6099,4051,8147,51,4147,2099,6195,1075,5171,3123,7219,563,4659,2611,6707,1587,5683,3635,7731,307,4403,2355,6451,1331,5427,3379,7475,819,4915,2867,6963,1843,5939,3891,7987,179,4275,2227,6323,1203,5299,3251,7347,691,4787,2739,6835,1715,5811,3763,7859,435,4531,2483,6579,1459,5555,3507,7603,947,5043,2995,7091,1971,6067,4019,8115,115,4211,2163,6259,1139,5235,3187,7283,627,4723,2675,6771,1651,5747,3699,7795,371,4467,2419,6515,1395,5491,3443,7539,883,4979,2931,7027,1907,6003,3955,8051,243,4339,2291,6387,1267,5363,3315,7411,755,4851,2803,6899,1779,5875,3827,7923,499,4595,2547,6643,1523,5619,3571,7667,1011,5107,3059,7155,2035,6131,4083,8179,11,4107,2059,6155,1035,5131,3083,7179,523,4619,2571,6667,1547,5643,3595,7691,267,4363,2315,6411,1291,5387,3339,7435,779,4875,2827,6923,1803,5899,3851,7947,139,4235,2187,6283,1163,5259,3211,7307,651,4747,2699,6795,1675,5771,3723,7819,395,4491,2443,6539,1419,5515,3467,7563,907,5003,2955,7051,1931,6027,3979,8075,75,4171,2123,6219,1099,5195,3147,7243,587,4683,2635,6731,1611,5707,3659,7755,331,4427,2379,6475,1355,5451,3403,7499,843,4939,2891,6987,1867,5963,3915,8011,203,4299,2251,6347,1227,5323,3275,7371,715,4811,2763,6859,1739,5835,3787,7883,459,4555,2507,6603,1483,5579,3531,7627,971,5067,3019,7115,1995,6091,4043,8139,43,4139,2091,6187,1067,5163,3115,7211,555,4651,2603,6699,1579,5675,3627,7723,299,4395,2347,6443,1323,5419,3371,7467,811,4907,2859,6955,1835,5931,3883,7979,171,4267,2219,6315,1195,5291,3243,7339,683,4779,2731,6827,1707,5803,3755,7851,427,4523,2475,6571,1451,5547,3499,7595,939,5035,2987,7083,1963,6059,4011,8107,107,4203,2155,6251,1131,5227,3179,7275,619,4715,2667,6763,1643,5739,3691,7787,363,4459,2411,6507,1387,5483,3435,7531,875,4971,2923,7019,1899,5995,3947,8043,235,4331,2283,6379,1259,5355,3307,7403,747,4843,2795,6891,1771,5867,3819,7915,491,4587,2539,6635,1515,5611,3563,7659,1003,5099,3051,7147,2027,6123,4075,8171,27,4123,2075,6171,1051,5147,3099,7195,539,4635,2587,6683,1563,5659,3611,7707,283,4379,2331,6427,1307,5403,3355,7451,795,4891,2843,6939,1819,5915,3867,7963,155,4251,2203,6299,1179,5275,3227,7323,667,4763,2715,6811,1691,5787,3739,7835,411,4507,2459,6555,1435,5531,3483,7579,923,5019,2971,7067,1947,6043,3995,8091,91,4187,2139,6235,1115,5211,3163,7259,603,4699,2651,6747,1627,5723,3675,7771,347,4443,2395,6491,1371,5467,3419,7515,859,4955,2907,7003,1883,5979,3931,8027,219,4315,2267,6363,1243,5339,3291,7387,731,4827,2779,6875,1755,5851,3803,7899,475,4571,2523,6619,1499,5595,3547,7643,987,5083,3035,7131,2011,6107,4059,8155,59,4155,2107,6203,1083,5179,3131,7227,571,4667,2619,6715,1595,5691,3643,7739,315,4411,2363,6459,1339,5435,3387,7483,827,4923,2875,6971,1851,5947,3899,7995,187,4283,2235,6331,1211,5307,3259,7355,699,4795,2747,6843,1723,5819,3771,7867,443,4539,2491,6587,1467,5563,3515,7611,955,5051,3003,7099,1979,6075,4027,8123,123,4219,2171,6267,1147,5243,3195,7291,635,4731,2683,6779,1659,5755,3707,7803,379,4475,2427,6523,1403,5499,3451,7547,891,4987,2939,7035,1915,6011,3963,8059,251,4347,2299,6395,1275,5371,3323,7419,763,4859,2811,6907,1787,5883,3835,7931,507,4603,2555,6651,1531,5627,3579,7675,1019,5115,3067,7163,2043,6139,4091,8187,7,4103,2055,6151,1031,5127,3079,7175,519,4615,2567,6663,1543,5639,3591,7687,263,4359,2311,6407,1287,5383,3335,7431,775,4871,2823,6919,1799,5895,3847,7943,135,4231,2183,6279,1159,5255,3207,7303,647,4743,2695,6791,1671,5767,3719,7815,391,4487,2439,6535,1415,5511,3463,7559,903,4999,2951,7047,1927,6023,3975,8071,71,4167,2119,6215,1095,5191,3143,7239,583,4679,2631,6727,1607,5703,3655,7751,327,4423,2375,6471,1351,5447,3399,7495,839,4935,2887,6983,1863,5959,3911,8007,199,4295,2247,6343,1223,5319,3271,7367,711,4807,2759,6855,1735,5831,3783,7879,455,4551,2503,6599,1479,5575,3527,7623,967,5063,3015,7111,1991,6087,4039,8135,39,4135,2087,6183,1063,5159,3111,7207,551,4647,2599,6695,1575,5671,3623,7719,295,4391,2343,6439,1319,5415,3367,7463,807,4903,2855,6951,1831,5927,3879,7975,167,4263,2215,6311,1191,5287,3239,7335,679,4775,2727,6823,1703,5799,3751,7847,423,4519,2471,6567,1447,5543,3495,7591,935,5031,2983,7079,1959,6055,4007,8103,103,4199,2151,6247,1127,5223,3175,7271,615,4711,2663,6759,1639,5735,3687,7783,359,4455,2407,6503,1383,5479,3431,7527,871,4967,2919,7015,1895,5991,3943,8039,231,4327,2279,6375,1255,5351,3303,7399,743,4839,2791,6887,1767,5863,3815,7911,487,4583,2535,6631,1511,5607,3559,7655,999,5095,3047,7143,2023,6119,4071,8167,23,4119,2071,6167,1047,5143,3095,7191,535,4631,2583,6679,1559,5655,3607,7703,279,4375,2327,6423,1303,5399,3351,7447,791,4887,2839,6935,1815,5911,3863,7959,151,4247,2199,6295,1175,5271,3223,7319,663,4759,2711,6807,1687,5783,3735,7831,407,4503,2455,6551,1431,5527,3479,7575,919,5015,2967,7063,1943,6039,3991,8087,87,4183,2135,6231,1111,5207,3159,7255,599,4695,2647,6743,1623,5719,3671,7767,343,4439,2391,6487,1367,5463,3415,7511,855,4951,2903,6999,1879,5975,3927,8023,215,4311,2263,6359,1239,5335,3287,7383,727,4823,2775,6871,1751,5847,3799,7895,471,4567,2519,6615,1495,5591,3543,7639,983,5079,3031,7127,2007,6103,4055,8151,55,4151,2103,6199,1079,5175,3127,7223,567,4663,2615,6711,1591,5687,3639,7735,311,4407,2359,6455,1335,5431,3383,7479,823,4919,2871,6967,1847,5943,3895,7991,183,4279,2231,6327,1207,5303,3255,7351,695,4791,2743,6839,1719,5815,3767,7863,439,4535,2487,6583,1463,5559,3511,7607,951,5047,2999,7095,1975,6071,4023,8119,119,4215,2167,6263,1143,5239,3191,7287,631,4727,2679,6775,1655,5751,3703,7799,375,4471,2423,6519,1399,5495,3447,7543,887,4983,2935,7031,1911,6007,3959,8055,247,4343,2295,6391,1271,5367,3319,7415,759,4855,2807,6903,1783,5879,3831,7927,503,4599,2551,6647,1527,5623,3575,7671,1015,5111,3063,7159,2039,6135,4087,8183,15,4111,2063,6159,1039,5135,3087,7183,527,4623,2575,6671,1551,5647,3599,7695,271,4367,2319,6415,1295,5391,3343,7439,783,4879,2831,6927,1807,5903,3855,7951,143,4239,2191,6287,1167,5263,3215,7311,655,4751,2703,6799,1679,5775,3727,7823,399,4495,2447,6543,1423,5519,3471,7567,911,5007,2959,7055,1935,6031,3983,8079,79,4175,2127,6223,1103,5199,3151,7247,591,4687,2639,6735,1615,5711,3663,7759,335,4431,2383,6479,1359,5455,3407,7503,847,4943,2895,6991,1871,5967,3919,8015,207,4303,2255,6351,1231,5327,3279,7375,719,4815,2767,6863,1743,5839,3791,7887,463,4559,2511,6607,1487,5583,3535,7631,975,5071,3023,7119,1999,6095,4047,8143,47,4143,2095,6191,1071,5167,3119,7215,559,4655,2607,6703,1583,5679,3631,7727,303,4399,2351,6447,1327,5423,3375,7471,815,4911,2863,6959,1839,5935,3887,7983,175,4271,2223,6319,1199,5295,3247,7343,687,4783,2735,6831,1711,5807,3759,7855,431,4527,2479,6575,1455,5551,3503,7599,943,5039,2991,7087,1967,6063,4015,8111,111,4207,2159,6255,1135,5231,3183,7279,623,4719,2671,6767,1647,5743,3695,7791,367,4463,2415,6511,1391,5487,3439,7535,879,4975,2927,7023,1903,5999,3951,8047,239,4335,2287,6383,1263,5359,3311,7407,751,4847,2799,6895,1775,5871,3823,7919,495,4591,2543,6639,1519,5615,3567,7663,1007,5103,3055,7151,2031,6127,4079,8175,31,4127,2079,6175,1055,5151,3103,7199,543,4639,2591,6687,1567,5663,3615,7711,287,4383,2335,6431,1311,5407,3359,7455,799,4895,2847,6943,1823,5919,3871,7967,159,4255,2207,6303,1183,5279,3231,7327,671,4767,2719,6815,1695,5791,3743,7839,415,4511,2463,6559,1439,5535,3487,7583,927,5023,2975,7071,1951,6047,3999,8095,95,4191,2143,6239,1119,5215,3167,7263,607,4703,2655,6751,1631,5727,3679,7775,351,4447,2399,6495,1375,5471,3423,7519,863,4959,2911,7007,1887,5983,3935,8031,223,4319,2271,6367,1247,5343,3295,7391,735,4831,2783,6879,1759,5855,3807,7903,479,4575,2527,6623,1503,5599,3551,7647,991,5087,3039,7135,2015,6111,4063,8159,63,4159,2111,6207,1087,5183,3135,7231,575,4671,2623,6719,1599,5695,3647,7743,319,4415,2367,6463,1343,5439,3391,7487,831,4927,2879,6975,1855,5951,3903,7999,191,4287,2239,6335,1215,5311,3263,7359,703,4799,2751,6847,1727,5823,3775,7871,447,4543,2495,6591,1471,5567,3519,7615,959,5055,3007,7103,1983,6079,4031,8127,127,4223,2175,6271,1151,5247,3199,7295,639,4735,2687,6783,1663,5759,3711,7807,383,4479,2431,6527,1407,5503,3455,7551,895,4991,2943,7039,1919,6015,3967,8063,255,4351,2303,6399,1279,5375,3327,7423,767,4863,2815,6911,1791,5887,3839,7935,511,4607,2559,6655,1535,5631,3583,7679,1023,5119,3071,7167,2047,6143,4095,8191]。

序列2：

Shorten_Q_half＝[1,4097,2049,6145,1025,5121,3073,7169,513,4609,2561,6657,1537,5633,3585,7681,257,4353,2305,6401,1281,5377,3329,7425,769,4865,2817,6913,1793,5889,3841,7937,129,4225,2177,6273,1153,5249,3201,7297,641,4737,2689,6785,1665,5761,3713,7809,385,4481,2433,6529,1409,5505,3457,7553,897,4993,2945,7041,1921,6017,3969,8065,65,4161,2113,6209,1089,5185,3137,7233,577,4673,2625,6721,1601,5697,3649,7745,321,4417,2369,6465,1345,5441,3393,7489,833,4929,2881,6977,1857,5953,3905,8001,193,4289,2241,6337,1217,5313,3265,7361,705,4801,2753,6849,1729,5825,3777,7873,449,4545,2497,6593,1473,5569,3521,7617,961,5057,3009,7105,1985,6081,4033,8129,33,4129,2081,6177,1057,5153,3105,7201,545,4641,2593,6689,1569,5665,3617,7713,289,4385,2337,6433,1313,5409,3361,7457,801,4897,2849,6945,1825,5921,3873,7969,161,4257,2209,6305,1185,5281,3233,7329,673,4769,2721,6817,1697,5793,3745,7841,417,4513,2465,6561,1441,5537,3489,7585,929,5025,2977,7073,1953,6049,4001,8097,97,4193,2145,6241,1121,5217,3169,7265,609,4705,2657,6753,1633,5729,3681,7777,353,4449,2401,6497,1377,5473,3425,7521,865,4961,2913,7009,1889,5985,3937,8033,225,4321,2273,6369,1249,5345,3297,7393,737,4833,2785,6881,1761,5857,3809,7905,481,4577,2529,6625,1505,5601,3553,7649,993,5089,3041,7137,2017,6113,4065,8161,17,4113,2065,6161,1041,5137,3089,7185,529,4625,2577,6673,1553,5649,3601,7697,273,4369,2321,6417,1297,5393,3345,7441,785,4881,2833,6929,1809,5905,3857,7953,145,4241,2193,6289,1169,5265,3217,7313,657,4753,2705,6801,1681,5777,3729,7825,401,4497,2449,6545,1425,5521,3473,7569,913,5009,2961,7057,1937,6033,3985,8081,81,4177,2129,6225,1105,5201,3153,7249,593,4689,2641,6737,1617,5713,3665,7761,337,4433,2385,6481,1361,5457,3409,7505,849,4945,2897,6993,1873,5969,3921,8017,209,4305,2257,6353,1233,5329,3281,7377,721,4817,2769,6865,1745,5841,3793,7889,465,4561,2513,6609,1489,5585,3537,7633,977,5073,3025,7121,2001,6097,4049,8145,49,4145,2097,6193,1073,5169,3121,7217,561,4657,2609,6705,1585,5681,3633,7729,305,4401,2353,6449,1329,5425,3377,7473,817,4913,2865,6961,1841,5937,3889,7985,177,4273,2225,6321,1201,5297,3249,7345,689,4785,2737,6833,1713,5809,3761,7857,433,4529,2481,6577,1457,5553,3505,7601,945,5041,2993,7089,1969,6065,4017,8113,113,4209,2161,6257,1137,5233,3185,7281,625,4721,2673,6769,1649,5745,3697,7793,369,4465,2417,6513,1393,5489,3441,7537,881,4977,2929,7025,1905,6001,3953,8049,241,4337,2289,6385,1265,5361,3313,7409,753,4849,2801,6897,1777,5873,3825,7921,497,4593,2545,6641,1521,5617,3569,7665,1009,5105,3057,7153,2033,6129,4081,8177,9,4105,2057,6153,1033,5129,3081,7177,521,4617,2569,6665,1545,5641,3593,7689,265,4361,2313,6409,1289,5385,3337,7433,777,4873,2825,6921,1801,5897,3849,7945,137,4233,2185,6281,1161,5257,3209,7305,649,4745,2697,6793,1673,5769,3721,7817,393,4489,2441,6537,1417,5513,3465,7561,905,5001,2953,7049,1929,6025,3977,8073,73,4169,2121,6217,1097,5193,3145,7241,585,4681,2633,6729,1609,5705,3657,7753,329,4425,2377,6473,1353,5449,3401,7497,841,4937,2889,6985,1865,5961,3913,8009,201,4297,2249,6345,1225,5321,3273,7369,713,4809,2761,6857,1737,5833,3785,7881,457,4553,2505,6601,1481,5577,3529,7625,969,5065,3017,7113,1993,6089,4041,8137,41,4137,2089,6185,1065,5161,3113,7209,553,4649,2601,6697,1577,5673,3625,7721,297,4393,2345,6441,1321,5417,3369,7465,809,4905,2857,6953,1833,5929,3881,7977,169,4265,2217,6313,1193,5289,3241,7337,681,4777,2729,6825,1705,5801,3753,7849,425,4521,2473,6569,1449,5545,3497,7593,937,5033,2985,7081,1961,6057,4009,8105,105,4201,2153,6249,1129,5225,3177,7273,617,4713,2665,6761,1641,5737,3689,7785,361,4457,2409,6505,1385,5481,3433,7529,873,4969,2921,7017,1897,5993,3945,8041,233,4329,2281,6377,1257,5353,3305,7401,745,4841,2793,6889,1769,5865,3817,7913,489,4585,2537,6633,1513,5609,3561,7657,1001,5097,3049,7145,2025,6121,4073,8169,25,4121,2073,6169,1049,5145,3097,7193,537,4633,2585,6681,1561,5657,3609,7705,281,4377,2329,6425,1305,5401,3353,7449,793,4889,2841,6937,1817,5913,3865,7961,153,4249,2201,6297,1177,5273,3225,7321,665,4761,2713,6809,1689,5785,3737,7833,409,4505,2457,6553,1433,5529,3481,7577,921,5017,2969,7065,1945,6041,3993,8089,89,4185,2137,6233,1113,5209,3161,7257,601,4697,2649,6745,1625,5721,3673,7769,345,4441,2393,6489,1369,5465,3417,7513,857,4953,2905,7001,1881,5977,3929,8025,217,4313,2265,6361,1241,5337,3289,7385,729,4825,2777,6873,1753,5849,3801,7897,473,4569,2521,6617,1497,5593,3545,7641,985,5081,3033,7129,2009,6105,4057,8153,57,4153,2105,6201,1081,5177,3129,7225,569,4665,2617,6713,1593,5689,3641,7737,313,4409,2361,6457,1337,5433,3385,7481,825,4921,2873,6969,1849,5945,3897,7993,185,4281,2233,6329,1209,5305,3257,7353,697,4793,2745,6841,1721,5817,3769,7865,441,4537,2489,6585,1465,5561,3513,7609,953,5049,3001,7097,1977,6073,4025,8121,121,4217,2169,6265,1145,5241,3193,7289,633,4729,2681,6777,1657,5753,3705,7801,377,4473,2425,6521,1401,5497,3449,7545,889,4985,2937,7033,1913,6009,3961,8057,249,4345,2297,6393,1273,5369,3321,7417,761,4857,2809,6905,1785,5881,3833,7929,505,4601,2553,6649,1529,5625,3577,7673,1017,5113,3065,7161,2041,6137,4089,8185,5,4101,2053,6149,1029,5125,3077,7173,517,4613,2565,6661,1541,5637,3589,7685,261,4357,2309,6405,1285,5381,3333,7429,773,4869,2821,6917,1797,5893,3845,7941,133,4229,2181,6277,1157,5253,3205,7301,645,4741,2693,6789,1669,5765,3717,7813,389,4485,2437,6533,1413,5509,3461,7557,901,4997,2949,7045,1925,6021,3973,8069,69,4165,2117,6213,1093,5189,3141,7237,581,4677,2629,6725,1605,5701,3653,7749,325,4421,2373,6469,1349,5445,3397,7493,837,4933,2885,6981,1861,5957,3909,8005,197,4293,2245,6341,1221,5317,3269,7365,709,4805,2757,6853,1733,5829,3781,7877,453,4549,2501,6597,1477,5573,3525,7621,965,5061,3013,7109,1989,6085,4037,8133,37,4133,2085,6181,1061,5157,3109,7205,549,4645,2597,6693,1573,5669,3621,7717,293,4389,2341,6437,1317,5413,3365,7461,805,4901,2853,6949,1829,5925,3877,7973,165,4261,2213,6309,1189,5285,3237,7333,677,4773,2725,6821,1701,5797,3749,7845,421,4517,2469,6565,1445,5541,3493,7589,933,5029,2981,7077,1957,6053,4005,8101,101,4197,2149,6245,1125,5221,3173,7269,613,4709,2661,6757,1637,5733,3685,7781,357,4453,2405,6501,1381,5477,3429,7525,869,4965,2917,7013,1893,5989,3941,8037,229,4325,2277,6373,1253,5349,3301,7397,741,4837,2789,6885,1765,5861,3813,7909,485,4581,2533,6629,1509,5605,3557,7653,997,5093,3045,7141,2021,6117,4069,8165,21,4117,2069,6165,1045,5141,3093,7189,533,4629,2581,6677,1557,5653,3605,7701,277,4373,2325,6421,1301,5397,3349,7445,789,4885,2837,6933,1813,5909,3861,7957,149,4245,2197,6293,1173,5269,3221,7317,661,4757,2709,6805,1685,5781,3733,7829,405,4501,2453,6549,1429,5525,3477,7573,917,5013,2965,7061,1941,6037,3989,8085,85,4181,2133,6229,1109,5205,3157,7253,597,4693,2645,6741,1621,5717,3669,7765,341,4437,2389,6485,1365,5461,3413,7509,853,4949,2901,6997,1877,5973,3925,8021,213,4309,2261,6357,1237,5333,3285,7381,725,4821,2773,6869,1749,5845,3797,7893,469,4565,2517,6613,1493,5589,3541,7637,981,5077,3029,7125,2005,6101,4053,8149,53,4149,2101,6197,1077,5173,3125,7221,565,4661,2613,6709,1589,5685,3637,7733,309,4405,2357,6453,1333,5429,3381,7477,821,4917,2869,6965,1845,5941,3893,7989,181,4277,2229,6325,1205,5301,3253,7349,693,4789,2741,6837,1717,5813,3765,7861,437,4533,2485,6581,1461,5557,3509,7605,949,5045,2997,7093,1973,6069,4021,8117,117,4213,2165,6261,1141,5237,3189,7285,629,4725,2677,6773,1653,5749,3701,7797,373,4469,2421,6517,1397,5493,3445,7541,885,4981,2933,7029,1909,6005,3957,8053,245,4341,2293,6389,1269,5365,3317,7413,757,4853,2805,6901,1781,5877,3829,7925,501,4597,2549,6645,1525,5621,3573,7669,1013,5109,3061,7157,2037,6133,4085,8181,13,4109,2061,6157,1037,5133,3085,7181,525,4621,2573,6669,1549,5645,3597,7693,269,4365,2317,6413,1293,5389,3341,7437,781,4877,2829,6925,1805,5901,3853,7949,141,4237,2189,6285,1165,5261,3213,7309,653,4749,2701,6797,1677,5773,3725,7821,397,4493,2445,6541,1421,5517,3469,7565,909,5005,2957,7053,1933,6029,3981,8077,77,4173,2125,6221,1101,5197,3149,7245,589,4685,2637,6733,1613,5709,3661,7757,333,4429,2381,6477,1357,5453,3405,7501,845,4941,2893,6989,1869,5965,3917,8013,205,4301,2253,6349,1229,5325,3277,7373,717,4813,2765,6861,1741,5837,3789,7885,461,4557,2509,6605,1485,5581,3533,7629,973,5069,3021,7117,1997,6093,4045,8141,45,4141,2093,6189,1069,5165,3117,7213,557,4653,2605,6701,1581,5677,3629,7725,301,4397,2349,6445,1325,5421,3373,7469,813,4909,2861,6957,1837,5933,3885,7981,173,4269,2221,6317,1197,5293,3245,7341,685,4781,2733,6829,1709,5805,3757,7853,429,4525,2477,6573,1453,5549,3501,7597,941,5037,2989,7085,1965,6061,4013,8109,109,4205,2157,6253,1133,5229,3181,7277,621,4717,2669,6765,1645,5741,3693,7789,365,4461,2413,6509,1389,5485,3437,7533,877,4973,2925,7021,1901,5997,3949,8045,237,4333,2285,6381,1261,5357,3309,7405,749,4845,2797,6893,1773,5869,3821,7917,493,4589,2541,6637,1517,5613,3565,7661,1005,5101,3053,7149,2029,6125,4077,8173,29,4125,2077,6173,1053,5149,3101,7197,541,4637,2589,6685,1565,5661,3613,7709,285,4381,2333,6429,1309,5405,3357,7453,797,4893,2845,6941,1821,5917,3869,7965,157,4253,2205,6301,1181,5277,3229,7325,669,4765,2717,6813,1693,5789,3741,7837,413,4509,2461,6557,1437,5533,3485,7581,925,5021,2973,7069,1949,6045,3997,8093,93,4189,2141,6237,1117,5213,3165,7261,605,4701,2653,6749,1629,5725,3677,7773,349,4445,2397,6493,1373,5469,3421,7517,861,4957,2909,7005,1885,5981,3933,8029,221,4317,2269,6365,1245,5341,3293,7389,733,4829,2781,6877,1757,5853,3805,7901,477,4573,2525,6621,1501,5597,3549,7645,989,5085,3037,7133,2013,6109,4061,8157,61,4157,2109,6205,1085,5181,3133,7229,573,4669,2621,6717,1597,5693,3645,7741,317,4413,2365,6461,1341,5437,3389,7485,829,4925,2877,6973,1853,5949,3901,7997,189,4285,2237,6333,1213,5309,3261,7357,701,4797,2749,6845,1725,5821,3773,7869,445,4541,2493,6589,1469,5565,3517,7613,957,5053,3005,7101,1981,6077,4029,8125,125,4221,2173,6269,1149,5245,3197,7293,637,4733,2685,6781,1661,5757,3709,7805,381,4477,2429,6525,1405,5501,3453,7549,893,4989,2941,7037,1917,6013,3965,8061,253,4349,2301,6397,1277,5373,3325,7421,765,4861,2813,6909,1789,5885,3837,7933,509,4605,2557,6653,1533,5629,3581,7677,1021,5117,3069,7165,2045,6141,4093,8189,3,4099,2051,6147,1027,5123,3075,7171,515,4611,2563,6659,1539,5635,3587,7683,259,4355,2307,6403,1283,5379,3331,7427,771,4867,2819,6915,1795,5891,3843,7939,131,4227,2179,6275,1155,5251,3203,7299,643,4739,2691,6787,1667,5763,3715,7811,387,4483,2435,6531,1411,5507,3459,7555,899,4995,2947,7043,1923,6019,3971,8067,67,4163,2115,6211,1091,5187,3139,7235,579,4675,2627,6723,1603,5699,3651,7747,323,4419,2371,6467,1347,5443,3395,7491,835,4931,2883,6979,1859,5955,3907,8003,195,4291,2243,6339,1219,5315,3267,7363,707,4803,2755,6851,1731,5827,3779,7875,451,4547,2499,6595,1475,5571,3523,7619,963,5059,3011,7107,1987,6083,4035,8131,35,4131,2083,6179,1059,5155,3107,7203,547,4643,2595,6691,1571,5667,3619,7715,291,4387,2339,6435,1315,5411,3363,7459,803,4899,2851,6947,1827,5923,3875,7971,163,4259,2211,6307,1187,5283,3235,7331,675,4771,2723,6819,1699,5795,3747,7843,419,4515,2467,6563,1443,5539,3491,7587,931,5027,2979,7075,1955,6051,4003,8099,99,4195,2147,6243,1123,5219,3171,7267,611,4707,2659,6755,1635,5731,3683,7779,355,4451,2403,6499,1379,5475,3427,7523,867,4963,2915,7011,1891,5987,3939,8035,227,4323,2275,6371,1251,5347,3299,7395,739,4835,2787,6883,1763,5859,3811,7907,483,4579,2531,6627,1507,5603,3555,7651,995,5091,3043,7139,2019,6115,4067,8163,19,4115,2067,6163,1043,5139,3091,7187,531,4627,2579,6675,1555,5651,3603,7699,275,4371,2323,6419,1299,5395,3347,7443,787,4883,2835,6931,1811,5907,3859,7955,147,4243,2195,6291,1171,5267,3219,7315,659,4755,2707,6803,1683,5779,3731,7827,403,4499,2451,6547,1427,5523,3475,7571,915,5011,2963,7059,1939,6035,3987,8083,83,4179,2131,6227,1107,5203,3155,7251,595,4691,2643,6739,1619,5715,3667,7763,339,4435,2387,6483,1363,5459,3411,7507,851,4947,2899,6995,1875,5971,3923,8019,211,4307,2259,6355,1235,5331,3283,7379,723,4819,2771,6867,1747,5843,3795,7891,467,4563,2515,6611,1491,5587,3539,7635,979,5075,3027,7123,2003,6099,4051,8147,51,4147,2099,6195,1075,5171,3123,7219,563,4659,2611,6707,1587,5683,3635,7731,307,4403,2355,6451,1331,5427,3379,7475,819,4915,2867,6963,1843,5939,3891,7987,179,4275,2227,6323,1203,5299,3251,7347,691,4787,2739,6835,1715,5811,3763,7859,435,4531,2483,6579,1459,5555,3507,7603,947,5043,2995,7091,1971,6067,4019,8115,115,4211,2163,6259,1139,5235,3187,7283,627,4723,2675,6771,1651,5747,3699,7795,371,4467,2419,6515,1395,5491,3443,7539,883,4979,2931,7027,1907,6003,3955,8051,243,4339,2291,6387,1267,5363,3315,7411,755,4851,2803,6899,1779,5875,3827,7923,499,4595,2547,6643,1523,5619,3571,7667,1011,5107,3059,7155,2035,6131,4083,8179,11,4107,2059,6155,1035,5131,3083,7179,523,4619,2571,6667,1547,5643,3595,7691,267,4363,2315,6411,1291,5387,3339,7435,779,4875,2827,6923,1803,5899,3851,7947,139,4235,2187,6283,1163,5259,3211,7307,651,4747,2699,6795,1675,5771,3723,7819,395,4491,2443,6539,1419,5515,3467,7563,907,5003,2955,7051,1931,6027,3979,8075,75,4171,2123,6219,1099,5195,3147,7243,587,4683,2635,6731,1611,5707,3659,7755,331,4427,2379,6475,1355,5451,3403,7499,843,4939,2891,6987,1867,5963,3915,8011,203,4299,2251,6347,1227,5323,3275,7371,715,4811,2763,6859,1739,5835,3787,7883,459,4555,2507,6603,1483,5579,3531,7627,971,5067,3019,7115,1995,6091,4043,8139,43,4139,2091,6187,1067,5163,3115,7211,555,4651,2603,6699,1579,5675,3627,7723,299,4395,2347,6443,1323,5419,3371,7467,811,4907,2859,6955,1835,5931,3883,7979,171,4267,2219,6315,1195,5291,3243,7339,683,4779,2731,6827,1707,5803,3755,7851,427,4523,2475,6571,1451,5547,3499,7595,939,5035,2987,7083,1963,6059,4011,8107,107,4203,2155,6251,1131,5227,3179,7275,619,4715,2667,6763,1643,5739,3691,7787,363,4459,2411,6507,1387,5483,3435,7531,875,4971,2923,7019,1899,5995,3947,8043,235,4331,2283,6379,1259,5355,3307,7403,747,4843,2795,6891,1771,5867,3819,7915,491,4587,2539,6635,1515,5611,3563,7659,1003,5099,3051,7147,2027,6123,4075,8171,27,4123,2075,6171,1051,5147,3099,7195,539,4635,2587,6683,1563,5659,3611,7707,283,4379,2331,6427,1307,5403,3355,7451,795,4891,2843,6939,1819,5915,3867,7963,155,4251,2203,6299,1179,5275,3227,7323,667,4763,2715,6811,1691,5787,3739,7835,411,4507,2459,6555,1435,5531,3483,7579,923,5019,2971,7067,1947,6043,3995,8091,91,4187,2139,6235,1115,5211,3163,7259,603,4699,2651,6747,1627,5723,3675,7771,347,4443,2395,6491,1371,5467,3419,7515,859,4955,2907,7003,1883,5979,3931,8027,219,4315,2267,6363,1243,5339,3291,7387,731,4827,2779,6875,1755,5851,3803,7899,475,4571,2523,6619,1499,5595,3547,7643,987,5083,3035,7131,2011,6107,4059,8155,59,4155,2107,6203,1083,5179,3131,7227,571,4667,2619,6715,1595,5691,3643,7739,315,4411,2363,6459,1339,5435,3387,7483,827,4923,2875,6971,1851,5947,3899,7995,187,4283,2235,6331,1211,5307,3259,7355,699,4795,2747,6843,1723,5819,3771,7867,443,4539,2491,6587,1467,5563,3515,7611,955,5051,3003,7099,1979,6075,4027,8123,123,4219,2171,6267,1147,5243,3195,7291,635,4731,2683,6779,1659,5755,3707,7803,379,4475,2427,6523,1403,5499,3451,7547,891,4987,2939,7035,1915,6011,3963,8059,251,4347,2299,6395,1275,5371,3323,7419,763,4859,2811,6907,1787,5883,3835,7931,507,4603,2555,6651,1531,5627,3579,7675,1019,5115,3067,7163,2043,6139,4091,8187,7,4103,2055,6151,1031,5127,3079,7175,519,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序列3：

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3074,7170,514,4610,2562,6658,1538,5634,3586,7682,258,4354,2306,6402,1282,5378,3330,7426,770,4866,2818,6914,1794,5890,3842,7938,130,4226,2178,6274,1154,5250,3202,7298,642,4738,2690,6786,1666,5762,3714,7810,386,4482,2434,6530,1410,5506,3458,7554,898,4994,2946,7042,1922,6018,3970,8066,66,4162,2114,6210,1090,5186,3138,7234,578,4674,2626,6722,1602,5698,3650,7746,322,4418,2370,6466,1346,5442,3394,7490,834,4930,2882,6978,1858,5954,3906,8002,194,4290,2242,6338,1218,5314,3266,7362,706,4802,2754,6850,1730,5826,3778,7874,450,4546,2498,6594,1474,5570,3522,7618,962,5058,3010,7106,1986,6082,4034,8130,34,4130,2082,6178,1058,5154,3106,7202,546,4642,2594,6690,1570,5666,3618,7714,290,4386,2338,6434,1314,5410,3362,7458,802,4898,2850,6946,1826,5922,3874,7970,162,4258,2210,6306,1186,5282,3234,7330,674,4770,2722,6818,1698,5794,3746,7842,418,4514,2466,6562,1442,5538,3490,7586,930,5026,2978,7074,1954,6050,4002,8098,98,4194,2146,6242,1122,5218,3170,7266,610,4706,2658,6754,1634,5730,3682,7778,354,4450,2402,6498,1378,5474,3426,7522,866,4962,2914,7010,1890,5986,3938,8034,226,4322,2274,6370,1250,5346,3298,7394,738,4834,2786,6882,1762,5858,3810,7906,482,4578,2530,6626,1506,5602,3554,7650,994,5090,3042,7138,2018,6114,4066,8162,18,4114,2066,6162,1042,5138,3090,7186,530,4626,2578,6674,1554,5650,3602,7698,274,4370,2322,6418,1298,5394,3346,7442,786,4882,2834,6930,1810,5906,3858,7954,146,4242,2194,6290,1170,5266,3218,7314,658,4754,2706,6802,1682,5778,3730,7826,402,4498,2450,6546,1426,5522,3474,7570,914,5010,2962,7058,1938,6034,3986,8082,82,4178,2130,6226,1106,5202,3154,7250,594,4690,2642,6738,1618,5714,3666,7762,338,4434,2386,6482,1362,5458,3410,7506,850,4946,2898,6994,1874,5970,3922,8018,210,4306,2258,6354,1234,5330,3282,7378,722,4818,2770,6866,1746,5842,3794,7890,466,4562,2514,6610,1490,5586,3538,7634,978,5074,3026,7122,2002,6098,4050,8146,50,4146,2098,6194,1074,5170,3122,7218,562,4658,2610,6706,1586,5682,3634,7730,306,4402,2354,6450,1330,5426,3378,7474,818,4914,2866,6962,1842,5938,3890,7986,178,4274,2226,6322,1202,5298,3250,7346,690,4786,2738,6834,1714,5810,3762,7858,434,4530,2482,6578,1458,5554,3506,7602,946,5042,2994,7090,1970,6066,4018,8114,114,4210,2162,6258,1138,5234,3186,7282,626,4722,2674,6770,1650,5746,3698,7794,370,4466,2418,6514,1394,5490,3442,7538,882,4978,2930,7026,1906,6002,3954,8050,242,4338,2290,6386,1266,5362,3314,7410,754,4850,2802,6898,1778,5874,3826,7922,498,4594,2546,6642,1522,5618,3570,7666,1010,5106,3058,7154,2034,6130,4082,8178,10,4106,2058,6154,1034,5130,3082,7178,522,4618,2570,6666,1546,5642,3594,7690,266,4362,2314,6410,1290,5386,3338,7434,778,4874,2826,6922,1802,5898,3850,7946,138,4234,2186,6282,1162,5258,3210,7306,650,4746,2698,6794,1674,5770,3722,7818,394,4490,2442,6538,1418,5514,3466,7562,906,5002,2954,7050,1930,6026,3978,8074,74,4170,2122,6218,1098,5194,3146,7242,586,4682,2634,6730,1610,5706,3658,7754,330,4426,2378,6474,1354,5450,3402,7498,842,4938,2890,6986,1866,5962,3914,8010,202,4298,2250,6346,1226,5322,3274,7370,714,4810,2762,6858,1738,5834,3786,7882,458,4554,2506,6602,1482,5578,3530,7626,970,5066,3018,7114,1994,6090,4042,8138,42,4138,2090,6186,1066,5162,3114,7210,554,4650,2602,6698,1578,5674,3626,7722,298,4394,2346,6442,1322,5418,3370,7466,810,4906,2858,6954,1834,5930,3882,7978,170,4266,2218,6314,1194,5290,3242,7338,682,4778,2730,6826,1706,5802,3754,7850,426,4522,2474,6570,1450,5546,3498,7594,938,5034,2986,7082,1962,6058,4010,8106,106,4202,2154,6250,1130,5226,3178,7274,618,4714,2666,6762,1642,5738,3690,7786,362,4458,2410,6506,1386,5482,3434,7530,874,4970,2922,7018,1898,5994,3946,8042,234,4330,2282,6378,1258,5354,3306,7402,746,4842,2794,6890,1770,5866,3818,7914,490,4586,2538,6634,1514,5610,3562,7658,1002,5098,3050,7146,2026,6122,4074,8170,26,4122,2074,6170,1050,5146,3098,7194,538,4634,2586,6682,1562,5658,3610,7706,282,4378,2330,6426,1306,5402,3354,7450,794,4890,2842,6938,1818,5914,3866,7962,154,4250,2202,6298,1178,5274,3226,7322,666,4762,2714,6810,1690,5786,3738,7834,410,4506,2458,6554,1434,5530,3482,7578,922,5018,2970,7066,1946,6042,3994,8090,90,4186,2138,6234,1114,5210,3162,7258,602,4698,2650,6746,1626,5722,3674,7770,346,4442,2394,6490,1370,5466,3418,7514,858,4954,2906,7002,1882,5978,3930,8026,218,4314,2266,6362,1242,5338,3290,7386,730,4826,2778,6874,1754,5850,3802,7898,474,4570,2522,6618,1498,5594,3546,7642,986,5082,3034,7130,2010,6106,4058,8154,58,4154,2106,6202,1082,5178,3130,7226,570,4666,2618,6714,1594,5690,3642,7738,314,4410,2362,6458,1338,5434,3386,7482,826,4922,2874,6970,1850,5946,3898,7994,186,4282,2234,6330,1210,5306,3258,7354,698,4794,2746,6842,1722,5818,3770,7866,442,4538,2490,6586,1466,5562,3514,7610,954,5050,3002,7098,1978,6074,4026,8122,122,4218,2170,6266,1146,5242,3194,7290,634,4730,2682,6778,1658,5754,3706,7802,378,4474,2426,6522,1402,5498,3450,7546,890,4986,2938,7034,1914,6010,3962,8058,250,4346,2298,6394,1274,5370,3322,7418,762,4858,2810,6906,1786,5882,3834,7930,506,4602,2554,6650,1530,5626,3578,7674,1018,5114,3066,7162,2042,6138,4090,8186,6,4102,2054,6150,1030,5126,3078,7174,518,4614,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79,3331,7427,771,4867,2819,6915,1795,5891,3843,7939,131,4227,2179,6275,1155,5251,3203,7299,643,4739,2691,6787,1667,5763,3715,7811,387,4483,2435,6531,1411,5507,3459,7555,899,4995,2947,7043,1923,6019,3971,8067,67,4163,2115,6211,1091,5187,3139,7235,579,4675,2627,6723,1603,5699,3651,7747,323,4419,2371,6467,1347,5443,3395,7491,835,4931,2883,6979,1859,5955,3907,8003,195,4291,2243,6339,1219,5315,3267,7363,707,4803,2755,6851,1731,5827,3779,7875,451,4547,2499,6595,1475,5571,3523,7619,963,5059,3011,7107,1987,6083,4035,8131,35,4131,2083,6179,1059,5155,3107,7203,547,4643,2595,6691,1571,5667,3619,7715,291,4387,2339,6435,1315,5411,3363,7459,803,4899,2851,6947,1827,5923,3875,7971,163,4259,2211,6307,1187,5283,3235,7331,675,4771,2723,6819,1699,5795,3747,7843,419,4515,2467,6563,1443,5539,3491,7587,931,5027,2979,7075,1955,6051,4003,8099,99,4195,2147,6243,1123,5219,3171,7267,611,4707,2659,6755,1635,5731,3683,7779,355,4451,2403,6499,1379,5475,3427,7523,867,4963,2915,7011,1891,5987,3939,8035,227,4323,2275,6371,1251,5347,3299,7395,739,4835,2787,6883,1763,5859,3811,7907,483,4579,2531,6627,1507,5603,3555,7651,995,5091,3043,7139,2019,6115,4067,8163,19,4115,2067,6163,1043,5139,3091,7187,531,4627,2579,6675,1555,5651,3603,7699,275,4371,2323,6419,1299,5395,3347,7443,787,4883,2835,6931,1811,5907,3859,7955,147,4243,2195,6291,1171,5267,3219,7315,659,4755,2707,6803,1683,5779,3731,7827,403,4499,2451,6547,1427,5523,3475,7571,915,5011,2963,7059,1939,6035,3987,8083,83,4179,2131,6227,1107,5203,3155,7251,595,4691,2643,6739,1619,5715,3667,7763,339,4435,2387,6483,1363,5459,3411,7507,851,4947,2899,6995,1875,5971,3923,8019,211,4307,2259,6355,1235,5331,3283,7379,723,4819,2771,6867,1747,5843,3795,7891,467,4563,2515,6611,1491,5587,3539,7635,979,5075,3027,7123,2003,6099,4051,8147,51,4147,2099,6195,1075,5171,3123,7219,563,4659,2611,6707,1587,5683,3635,7731,307,4403,2355,6451,1331,5427,3379,7475,819,4915,2867,6963,1843,5939,3891,7987,179,4275,2227,6323,1203,5299,3251,7347,691,4787,2739,6835,1715,5811,3763,7859,435,4531,2483,6579,1459,5555,3507,7603,947,5043,2995,7091,1971,6067,4019,8115,115,4211,2163,6259,1139,5235,3187,7283,627,4723,2675,6771,1651,5747,3699,7795,371,4467,2419,6515,1395,5491,3443,7539,883,4979,2931,7027,1907,6003,3955,8051,243,4339,2291,6387,1267,5363,3315,7411,755,4851,2803,6899,1779,5875,3827,7923,499,4595,2547,6643,1523,5619,3571,7667,1011,5107,3059,7155,2035,6131,4083,8179,11,4107,2059,6155,1035,5131,3083,7179,523,4619,2571,6667,1547,5643,3595,7691,267,4363,2315,6411,1291,5387,3339,7435,779,4875,2827,6923,1803,5899,3851,7947,139,4235,2187,6283,1163,5259,3211,7307,651,4747,2699,6795,1675,5771,3723,7819,395,4491,2443,6539,1419,5515,3467,7563,907,5003,2955,7051,1931,6027,3979,8075,75,4171,2123,6219,1099,5195,3147,7243,587,4683,2635,6731,1611,5707,3659,7755,331,4427,2379,6475,1355,5451,3403,7499,843,4939,2891,6987,1867,5963,3915,8011,203,4299,2251,6347,1227,5323,3275,7371,715,4811,2763,6859,1739,5835,3787,7883,459,4555,2507,6603,1483,5579,3531,7627,971,5067,3019,7115,1995,6091,4043,8139,43,4139,2091,6187,1067,5163,3115,7211,555,4651,2603,6699,1579,5675,3627,7723,299,4395,2347,6443,1323,5419,3371,7467,811,4907,2859,6955,1835,5931,3883,7979,171,4267,2219,6315,1195,5291,3243,7339,683,4779,2731,6827,1707,5803,3755,7851,427,4523,2475,6571,1451,5547,3499,7595,939,5035,2987,7083,1963,6059,4011,8107,107,4203,2155,6251,1131,5227,3179,7275,619,4715,2667,6763,1643,5739,3691,7787,363,4459,2411,6507,1387,5483,3435,7531,875,4971,2923,7019,1899,5995,3947,8043,235,4331,2283,6379,1259,5355,3307,7403,747,4843,2795,6891,1771,5867,3819,7915,491,4587,2539,6635,1515,5611,3563,7659,1003,5099,3051,7147,2027,6123,4075,8171,27,4123,2075,6171,1051,5147,3099,7195,539,4635,2587,6683,1563,5659,3611,7707,283,4379,2331,6427,1307,5403,3355,7451,795,4891,2843,6939,1819,5915,3867,7963,155,4251,2203,6299,1179,5275,3227,7323,667,4763,2715,6811,1691,5787,3739,7835,411,4507,2459,6555,1435,5531,3483,7579,923,5019,2971,7067,1947,6043,3995,8091,91,4187,2139,6235,1115,5211,3163,7259,603,4699,2651,6747,1627,5723,3675,7771,347,4443,2395,6491,1371,5467,3419,7515,859,4955,2907,7003,1883,5979,3931,8027,219,4315,2267,6363,1243,5339,3291,7387,731,4827,2779,6875,1755,5851,3803,7899,475,4571,2523,6619,1499,5595,3547,7643,987,5083,3035,7131,2011,6107,4059,8155,59,4155,2107,6203,1083,5179,3131,7227,571,4667,2619,6715,1595,5691,3643,7739,315,4411,2363,6459,1339,5435,3387,7483,827,4923,2875,6971,1851,5947,3899,7995,187,4283,2235,6331,1211,5307,3259,7355,699,4795,2747,6843,1723,5819,3771,7867,443,4539,2491,6587,1467,5563,3515,7611,955,5051,3003,7099,1979,6075,4027,8123,123,4219,2171,6267,1147,5243,3195,7291,635,4731,2683,6779,1659,5755,3707,7803,379,4475,2427,6523,1403,5499,3451,7547,891,4987,2939,7035,1915,6011,3963,8059,251,4347,2299,6395,1275,5371,3323,7419,763,4859,2811,6907,1787,5883,3835,7931,507,4603,2555,6651,1531,5627,3579,7675,1019,5115,3067,7163,2043,6139,4091,8187,7,4103,2055,6151,1031,5127,3079,7175,519,4615,2567,6663,1543,5639,3591,7687,263,4359,2311,6407,1287,5383,3335,7431,775,4871,2823,6919,1799,5895,3847,7943,135,4231,2183,6279,1159,5255,3207,7303,647,4743,2695,6791,1671,5767,3719,7815,391,4487,2439,6535,1415,5511,3463,7559,903,4999,2951,7047,1927,6023,3975,8071,71,4167,2119,6215,1095,5191,3143,7239,583,4679,2631,6727,1607,5703,3655,7751,327,4423,2375,6471,1351,5447,3399,7495,839,4935,2887,6983,1863,5959,3911,8007,199,4295,2247,6343,1223,5319,3271,7367,711,4807,2759,6855,1735,5831,3783,7879,455,4551,2503,6599,1479,5575,3527,7623,967,5063,3015,7111,1991,6087,4039,8135,39,4135,2087,6183,1063,5159,3111,7207,551,4647,2599,6695,1575,5671,3623,7719,295,4391,2343,6439,1319,5415,3367,7463,807,4903,2855,6951,1831,5927,3879,7975,167,4263,2215,6311,1191,5287,3239,7335,679,4775,2727,6823,1703,5799,3751,7847,423,4519,2471,6567,1447,5543,3495,7591,935,5031,2983,7079,1959,6055,4007,8103,103,4199,2151,6247,1127,5223,3175,7271,615,4711,2663,6759,1639,5735,3687,7783,359,4455,2407,6503,1383,5479,3431,7527,871,4967,2919,7015,1895,5991,3943,8039,231,4327,2279,6375,1255,5351,3303,7399,743,4839,2791,6887,1767,5863,3815,7911,487,4583,2535,6631,1511,5607,3559,7655,999,5095,3047,7143,2023,6119,4071,8167,23,4119,2071,6167,1047,5143,3095,7191,535,4631,2583,6679,1559,5655,3607,7703,279,4375,2327,6423,1303,5399,3351,7447,791,4887,2839,6935,1815,5911,3863,7959,151,4247,2199,6295,1175,5271,3223,7319,663,4759,2711,6807,1687,5783,3735,7831,407,4503,2455,6551,1431,5527,3479,7575,919,5015,2967,7063,1943,6039,3991,8087,87,4183,2135,6231,1111,5207,3159,7255,599,4695,2647,6743,1623,5719,3671,7767,343,4439,2391,6487,1367,5463,3415,7511,855,4951,2903,6999,1879,5975,3927,8023,215,4311,2263,6359,1239,5335,3287,7383,727,4823,2775,6871,1751,5847,3799,7895,471,4567,2519,6615,1495,5591,3543,7639,983,5079,3031,7127,2007,6103,4055,8151,55,4151,2103,6199,1079,5175,3127,7223,567,4663,2615,6711,1591,5687,3639,7735,311,4407,2359,6455,1335,5431,3383,7479,823,4919,2871,6967,1847,5943,3895,7991,183,4279,2231,6327,1207,5303,3255,7351,695,4791,2743,6839,1719,5815,3767,7863,439,4535,2487,6583,1463,5559,3511,7607,951,5047,2999,7095,1975,6071,4023,8119,119,4215,2167,6263,1143,5239,3191,7287,631,4727,2679,6775,1655,5751,3703,7799,375,4471,2423,6519,1399,5495,3447,7543,887,4983,2935,7031,1911,6007,3959,8055,247,4343,2295,6391,1271,5367,3319,7415,759,4855,2807,6903,1783,5879,3831,7927,503,4599,2551,6647,1527,5623,3575,7671,1015,5111,3063,7159,2039,6135,4087,8183,15,4111,2063,6159,1039,5135,3087,7183,527,4623,2575,6671,1551,5647,3599,7695,271,4367,2319,6415,1295,5391,3343,7439,783,4879,2831,6927,1807,5903,3855,7951,143,4239,2191,6287,1167,5263,3215,7311,655,4751,2703,6799,1679,5775,3727,7823,399,4495,2447,6543,1423,5519,3471,7567,911,5007,2959,7055,1935,6031,3983,8079,79,4175,2127,6223,1103,5199,3151,7247,591,4687,2639,6735,1615,5711,3663,7759,335,4431,2383,6479,1359,5455,3407,7503,847,4943,2895,6991,1871,5967,3919,8015,207,4303,2255,6351,1231,5327,3279,7375,719,4815,2767,6863,1743,5839,3791,7887,463,4559,2511,6607,1487,5583,3535,7631,975,5071,3023,7119,1999,6095,4047,8143,47,4143,2095,6191,1071,5167,3119,7215,559,4655,2607,6703,1583,5679,3631,7727,303,4399,2351,6447,1327,5423,3375,7471,815,4911,2863,6959,1839,5935,3887,7983,175,4271,2223,6319,1199,5295,3247,7343,687,4783,2735,6831,1711,5807,3759,7855,431,4527,2479,6575,1455,5551,3503,7599,943,5039,2991,7087,1967,6063,4015,8111,111,4207,2159,6255,1135,5231,3183,7279,623,4719,2671,6767,1647,5743,3695,7791,367,4463,2415,6511,1391,5487,3439,7535,879,4975,2927,7023,1903,5999,3951,8047,239,4335,2287,6383,1263,5359,3311,7407,751,4847,2799,6895,1775,5871,3823,7919,495,4591,2543,6639,1519,5615,3567,7663,1007,5103,3055,7151,2031,6127,4079,8175,31,4127,2079,6175,1055,5151,3103,7199,543,4639,2591,6687,1567,5663,3615,7711,287,4383,2335,6431,1311,5407,3359,7455,799,4895,2847,6943,1823,5919,3871,7967,159,4255,2207,6303,1183,5279,3231,7327,671,4767,2719,6815,1695,5791,3743,7839,415,4511,2463,6559,1439,5535,3487,7583,927,5023,2975,7071,1951,6047,3999,8095,95,4191,2143,6239,1119,5215,3167,7263,607,4703,2655,6751,1631,5727,3679,7775,351,4447,2399,6495,1375,5471,3423,7519,863,4959,2911,7007,1887,5983,3935,8031,223,4319,2271,6367,1247,5343,3295,7391,735,4831,2783,6879,1759,5855,3807,7903,479,4575,2527,6623,1503,5599,3551,7647,991,5087,3039,7135,2015,6111,4063,8159,63,4159,2111,6207,1087,5183,3135,7231,575,4671,2623,6719,1599,5695,3647,7743,319,4415,2367,6463,1343,5439,3391,7487,831,4927,2879,6975,1855,5951,3903,7999,191,4287,2239,6335,1215,5311,3263,7359,703,4799,2751,6847,1727,5823,3775,7871,447,4543,2495,6591,1471,5567,3519,7615,959,5055,3007,7103,1983,6079,4031,8127,127,4223,2175,6271,1151,5247,3199,7295,639,4735,2687,6783,1663,5759,3711,7807,383,4479,2431,6527,1407,5503,3455,7551,895,4991,2943,7039,1919,6015,3967,8063,255,4351,2303,6399,1279,5375,3327,7423,767,4863,2815,6911,1791,5887,3839,7935,511,4607,2559,6655,1535,5631,3583,7679,1023,5119,3071,7167,2047,6143,4095,8191]。

当N＝8192，序列1a即为序列1，序列2a即为序列2，序列3a即为序列3；

当N＝4096，

序列1b为：

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23,3171,611,2659,1635,3683,355,2403,1379,3427,867,2915,1891,3939,227,2275,1251,3299,739,2787,1763,3811,483,2531,1507,3555,995,3043,2019,4067,19,2067,1043,3091,531,2579,1555,3603,275,2323,1299,3347,787,2835,1811,3859,147,2195,1171,3219,659,2707,1683,3731,403,2451,1427,3475,915,2963,1939,3987,83,2131,1107,3155,595,2643,1619,3667,339,2387,1363,3411,851,2899,1875,3923,211,2259,1235,3283,723,2771,1747,3795,467,2515,1491,3539,979,3027,2003,4051,51,2099,1075,3123,563,2611,1587,3635,307,2355,1331,3379,819,2867,1843,3891,179,2227,1203,3251,691,2739,1715,3763,435,2483,1459,3507,947,2995,1971,4019,115,2163,1139,3187,627,2675,1651,3699,371,2419,1395,3443,883,2931,1907,3955,243,2291,1267,3315,755,2803,1779,3827,499,2547,1523,3571,1011,3059,2035,4083,11,2059,1035,3083,523,2571,1547,3595,267,2315,1291,3339,779,2827,1803,3851,139,2187,1163,3211,651,2699,1675,3723,395,2443,1419,3467,907,2955,1931,3979,75,2123,1099,3147,587,2635,1611,3659,331,2379,1355,3403,843,2891,1867,3915,203,2251,1227,3275,715,2763,1739,3787,459,2507,1483,3531,971,3019,1995,4043,43,2091,1067,3115,555,2603,1579,3627,299,2347,1323,3371,811,2859,1835,3883,171,2219,1195,3243,683,2731,1707,3755,427,2475,1451,3499,939,2987,1963,4011,107,2155,1131,3179,619,2667,1643,3691,363,2411,1387,3435,875,2923,1899,3947,235,2283,1259,3307,747,2795,1771,3819,491,2539,1515,3563,1003,3051,2027,4075,27,2075,1051,3099,539,2587,1563,3611,283,2331,1307,3355,795,2843,1819,3867,155,2203,1179,3227,667,2715,1691,3739,411,2459,1435,3483,923,2971,1947,3995,91,2139,1115,3163,603,2651,1627,3675,347,2395,1371,3419,859,2907,1883,3931,219,2267,1243,3291,731,2779,1755,3803,475,2523,1499,3547,987,3035,2011,4059,59,2107,1083,3131,571,2619,1595,3643,315,2363,1339,3387,827,2875,1851,3899,187,2235,1211,3259,699,2747,1723,3771,443,2491,1467,3515,955,3003,1979,4027,123,2171,1147,3195,635,2683,1659,3707,379,2427,1403,3451,891,2939,1915,3963,251,2299,1275,3323,763,2811,1787,3835,507,2555,1531,3579,1019,3067,2043,4091,7,2055,1031,3079,519,2567,1543,3591,263,2311,1287,3335,775,2823,1799,3847,135,2183,1159,3207,647,2695,1671,3719,391,2439,1415,3463,903,2951,1927,3975,71,2119,1095,3143,583,2631,1607,3655,327,2375,1351,3399,839,2887,1863,3911,199,2247,1223,3271,711,2759,1735,3783,455,2503,1479,3527,967,3015,1991,4039,39,2087,1063,3111,551,2599,1575,3623,295,2343,1319,3367,807,2855,1831,3879,167,2215,1191,3239,679,2727,1703,3751,423,2471,1447,3495,935,2983,1959,4007,103,2151,1127,3175,615,2663,1639,3687,359,2407,1383,3431,871,2919,1895,3943,231,2279,1255,3303,743,2791,1767,3815,487,2535,1511,3559,999,3047,2023,4071,23,2071,1047,3095,535,2583,1559,3607,279,2327,1303,3351,791,2839,1815,3863,151,2199,1175,3223,663,2711,1687,3735,407,2455,1431,3479,919,2967,1943,3991,87,2135,1111,3159,599,2647,1623,3671,343,2391,1367,3415,855,2903,1879,3927,215,2263,1239,3287,727,2775,1751,3799,471,2519,1495,3543,983,3031,2007,4055,55,2103,1079,3127,567,2615,1591,3639,311,2359,1335,3383,823,2871,1847,3895,183,2231,1207,3255,695,2743,1719,3767,439,2487,1463,3511,951,2999,1975,4023,119,2167,1143,3191,631,2679,1655,3703,375,2423,1399,3447,887,2935,1911,3959,247,2295,1271,3319,759,2807,1783,3831,503,2551,1527,3575,1015,3063,2039,4087,15,2063,1039,3087,527,2575,1551,3599,271,2319,1295,3343,783,2831,1807,3855,143,2191,1167,3215,655,2703,1679,3727,399,2447,1423,3471,911,2959,1935,3983,79,2127,1103,3151,591,2639,1615,3663,335,2383,1359,3407,847,2895,1871,3919,207,2255,1231,3279,719,2767,1743,3791,463,2511,1487,3535,975,3023,1999,4047,47,2095,1071,3119,559,2607,1583,3631,303,2351,1327,3375,815,2863,1839,3887,175,2223,1199,3247,687,2735,1711,3759,431,2479,1455,3503,943,2991,1967,4015,111,2159,1135,3183,623,2671,1647,3695,367,2415,1391,3439,879,2927,1903,3951,239,2287,1263,3311,751,2799,1775,3823,495,2543,1519,3567,1007,3055,2031,4079,31,2079,1055,3103,543,2591,1567,3615,287,2335,1311,3359,799,2847,1823,3871,159,2207,1183,3231,671,2719,1695,3743,415,2463,1439,3487,927,2975,1951,3999,95,2143,1119,3167,607,2655,1631,3679,351,2399,1375,3423,863,2911,1887,3935,223,2271,1247,3295,735,2783,1759,3807,479,2527,1503,3551,991,3039,2015,4063,63,2111,1087,3135,575,2623,1599,3647,319,2367,1343,3391,831,2879,1855,3903,191,2239,1215,3263,703,2751,1727,3775,447,2495,1471,3519,959,3007,1983,4031,127,2175,1151,3199,639,2687,1663,3711,383,2431,1407,3455,895,2943,1919,3967,255,2303,1279,3327,767,2815,1791,3839,511,2559,1535,3583,1023,3071,2047,4095]。

序列2b为：

Shorten_Q_half＝[1,2049,1025,3073,513,2561,1537,3585,257,2305,1281,3329,769,2817,1793,3841,129,2177,1153,3201,641,2689,1665,3713,385,2433,1409,3457,897,2945,1921,3969,65,2113,1089,3137,577,2625,1601,3649,321,2369,1345,3393,833,2881,1857,3905,193,2241,1217,3265,705,2753,1729,3777,449,2497,1473,3521,961,3009,1985,4033,33,2081,1057,3105,545,2593,1569,3617,289,2337,1313,3361,801,2849,1825,3873,161,2209,1185,3233,673,2721,1697,3745,417,2465,1441,3489,929,2977,1953,4001,97,2145,1121,3169,609,2657,1633,3681,353,2401,1377,3425,865,2913,1889,3937,225,2273,1249,3297,737,2785,1761,3809,481,2529,1505,3553,993,3041,2017,4065,17,2065,1041,3089,529,2577,1553,3601,273,2321,1297,3345,785,2833,1809,3857,145,2193,1169,3217,657,2705,1681,3729,401,2449,1425,3473,913,2961,1937,3985,81,2129,1105,3153,593,2641,1617,3665,337,2385,1361,3409,849,2897,1873,3921,209,2257,1233,3281,721,2769,1745,3793,465,2513,1489,3537,977,3025,2001,4049,49,2097,1073,3121,561,2609,1585,3633,305,2353,1329,3377,817,2865,1841,3889,177,2225,1201,3249,689,2737,1713,3761,433,2481,1457,3505,945,2993,1969,4017,113,2161,1137,3185,625,2673,1649,3697,369,2417,1393,3441,881,2929,1905,3953,241,2289,1265,3313,753,2801,1777,3825,497,2545,1521,3569,1009,3057,2033,4081,9,2057,1033,3081,521,2569,1545,3593,265,2313,1289,3337,777,2825,1801,3849,137,2185,1161,3209,649,2697,1673,3721,393,2441,1417,3465,905,2953,1929,3977,73,2121,1097,3145,585,2633,1609,3657,329,2377,1353,3401,841,2889,1865,3913,201,2249,1225,3273,713,2761,1737,3785,457,2505,1481,3529,969,3017,1993,4041,41,2089,1065,3113,553,2601,1577,3625,297,2345,1321,3369,809,2857,1833,3881,169,2217,1193,3241,681,2729,1705,3753,425,2473,1449,3497,937,2985,1961,4009,105,2153,1129,3177,617,2665,1641,3689,361,2409,1385,3433,873,2921,1897,3945,233,2281,1257,3305,745,2793,1769,3817,489,2537,1513,3561,1001,3049,2025,4073,25,2073,1049,3097,537,2585,1561,3609,281,2329,1305,3353,793,2841,1817,3865,153,2201,1177,3225,665,2713,1689,3737,409,2457,1433,3481,921,2969,1945,3993,89,2137,1113,3161,601,2649,1625,3673,345,2393,1369,3417,857,2905,1881,3929,217,2265,1241,3289,729,2777,1753,3801,473,2521,1497,3545,985,3033,2009,4057,57,2105,1081,3129,569,2617,1593,3641,313,2361,1337,3385,825,2873,1849,3897,185,2233,1209,3257,697,2745,1721,3769,441,2489,1465,3513,953,3001,1977,4025,121,2169,1145,3193,633,2681,1657,3705,377,2425,1401,3449,889,2937,1913,3961,249,2297,1273,3321,761,2809,1785,3833,505,2553,1529,3577,1017,3065,2041,4089,5,2053,1029,3077,517,2565,1541,3589,261,2309,1285,3333,773,2821,1797,3845,133,2181,1157,3205,645,2693,1669,3717,389,2437,1413,3461,901,2949,1925,3973,69,2117,1093,3141,581,2629,1605,3653,325,2373,1349,3397,837,2885,1861,3909,197,2245,1221,3269,709,2757,1733,3781,453,2501,1477,3525,965,3013,1989,4037,37,2085,1061,3109,549,2597,1573,3621,293,2341,1317,3365,805,2853,1829,3877,165,2213,1189,3237,677,2725,1701,3749,421,2469,1445,3493,933,2981,1957,4005,101,2149,1125,3173,613,2661,1637,3685,357,2405,1381,3429,869,2917,1893,3941,229,2277,1253,3301,741,2789,1765,3813,485,2533,1509,3557,997,3045,2021,4069,21,2069,1045,3093,533,2581,1557,3605,277,2325,1301,3349,789,2837,1813,3861,149,2197,1173,3221,661,2709,1685,3733,405,2453,1429,3477,917,2965,1941,3989,85,2133,1109,3157,597,2645,1621,3669,341,2389,1365,3413,853,2901,1877,3925,213,2261,1237,3285,725,2773,1749,3797,469,2517,1493,3541,981,3029,2005,4053,53,2101,1077,3125,565,2613,1589,3637,309,2357,1333,3381,821,2869,1845,3893,181,2229,1205,3253,693,2741,1717,3765,437,2485,1461,3509,949,2997,1973,4021,117,2165,1141,3189,629,2677,1653,3701,373,2421,1397,3445,885,2933,1909,3957,245,2293,1269,3317,757,2805,1781,3829,501,2549,1525,3573,1013,3061,2037,4085,13,2061,1037,3085,525,2573,1549,3597,269,2317,1293,3341,781,2829,1805,3853,141,2189,1165,3213,653,2701,1677,3725,397,2445,1421,3469,909,2957,1933,3981,77,2125,1101,3149,589,2637,1613,3661,333,2381,1357,3405,845,2893,1869,3917,205,2253,1229,3277,717,2765,1741,3789,461,2509,1485,3533,973,3021,1997,4045,45,2093,1069,3117,557,2605,1581,3629,301,2349,1325,3373,813,2861,1837,3885,173,2221,1197,3245,685,2733,1709,3757,429,2477,1453,3501,941,2989,1965,4013,109,2157,1133,3181,621,2669,1645,3693,365,2413,1389,3437,877,2925,1901,3949,237,2285,1261,3309,749,2797,1773,3821,493,2541,1517,3565,1005,3053,2029,4077,29,2077,1053,3101,541,2589,1565,3613,285,2333,1309,3357,797,2845,1821,3869,157,2205,1181,3229,669,2717,1693,3741,413,2461,1437,3485,925,2973,1949,3997,93,2141,1117,3165,605,2653,1629,3677,349,2397,1373,3421,861,2909,1885,3933,221,2269,1245,3293,733,2781,1757,3805,477,2525,1501,3549,989,3037,2013,4061,61,2109,1085,3133,573,2621,1597,3645,317,2365,1341,3389,829,2877,1853,3901,189,2237,1213,3261,701,2749,1725,3773,445,2493,1469,3517,957,3005,1981,4029,125,2173,1149,3197,637,2685,1661,3709,381,2429,1405,3453,893,2941,1917,3965,253,2301,1277,3325,765,2813,1789,3837,509,2557,1533,3581,1021,3069,2045,4093,3,2051,1027,3075,515,2563,1539,3587,259,2307,1283,3331,771,2819,1795,3843,131,2179,1155,3203,643,2691,1667,3715,387,2435,1411,3459,899,2947,1923,3971,67,2115,1091,3139,579,2627,1603,3651,323,2371,1347,3395,835,2883,1859,3907,195,2243,1219,3267,707,2755,1731,3779,451,2499,1475,3523,963,3011,1987,4035,35,2083,1059,3107,547,2595,1571,3619,291,2339,1315,3363,803,2851,1827,3875,163,2211,1187,3235,675,2723,1699,3747,419,2467,1443,3491,931,2979,1955,4003,99,2147,1123,3171,611,2659,1635,3683,355,2403,1379,3427,867,2915,1891,3939,227,2275,1251,3299,739,2787,1763,3811,483,2531,1507,3555,995,3043,2019,4067,19,2067,1043,3091,531,2579,1555,3603,275,2323,1299,3347,787,2835,1811,3859,147,2195,1171,3219,659,2707,1683,3731,403,2451,1427,3475,915,2963,1939,3987,83,2131,1107,3155,595,2643,1619,3667,339,2387,1363,3411,851,2899,1875,3923,211,2259,1235,3283,723,2771,1747,3795,467,2515,1491,3539,979,3027,2003,4051,51,2099,1075,3123,563,2611,1587,3635,307,2355,1331,3379,819,2867,1843,3891,179,2227,1203,3251,691,2739,1715,3763,435,2483,1459,3507,947,2995,1971,4019,115,2163,1139,3187,627,2675,1651,3699,371,2419,1395,3443,883,2931,1907,3955,243,2291,1267,3315,755,2803,1779,3827,499,2547,1523,3571,1011,3059,2035,4083,11,2059,1035,3083,523,2571,1547,3595,267,2315,1291,3339,779,2827,1803,3851,139,2187,1163,3211,651,2699,1675,3723,395,2443,1419,3467,907,2955,1931,3979,75,2123,1099,3147,587,2635,1611,3659,331,2379,1355,3403,843,2891,1867,3915,203,2251,1227,3275,715,2763,1739,3787,459,2507,1483,3531,971,3019,1995,4043,43,2091,1067,3115,555,2603,1579,3627,299,2347,1323,3371,811,2859,1835,3883,171,2219,1195,3243,683,2731,1707,3755,427,2475,1451,3499,939,2987,1963,4011,107,2155,1131,3179,619,2667,1643,3691,363,2411,1387,3435,875,2923,1899,3947,235,2283,1259,3307,747,2795,1771,3819,491,2539,1515,3563,1003,3051,2027,4075,27,2075,1051,3099,539,2587,1563,3611,283,2331,1307,3355,795,2843,1819,3867,155,2203,1179,3227,667,2715,1691,3739,411,2459,1435,3483,923,2971,1947,3995,91,2139,1115,3163,603,2651,1627,3675,347,2395,1371,3419,859,2907,1883,3931,219,2267,1243,3291,731,2779,1755,3803,475,2523,1499,3547,987,3035,2011,4059,59,2107,1083,3131,571,2619,1595,3643,315,2363,1339,3387,827,2875,1851,3899,187,2235,1211,3259,699,2747,1723,3771,443,2491,1467,3515,955,3003,1979,4027,123,2171,1147,3195,635,2683,1659,3707,379,2427,1403,3451,891,2939,1915,3963,251,2299,1275,3323,763,2811,1787,3835,507,2555,1531,3579,1019,3067,2043,4091,7,2055,1031,3079,519,2567,1543,3591,263,2311,1287,3335,775,2823,1799,3847,135,2183,1159,3207,647,2695,1671,3719,391,2439,1415,3463,903,2951,1927,3975,71,2119,1095,3143,583,2631,1607,3655,327,2375,1351,3399,839,2887,1863,3911,199,2247,1223,3271,711,2759,1735,3783,455,2503,1479,3527,967,3015,1991,4039,39,2087,1063,3111,551,2599,1575,3623,295,2343,1319,3367,807,2855,1831,3879,167,2215,1191,3239,679,2727,1703,3751,423,2471,1447,3495,935,2983,1959,4007,103,2151,1127,3175,615,2663,1639,3687,359,2407,1383,3431,871,2919,1895,3943,231,2279,1255,3303,743,2791,1767,3815,487,2535,1511,3559,999,3047,2023,4071,23,2071,1047,3095,535,2583,1559,3607,279,2327,1303,3351,791,2839,1815,3863,151,2199,1175,3223,663,2711,1687,3735,407,2455,1431,3479,919,2967,1943,3991,87,2135,1111,3159,599,2647,1623,3671,343,2391,1367,3415,855,2903,1879,3927,215,2263,1239,3287,727,2775,1751,3799,471,2519,1495,3543,983,3031,2007,4055,55,2103,1079,3127,567,2615,1591,3639,311,2359,1335,3383,823,2871,1847,3895,183,2231,1207,3255,695,2743,1719,3767,439,2487,1463,3511,951,2999,1975,4023,119,2167,1143,3191,631,2679,1655,3703,375,2423,1399,3447,887,2935,1911,3959,247,2295,1271,3319,759,2807,1783,3831,503,2551,1527,3575,1015,3063,2039,4087,15,2063,1039,3087,527,2575,1551,3599,271,2319,1295,3343,783,2831,1807,3855,143,2191,1167,3215,655,2703,1679,3727,399,2447,1423,3471,911,2959,1935,3983,79,2127,1103,3151,591,2639,1615,3663,335,2383,1359,3407,847,2895,1871,3919,207,2255,1231,3279,719,2767,1743,3791,463,2511,1487,3535,975,3023,1999,4047,47,2095,1071,3119,559,2607,1583,3631,303,2351,1327,3375,815,2863,1839,3887,175,2223,1199,3247,687,2735,1711,3759,431,2479,1455,3503,943,2991,1967,4015,111,2159,1135,3183,623,2671,1647,3695,367,2415,1391,3439,879,2927,1903,3951,239,2287,1263,3311,751,2799,1775,3823,495,2543,1519,3567,1007,3055,2031,4079,31,2079,1055,3103,543,2591,1567,3615,287,2335,1311,3359,799,2847,1823,3871,159,2207,1183,3231,671,2719,1695,3743,415,2463,1439,3487,927,2975,1951,3999,95,2143,1119,3167,607,2655,1631,3679,351,2399,1375,3423,863,2911,1887,3935,223,2271,1247,3295,735,2783,1759,3807,479,2527,1503,3551,991,3039,2015,4063,63,2111,1087,3135,575,2623,1599,3647,319,2367,1343,3391,831,2879,1855,3903,191,2239,1215,3263,703,2751,1727,3775,447,2495,1471,3519,959,3007,1983,4031,127,2175,1151,3199,639,2687,1663,3711,383,2431,1407,3455,895,2943,1919,3967,255,2303,1279,3327,767,2815,1791,3839,511,2559,1535,3583,1023,3071,2047,4095]。

序列3b为：

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3074,7170,514,4610,2562,6658,1538,5634,3586,7682,258,4354,2306,6402,1282,5378,3330,7426,770,4866,2818,6914,1794,5890,3842,7938,130,4226,2178,6274,1154,5250,3202,7298,642,4738,2690,6786,1666,5762,3714,7810,386,4482,2434,6530,1410,5506,3458,7554,898,4994,2946,7042,1922,6018,3970,8066,66,4162,2114,6210,1090,5186,3138,7234,578,4674,2626,6722,1602,5698,3650,7746,322,4418,2370,6466,1346,5442,3394,7490,834,4930,2882,6978,1858,5954,3906,8002,194,4290,2242,6338,1218,5314,3266,7362,706,4802,2754,6850,1730,5826,3778,7874,450,4546,2498,6594,1474,5570,3522,7618,962,5058,3010,7106,1986,6082,4034,8130,34,4130,2082,6178,1058,5154,3106,7202,546,4642,2594,6690,1570,5666,3618,7714,290,4386,2338,6434,1314,5410,3362,7458,802,4898,2850,6946,1826,5922,3874,7970,162,4258,2210,6306,1186,5282,3234,7330,674,4770,2722,6818,1698,5794,3746,7842,418,4514,2466,6562,1442,5538,3490,7586,930,5026,2978,7074,1954,6050,4002,8098,98,4194,2146,6242,1122,5218,3170,7266,610,4706,2658,6754,1634,5730,3682,7778,354,4450,2402,6498,1378,5474,3426,7522,866,4962,2914,7010,1890,5986,3938,8034,226,4322,2274,6370,1250,5346,3298,7394,738,4834,2786,6882,1762,5858,3810,7906,482,4578,2530,6626,1506,5602,3554,7650,994,5090,3042,7138,2018,6114,4066,8162,18,4114,2066,6162,1042,5138,3090,7186,530,4626,2578,6674,1554,5650,3602,7698,274,4370,2322,6418,1298,5394,3346,7442,786,4882,2834,6930,1810,5906,3858,7954,146,4242,2194,6290,1170,5266,3218,7314,658,4754,2706,6802,1682,5778,3730,7826,402,4498,2450,6546,1426,5522,3474,7570,914,5010,2962,7058,1938,6034,3986,8082,82,4178,2130,6226,1106,5202,3154,7250,594,4690,2642,6738,1618,5714,3666,7762,338,4434,2386,6482,1362,5458,3410,7506,850,4946,2898,6994,1874,5970,3922,8018,210,4306,2258,6354,1234,5330,3282,7378,722,4818,2770,6866,1746,5842,3794,7890,466,4562,2514,6610,1490,5586,3538,7634,978,5074,3026,7122,2002,6098,4050,8146,50,4146,2098,6194,1074,5170,3122,7218,562,4658,2610,6706,1586,5682,3634,7730,306,4402,2354,6450,1330,5426,3378,7474,818,4914,2866,6962,1842,5938,3890,7986,178,4274,2226,6322,1202,5298,3250,7346,690,4786,2738,6834,1714,5810,3762,7858,434,4530,2482,6578,1458,5554,3506,7602,946,5042,2994,7090,1970,6066,4018,8114,114,4210,2162,6258,1138,5234,3186,7282,626,4722,2674,6770,1650,5746,3698,7794,370,4466,2418,6514,1394,5490,3442,7538,882,4978,2930,7026,1906,6002,3954,8050,242,4338,2290,6386,1266,5362,3314,7410,754,4850,2802,6898,1778,5874,3826,7922,498,4594,2546,6642,1522,5618,3570,7666,1010,5106,3058,7154,2034,6130,4082,8178,10,4106,2058,6154,1034,5130,3082,7178,522,4618,2570,6666,1546,5642,3594,7690,266,4362,2314,6410,1290,5386,3338,7434,778,4874,2826,6922,1802,5898,3850,7946,138,4234,2186,6282,1162,5258,3210,7306,650,4746,2698,6794,1674,5770,3722,7818,394,4490,2442,6538,1418,5514,3466,7562,906,5002,2954,7050,1930,6026,3978,8074,74,4170,2122,6218,1098,5194,3146,7242,586,4682,2634,6730,1610,5706,3658,7754,330,4426,2378,6474,1354,5450,3402,7498,842,4938,2890,6986,1866,5962,3914,8010,202,4298,2250,6346,1226,5322,3274,7370,714,4810,2762,6858,1738,5834,3786,7882,458,4554,2506,6602,1482,5578,3530,7626,970,5066,3018,7114,1994,6090,4042,8138,42,4138,2090,6186,1066,5162,3114,7210,554,4650,2602,6698,1578,5674,3626,7722,298,4394,2346,6442,1322,5418,3370,7466,810,4906,2858,6954,1834,5930,3882,7978,170,4266,2218,6314,1194,5290,3242,7338,682,4778,2730,6826,1706,5802,3754,7850,426,4522,2474,6570,1450,5546,3498,7594,938,5034,2986,7082,1962,6058,4010,8106,106,4202,2154,6250,1130,5226,3178,7274,618,4714,2666,6762,1642,5738,3690,7786,362,4458,2410,6506,1386,5482,3434,7530,874,4970,2922,7018,1898,5994,3946,8042,234,4330,2282,6378,1258,5354,3306,7402,746,4842,2794,6890,1770,5866,3818,7914,490,4586,2538,6634,1514,5610,3562,7658,1002,5098,3050,7146,2026,6122,4074,8170,26,4122,2074,6170,1050,5146,3098,7194,538,4634,2586,6682,1562,5658,3610,7706,282,4378,2330,6426,1306,5402,3354,7450,794,4890,2842,6938,1818,5914,3866,7962,154,4250,2202,6298,1178,5274,3226,7322,666,4762,2714,6810,1690,5786,3738,7834,410,4506,2458,6554,1434,5530,3482,7578,922,5018,2970,7066,1946,6042,3994,8090,90,4186,2138,6234,1114,5210,3162,7258,602,4698,2650,6746,1626,5722,3674,7770,346,4442,2394,6490,1370,5466,3418,7514,858,4954,2906,7002,1882,5978,3930,8026,218,4314,2266,6362,1242,5338,3290,7386,730,4826,2778,6874,1754,5850,3802,7898,474,4570,2522,6618,1498,5594,3546,7642,986,5082,3034,7130,2010,6106,4058,8154,58,4154,2106,6202,1082,5178,3130,7226,570,4666,2618,6714,1594,5690,3642,7738,314,4410,2362,6458,1338,5434,3386,7482,826,4922,2874,6970,1850,5946,3898,7994,186,4282,2234,6330,1210,5306,3258,7354,698,4794,2746,6842,1722,5818,3770,7866,442,4538,2490,6586,1466,5562,3514,7610,954,5050,3002,7098,1978,6074,4026,8122,122,4218,2170,6266,1146,5242,3194,7290,634,4730,2682,6778,1658,5754,3706,7802,378,4474,2426,6522,1402,5498,3450,7546,890,4986,2938,7034,1914,6010,3962,8058,250,4346,2298,6394,1274,5370,3322,7418,762,4858,2810,6906,1786,5882,3834,7930,506,4602,2554,6650,1530,5626,3578,7674,1018,5114,3066,7162,2042,6138,4090,8186,6,4102,2054,6150,1030,5126,3078,7174,518,4614,2566,6662,1542,5638,3590,7686,262,4358,2310,6406,1286,5382,3334,7430,774,4870,2822,6918,1798,5894,3846,7942,134,4230,2182,6278,1158,5254,3206,7302,646,4742,2694,6790,1670,5766,3718,7814,390,4486,2438,6534,1414,5510,3462,7558,902,4998,2950,7046,1926,6022,3974,8070,70,4166,2118,6214,1094,5190,3142,7238,582,4678,2630,6726,1606,5702,3654,7750,326,4422,2374,6470,1350,5446,3398,7494,838,4934,2886,6982,1862,5958,3910,8006,198,4294,2246,6342,1222,5318,3270,7366,710,4806,2758,6854,1734,5830,3782,7878,454,4550,2502,6598,1478,5574,3526,7622,966,5062,3014,7110,1990,6086,4038,8134,38,4134,2086,6182,1062,5158,3110,7206,550,4646,2598,6694,1574,5670,3622,7718,294,4390,2342,6438,1318,5414,3366,7462,806,4902,2854,6950,1830,5926,3878,7974,166,4262,2214,6310,1190,5286,3238,7334,678,4774,2726,6822,1702,5798,3750,7846,422,4518,2470,6566,1446,5542,3494,7590,934,5030,2982,7078,1958,6054,4006,8102,102,4198,2150,6246,1126,5222,3174,7270,614,4710,2662,6758,1638,5734,3686,7782,358,4454,2406,6502,1382,5478,3430,7526,870,4966,2918,7014,1894,5990,3942,8038,230,4326,2278,6374,1254,5350,3302,7398,742,4838,2790,6886,1766,5862,3814,7910,486,4582,2534,6630,1510,5606,3558,7654,998,5094,3046,7142,2022,6118,4070,8166,22,4118,2070,6166,1046,5142,3094,7190,534,4630,2582,6678,1558,5654,3606,7702,278,4374,2326,6422,1302,5398,3350,7446,790,4886,2838,6934,1814,5910,3862,7958,150,4246,2198,6294,1174,5270,3222,7318,662,4758,2710,6806,1686,5782,3734,7830,406,4502,2454,6550,1430,5526,3478,7574,918,5014,2966,7062,1942,6038,3990,8086,86,4182,2134,6230,1110,5206,3158,7254,598,4694,2646,6742,1622,5718,3670,7766,342,4438,2390,6486,1366,5462,3414,7510,854,4950,2902,6998,1878,5974,3926,8022,214,4310,2262,6358,1238,5334,3286,7382,726,4822,2774,6870,1750,5846,3798,7894,470,4566,2518,6614,1494,5590,3542,7638,982,5078,3030,7126,2006,6102,4054,8150,54,4150,2102,6198,1078,5174,3126,7222,566,4662,2614,6710,1590,5686,3638,7734,310,4406,2358,6454,1334,5430,3382,7478,822,4918,2870,6966,1846,5942,3894,7990,182,4278,2230,6326,1206,5302,3254,7350,694,4790,2742,6838,1718,5814,3766,7862,438,4534,2486,6582,1462,5558,3510,7606,950,5046,2998,7094,1974,6070,4022,8118,118,4214,2166,6262,1142,5238,3190,7286,630,4726,2678,6774,1654,5750,3702,7798,374,4470,2422,6518,1398,5494,3446,7542,886,4982,2934,7030,1910,6006,3958,8054,246,4342,2294,6390,1270,5366,3318,7414,758,4854,2806,6902,1782,5878,3830,7926,502,4598,2550,6646,1526,5622,3574,7670,1014,5110,3062,7158,2038,6134,4086,8182,14,4110,2062,6158,1038,5134,3086,7182,526,4622,2574,6670,1550,5646,3598,7694,270,4366,2318,6414,1294,5390,3342,7438,782,4878,2830,6926,1806,5902,3854,7950,142,4238,2190,6286,1166,5262,3214,7310,654,4750,2702,6798,1678,5774,3726,7822,398,4494,2446,6542,1422,5518,3470,7566,910,5006,2958,7054,1934,6030,3982,8078,78,4174,2126,6222,1102,5198,3150,7246,590,4686,2638,6734,1614,5710,3662,7758,334,4430,2382,6478,1358,5454,3406,7502,846,4942,2894,6990,1870,5966,3918,8014,206,4302,2254,6350,1230,5326,3278,7374,718,4814,2766,6862,1742,5838,3790,7886,462,4558,2510,6606,1486,5582,3534,7630,974,5070,3022,7118,1998,6094,4046,8142,46,4142,2094,6190,1070,5166,3118,7214,558,4654,2606,6702,1582,5678,3630,7726,302,4398,2350,6446,1326,5422,3374,7470,814,4910,2862,6958,1838,5934,3886,7982,174,4270,2222,6318,1198,5294,3246,7342,686,4782,2734,6830,1710,5806,3758,7854,430,4526,2478,6574,1454,5550,3502,7598,942,5038,2990,7086,1966,6062,4014,8110,110,4206,2158,6254,1134,5230,3182,7278,622,4718,2670,6766,1646,5742,3694,7790,366,4462,2414,6510,1390,5486,3438,7534,878,4974,2926,7022,1902,5998,3950,8046,238,4334,2286,6382,1262,5358,3310,7406,750,4846,2798,6894,1774,5870,3822,7918,494,4590,2542,6638,1518,5614,3566,7662,1006,5102,3054,7150,2030,6126,4078,8174,30,4126,2078,6174,1054,5150,3102,7198,542,4638,2590,6686,1566,5662,3614,7710,286,4382,2334,6430,1310,5406,3358,7454,798,4894,2846,6942,1822,5918,3870,7966,158,4254,2206,6302,1182,5278,3230,7326,670,4766,2718,6814,1694,5790,3742,7838,414,4510,2462,6558,1438,5534,3486,7582,926,5022,2974,7070,1950,6046,3998,8094,94,4190,2142,6238,1118,5214,3166,7262,606,4702,2654,6750,1630,5726,3678,7774,350,4446,2398,6494,1374,5470,3422,7518,862,4958,2910,7006,1886,5982,3934,8030,222,4318,2270,6366,1246,5342,3294,7390,734,4830,2782,6878,1758,5854,3806,7902,478,4574,2526,6622,1502,5598,3550,7646,990,5086,3038,7134,2014,6110,4062,8158,62,4158,2110,6206,1086,5182,3134,7230,574,4670,2622,6718,1598,5694,3646,7742,318,4414,2366,6462,1342,5438,3390,7486,830,4926,2878,6974,1854,5950,3902,7998,190,4286,2238,6334,1214,5310,3262,7358,702,4798,2750,6846,1726,5822,3774,7870,446,4542,2494,6590,1470,5566,3518,7614,958,5054,3006,7102,1982,6078,4030,8126,126,4222,2174,6270,1150,5246,3198,7294,638,4734,2686,6782,1662,5758,3710,7806,382,4478,2430,6526,1406,5502,3454,7550,894,4990,2942,7038,1918,6014,3966,8062,254,4350,2302,6398,1278,5374,3326,7422,766,4862,2814,6910,1790,5886,3838,7934,510,4606,2558,6654,1534,5630,3582,7678,1022,5118,3070,7166,2046,6142,4094,8190]。

当N＝2048，

序列1c为：

Shorten_Q＝[0,1024,512,1536,256,1280,768,1792,128,1152,640,1664,384,1408,896,1920,64,1088,576,1600,320,1344,832,1856,192,1216,704,1728,448,1472,960,1984,32,1056,544,1568,288,1312,800,1824,160,1184,672,1696,416,1440,928,1952,96,1120,608,1632,352,1376,864,1888,224,1248,736,1760,480,1504,992,2016,16,1040,528,1552,272,1296,784,1808,144,1168,656,1680,400,1424,912,1936,80,1104,592,1616,336,1360,848,1872,208,1232,720,1744,464,1488,976,2000,48,1072,560,1584,304,1328,816,1840,176,1200,688,1712,432,1456,944,1968,112,1136,624,1648,368,1392,880,1904,240,1264,752,1776,496,1520,1008,2032,8,1032,520,1544,264,1288,776,1800,136,1160,648,1672,392,1416,904,1928,72,1096,584,1608,328,1352,840,1864,200,1224,712,1736,456,1480,968,1992,40,1064,552,1576,296,1320,808,1832,168,1192,680,1704,424,1448,936,1960,104,1128,616,1640,360,1384,872,1896,232,1256,744,1768,488,1512,1000,2024,24,1048,536,1560,280,1304,792,1816,152,1176,664,1688,408,1432,920,1944,88,1112,600,1624,344,1368,856,1880,216,1240,728,1752,472,1496,984,2008,56,1080,568,1592,312,1336,824,1848,184,1208,696,1720,440,1464,952,1976,120,1144,632,1656,376,1400,888,1912,248,1272,760,1784,504,1528,1016,2040,4,1028,516,1540,260,1284,772,1796,132,1156,644,1668,388,1412,900,1924,68,1092,580,1604,324,1348,836,1860,196,1220,708,1732,452,1476,964,1988,36,1060,548,1572,292,1316,804,1828,164,1188,676,1700,420,1444,932,1956,100,1124,612,1636,356,1380,868,1892,228,1252,740,1764,484,1508,996,2020,20,1044,532,1556,276,1300,788,1812,148,1172,660,1684,404,1428,916,1940,84,1108,596,1620,340,1364,852,1876,212,1236,724,1748,468,1492,980,2004,52,1076,564,1588,308,1332,820,1844,180,1204,692,1716,436,1460,948,1972,116,1140,628,1652,372,1396,884,1908,244,1268,756,1780,500,1524,1012,2036,12,1036,524,1548,268,1292,780,1804,140,1164,652,1676,396,1420,908,1932,76,1100,588,1612,332,1356,844,1868,204,1228,716,1740,460,1484,972,1996,44,1068,556,1580,300,1324,812,1836,172,1196,684,1708,428,1452,940,1964,108,1132,620,1644,364,1388,876,1900,236,1260,748,1772,492,1516,1004,2028,28,1052,540,1564,284,1308,796,1820,156,1180,668,1692,412,1436,924,1948,92,1116,604,1628,348,1372,860,1884,220,1244,732,1756,476,1500,988,2012,60,1084,572,1596,316,1340,828,1852,188,1212,700,1724,444,1468,956,1980,124,1148,636,1660,380,1404,892,1916,252,1276,764,1788,508,1532,1020,2044,2,1026,514,1538,258,1282,770,1794,130,1154,642,1666,386,1410,898,1922,66,1090,578,1602,322,1346,834,1858,194,1218,706,1730,450,1474,962,1986,34,1058,546,1570,290,1314,802,1826,162,1186,674,1698,418,1442,930,1954,98,1122,610,1634,354,1378,866,1890,226,1250,738,1762,482,1506,994,2018,18,1042,530,1554,274,1298,786,1810,146,1170,658,1682,402,1426,914,1938,82,1106,594,1618,338,1362,850,1874,210,1234,722,1746,466,1490,978,2002,50,1074,562,1586,306,1330,818,1842,178,1202,690,1714,434,1458,946,1970,114,1138,626,1650,370,1394,882,1906,242,1266,754,1778,498,1522,1010,2034,10,1034,522,1546,266,1290,778,1802,138,1162,650,1674,394,1418,906,1930,74,1098,586,1610,330,1354,842,1866,202,1226,714,1738,458,1482,970,1994,42,1066,554,1578,298,1322,810,1834,170,1194,682,1706,426,1450,938,1962,106,1130,618,1642,362,1386,874,1898,234,1258,746,1770,490,1514,1002,2026,26,1050,538,1562,282,1306,794,1818,154,1178,666,1690,410,1434,922,1946,90,1114,602,1626,346,1370,858,1882,218,1242,730,1754,474,1498,986,2010,58,1082,570,1594,314,1338,826,1850,186,1210,698,1722,442,1466,954,1978,122,1146,634,1658,378,1402,890,1914,250,1274,762,1786,506,1530,1018,2042,6,1030,518,1542,262,1286,774,1798,134,1158,646,1670,390,1414,902,1926,70,1094,582,1606,326,1350,838,1862,198,1222,710,1734,454,1478,966,1990,38,1062,550,1574,294,1318,806,1830,166,1190,678,1702,422,1446,934,1958,102,1126,614,1638,358,1382,870,1894,230,1254,742,1766,486,1510,998,2022,22,1046,534,1558,278,1302,790,1814,150,1174,662,1686,406,1430,918,1942,86,1110,598,1622,342,1366,854,1878,214,1238,726,1750,470,1494,982,2006,54,1078,566,1590,310,1334,822,1846,182,1206,694,1718,438,1462,950,1974,118,1142,630,1654,374,1398,886,1910,246,1270,758,1782,502,1526,1014,2038,14,1038,526,1550,270,1294,782,1806,142,1166,654,1678,398,1422,910,1934,78,1102,590,1614,334,1358,846,1870,206,1230,718,1742,462,1486,974,1998,46,1070,558,1582,302,1326,814,1838,174,1198,686,1710,430,1454,942,1966,110,1134,622,1646,366,1390,878,1902,238,1262,750,1774,494,1518,1006,2030,30,1054,542,1566,286,1310,798,1822,158,1182,670,1694,414,1438,926,1950,94,1118,606,1630,350,1374,862,1886,222,1246,734,1758,478,1502,990,2014,62,1086,574,1598,318,1342,830,1854,190,1214,702,1726,446,1470,958,1982,126,1150,638,1662,382,1406,894,1918,254,1278,766,1790,510,1534,1022,2046,1,1025,513,1537,257,1281,769,1793,129,1153,641,1665,385,1409,897,1921,65,1089,577,1601,321,1345,833,1857,193,1217,705,1729,449,1473,961,1985,33,1057,545,1569,289,1313,801,1825,161,1185,673,1697,417,1441,929,1953,97,1121,609,1633,353,1377,865,1889,225,1249,737,1761,481,1505,993,2017,17,1041,529,1553,273,1297,785,1809,145,1169,657,1681,401,1425,913,1937,81,1105,593,1617,337,1361,849,1873,209,1233,721,1745,465,1489,977,2001,49,1073,561,1585,305,1329,817,1841,177,1201,689,1713,433,1457,945,1969,113,1137,625,1649,369,1393,881,1905,241,1265,753,1777,497,1521,1009,2033,9,1033,521,1545,265,1289,777,1801,137,1161,649,1673,393,1417,905,1929,73,1097,585,1609,329,1353,841,1865,201,1225,713,1737,457,1481,969,1993,41,1065,553,1577,297,1321,809,1833,169,1193,681,1705,425,1449,937,1961,105,1129,617,1641,361,1385,873,1897,233,1257,745,1769,489,1513,1001,2025,25,1049,537,1561,281,1305,793,1817,153,1177,665,1689,409,1433,921,1945,89,1113,601,1625,345,1369,857,1881,217,1241,729,1753,473,1497,985,2009,57,1081,569,1593,313,1337,825,1849,185,1209,697,1721,441,1465,953,1977,121,1145,633,1657,377,1401,889,1913,249,1273,761,1785,505,1529,1017,2041,5,1029,517,1541,261,1285,773,1797,133,1157,645,1669,389,1413,901,1925,69,1093,581,1605,325,1349,837,1861,197,1221,709,1733,453,1477,965,1989,37,1061,549,1573,293,1317,805,1829,165,1189,677,1701,421,1445,933,1957,101,1125,613,1637,357,1381,869,1893,229,1253,741,1765,485,1509,997,2021,21,1045,533,1557,277,1301,789,1813,149,1173,661,1685,405,1429,917,1941,85,1109,597,1621,341,1365,853,1877,213,1237,725,1749,469,1493,981,2005,53,1077,565,1589,309,1333,821,1845,181,1205,693,1717,437,1461,949,1973,117,1141,629,1653,373,1397,885,1909,245,1269,757,1781,501,1525,1013,2037,13,1037,525,1549,269,1293,781,1805,141,1165,653,1677,397,1421,909,1933,77,1101,589,1613,333,1357,845,1869,205,1229,717,1741,461,1485,973,1997,45,1069,557,1581,301,1325,813,1837,173,1197,685,1709,429,1453,941,1965,109,1133,621,1645,365,1389,877,1901,237,1261,749,1773,493,1517,1005,2029,29,1053,541,1565,285,1309,797,1821,157,1181,669,1693,413,1437,925,1949,93,1117,605,1629,349,1373,861,1885,221,1245,733,1757,477,1501,989,2013,61,1085,573,1597,317,1341,829,1853,189,1213,701,1725,445,1469,957,1981,125,1149,637,1661,381,1405,893,1917,253,1277,765,1789,509,1533,1021,2045,3,1027,515,1539,259,1283,771,1795,131,1155,643,1667,387,1411,899,1923,67,1091,579,1603,323,1347,835,1859,195,1219,707,1731,451,1475,963,1987,35,1059,547,1571,291,1315,803,1827,163,1187,675,1699,419,1443,931,1955,99,1123,611,1635,355,1379,867,1891,227,1251,739,1763,483,1507,995,2019,19,1043,531,1555,275,1299,787,1811,147,1171,659,1683,403,1427,915,1939,83,1107,595,1619,339,1363,851,1875,211,1235,723,1747,467,1491,979,2003,51,1075,563,1587,307,1331,819,1843,179,1203,691,1715,435,1459,947,1971,115,1139,627,1651,371,1395,883,1907,243,1267,755,1779,499,1523,1011,2035,11,1035,523,1547,267,1291,779,1803,139,1163,651,1675,395,1419,907,1931,75,1099,587,1611,331,1355,843,1867,203,1227,715,1739,459,1483,971,1995,43,1067,555,1579,299,1323,811,1835,171,1195,683,1707,427,1451,939,1963,107,1131,619,1643,363,1387,875,1899,235,1259,747,1771,491,1515,1003,2027,27,1051,539,1563,283,1307,795,1819,155,1179,667,1691,411,1435,923,1947,91,1115,603,1627,347,1371,859,1883,219,1243,731,1755,475,1499,987,2011,59,1083,571,1595,315,1339,827,1851,187,1211,699,1723,443,1467,955,1979,123,1147,635,1659,379,1403,891,1915,251,1275,763,1787,507,1531,1019,2043,7,1031,519,1543,263,1287,775,1799,135,1159,647,1671,391,1415,903,1927,71,1095,583,1607,327,1351,839,1863,199,1223,711,1735,455,1479,967,1991,39,1063,551,1575,295,1319,807,1831,167,1191,679,1703,423,1447,935,1959,103,1127,615,1639,359,1383,871,1895,231,1255,743,1767,487,1511,999,2023,23,1047,535,1559,279,1303,791,1815,151,1175,663,1687,407,1431,919,1943,87,1111,599,1623,343,1367,855,1879,215,1239,727,1751,471,1495,983,2007,55,1079,567,1591,311,1335,823,1847,183,1207,695,1719,439,1463,951,1975,119,1143,631,1655,375,1399,887,1911,247,1271,759,1783,503,1527,1015,2039,15,1039,527,1551,271,1295,783,1807,143,1167,655,1679,399,1423,911,1935,79,1103,591,1615,335,1359,847,1871,207,1231,719,1743,463,1487,975,1999,47,1071,559,1583,303,1327,815,1839,175,1199,687,1711,431,1455,943,1967,111,1135,623,1647,367,1391,879,1903,239,1263,751,1775,495,1519,1007,2031,31,1055,543,1567,287,1311,799,1823,159,1183,671,1695,415,1439,927,1951,95,1119,607,1631,351,1375,863,1887,223,1247,735,1759,479,1503,991,2015,63,1087,575,1599,319,1343,831,1855,191,1215,703,1727,447,1471,959,1983,127,1151,639,1663,383,1407,895,1919,255,1279,767,1791,511,1535,1023,2047]。

序列2c为：

Shorten_Q_half＝[1,1025,513,1537,257,1281,769,1793,129,1153,641,1665,385,1409,897,1921,65,1089,577,1601,321,1345,833,1857,193,1217,705,1729,449,1473,961,1985,33,1057,545,1569,289,1313,801,1825,161,1185,673,1697,417,1441,929,1953,97,1121,609,1633,353,1377,865,1889,225,1249,737,1761,481,1505,993,2017,17,1041,529,1553,273,1297,785,1809,145,1169,657,1681,401,1425,913,1937,81,1105,593,1617,337,1361,849,1873,209,1233,721,1745,465,1489,977,2001,49,1073,561,1585,305,1329,817,1841,177,1201,689,1713,433,1457,945,1969,113,1137,625,1649,369,1393,881,1905,241,1265,753,1777,497,1521,1009,2033,9,1033,521,1545,265,1289,777,1801,137,1161,649,1673,393,1417,905,1929,73,1097,585,1609,329,1353,841,1865,201,1225,713,1737,457,1481,969,1993,41,1065,553,1577,297,1321,809,1833,169,1193,681,1705,425,1449,937,1961,105,1129,617,1641,361,1385,873,1897,233,1257,745,1769,489,1513,1001,2025,25,1049,537,1561,281,1305,793,1817,153,1177,665,1689,409,1433,921,1945,89,1113,601,1625,345,1369,857,1881,217,1241,729,1753,473,1497,985,2009,57,1081,569,1593,313,1337,825,1849,185,1209,697,1721,441,1465,953,1977,121,1145,633,1657,377,1401,889,1913,249,1273,761,1785,505,1529,1017,2041,5,1029,517,1541,261,1285,773,1797,133,1157,645,1669,389,1413,901,1925,69,1093,581,1605,325,1349,837,1861,197,1221,709,1733,453,1477,965,1989,37,1061,549,1573,293,1317,805,1829,165,1189,677,1701,421,1445,933,1957,101,1125,613,1637,357,1381,869,1893,229,1253,741,1765,485,1509,997,2021,21,1045,533,1557,277,1301,789,1813,149,1173,661,1685,405,1429,917,1941,85,1109,597,1621,341,1365,853,1877,213,1237,725,1749,469,1493,981,2005,53,1077,565,1589,309,1333,821,1845,181,1205,693,1717,437,1461,949,1973,117,1141,629,1653,373,1397,885,1909,245,1269,757,1781,501,1525,1013,2037,13,1037,525,1549,269,1293,781,1805,141,1165,653,1677,397,1421,909,1933,77,1101,589,1613,333,1357,845,1869,205,1229,717,1741,461,1485,973,1997,45,1069,557,1581,301,1325,813,1837,173,1197,685,1709,429,1453,941,1965,109,1133,621,1645,365,1389,877,1901,237,1261,749,1773,493,1517,1005,2029,29,1053,541,1565,285,1309,797,1821,157,1181,669,1693,413,1437,925,1949,93,1117,605,1629,349,1373,861,1885,221,1245,733,1757,477,1501,989,2013,61,1085,573,1597,317,1341,829,1853,189,1213,701,1725,445,1469,957,1981,125,1149,637,1661,381,1405,893,1917,253,1277,765,1789,509,1533,1021,2045,3,1027,515,1539,259,1283,771,1795,131,1155,643,1667,387,1411,899,1923,67,1091,579,1603,323,1347,835,1859,195,1219,707,1731,451,1475,963,1987,35,1059,547,1571,291,1315,803,1827,163,1187,675,1699,419,1443,931,1955,99,1123,611,1635,355,1379,867,1891,227,1251,739,1763,483,1507,995,2019,19,1043,531,1555,275,1299,787,1811,147,1171,659,1683,403,1427,915,1939,83,1107,595,1619,339,1363,851,1875,211,1235,723,1747,467,1491,979,2003,51,1075,563,1587,307,1331,819,1843,179,1203,691,1715,435,1459,947,1971,115,1139,627,1651,371,1395,883,1907,243,1267,755,1779,499,1523,1011,2035,11,1035,523,1547,267,1291,779,1803,139,1163,651,1675,395,1419,907,1931,75,1099,587,1611,331,1355,843,1867,203,1227,715,1739,459,1483,971,1995,43,1067,555,1579,299,1323,811,1835,171,1195,683,1707,427,1451,939,1963,107,1131,619,1643,363,1387,875,1899,235,1259,747,1771,491,1515,1003,2027,27,1051,539,1563,283,1307,795,1819,155,1179,667,1691,411,1435,923,1947,91,1115,603,1627,347,1371,859,1883,219,1243,731,1755,475,1499,987,2011,59,1083,571,1595,315,1339,827,1851,187,1211,699,1723,443,1467,955,1979,123,1147,635,1659,379,1403,891,1915,251,1275,763,1787,507,1531,1019,2043,7,1031,519,1543,263,1287,775,1799,135,1159,647,1671,391,1415,903,1927,71,1095,583,1607,327,1351,839,1863,199,1223,711,1735,455,1479,967,1991,39,1063,551,1575,295,1319,807,1831,167,1191,679,1703,423,1447,935,1959,103,1127,615,1639,359,1383,871,1895,231,1255,743,1767,487,1511,999,2023,23,1047,535,1559,279,1303,791,1815,151,1175,663,1687,407,1431,919,1943,87,1111,599,1623,343,1367,855,1879,215,1239,727,1751,471,1495,983,2007,55,1079,567,1591,311,1335,823,1847,183,1207,695,1719,439,1463,951,1975,119,1143,631,1655,375,1399,887,1911,247,1271,759,1783,503,1527,1015,2039,15,1039,527,1551,271,1295,783,1807,143,1167,655,1679,399,1423,911,1935,79,1103,591,1615,335,1359,847,1871,207,1231,719,1743,463,1487,975,1999,47,1071,559,1583,303,1327,815,1839,175,1199,687,1711,431,1455,943,1967,111,1135,623,1647,367,1391,879,1903,239,1263,751,1775,495,1519,1007,2031,31,1055,543,1567,287,1311,799,1823,159,1183,671,1695,415,1439,927,1951,95,1119,607,1631,351,1375,863,1887,223,1247,735,1759,479,1503,991,2015,63,1087,575,1599,319,1343,831,1855,191,1215,703,1727,447,1471,959,1983,127,1151,639,1663,383,1407,895,1919,255,1279,767,1791,511,1535,1023,2047]。

序列3c为；

Shorten_Z＝[0,4096,2048,6144,1024,5120,3072,7168,512,4608,2560,6656,1536,5632,3584,7680,256,4352,2304,6400,1280,5376,3328,7424,768,4864,2816,6912,1792,5888,3840,7936,128,4224,2176,6272,1152,5248,3200,7296,640,4736,2688,6784,1664,5760,3712,7808,384,4480,2432,6528,1408,5504,3456,7552,896,4992,2944,7040,1920,6016,3968,8064,64,4160,2112,6208,1088,5184,3136,7232,576,4672,2624,6720,1600,5696,3648,7744,320,4416,2368,6464,1344,5440,3392,7488,832,4928,2880,6976,1856,5952,3904,8000,192,4288,2240,6336,1216,5312,3264,7360,704,4800,2752,6848,1728,5824,3776,7872,448,4544,2496,6592,1472,5568,3520,7616,960,5056,3008,7104,1984,6080,4032,8128,32,4128,2080,6176,1056,5152,3104,7200,544,4640,2592,6688,1568,5664,3616,7712,288,4384,2336,6432,1312,5408,3360,7456,800,4896,2848,6944,1824,5920,3872,7968,160,4256,2208,6304,1184,5280,3232,7328,672,4768,2720,6816,1696,5792,3744,7840,416,4512,2464,6560,1440,5536,3488,7584,928,5024,2976,7072,1952,6048,4000,8096,96,4192,2144,6240,1120,5216,3168,7264,608,4704,2656,6752,1632,5728,3680,7776,352,4448,2400,6496,1376,5472,3424,7520,864,4960,2912,7008,1888,5984,3936,8032,224,4320,2272,6368,1248,5344,3296,7392,736,4832,2784,6880,1760,5856,3808,7904,480,4576,2528,6624,1504,5600,3552,7648,992,5088,3040,7136,2016,6112,4064,8160,16,4112,2064,6160,1040,5136,3088,7184,528,4624,2576,6672,1552,5648,3600,7696,272,4368,2320,6416,1296,5392,3344,7440,784,4880,2832,6928,1808,5904,3856,7952,144,4240,2192,6288,1168,5264,3216,7312,656,4752,2704,6800,1680,5776,3728,7824,400,4496,2448,6544,1424,5520,3472,7568,912,5008,2960,7056,1936,6032,3984,8080,80,4176,2128,6224,1104,5200,3152,7248,592,4688,2640,6736,1616,5712,3664,7760,336,4432,2384,6480,1360,5456,3408,7504,848,4944,2896,6992,1872,5968,3920,8016,208,4304,2256,6352,1232,5328,3280,7376,720,4816,2768,6864,1744,5840,3792,7888,464,4560,2512,6608,1488,5584,3536,7632,976,5072,3024,7120,2000,6096,4048,8144,48,4144,2096,6192,1072,5168,3120,7216,560,4656,2608,6704,1584,5680,3632,7728,304,4400,2352,6448,1328,5424,3376,7472,816,4912,2864,6960,1840,5936,3888,7984,176,4272,2224,6320,1200,5296,3248,7344,688,4784,2736,6832,1712,5808,3760,7856,432,4528,2480,6576,1456,5552,3504,7600,944,5040,2992,7088,1968,6064,4016,8112,112,4208,2160,6256,1136,5232,3184,7280,624,4720,2672,6768,1648,5744,3696,7792,368,4464,2416,6512,1392,5488,3440,7536,880,4976,2928,7024,1904,6000,3952,8048,240,4336,2288,6384,1264,5360,3312,7408,752,4848,2800,6896,1776,5872,3824,7920,496,4592,2544,6640,1520,5616,3568,7664,1008,5104,3056,7152,2032,6128,4080,8176,8,4104,2056,6152,1032,5128,3080,7176,520,4616,2568,6664,1544,5640,3592,7688,264,4360,2312,6408,1288,5384,3336,7432,776,4872,2824,6920,1800,5896,3848,7944,136,4232,2184,6280,1160,5256,3208,7304,648,4744,2696,6792,1672,5768,3720,7816,392,4488,2440,6536,1416,5512,3464,7560,904,5000,2952,7048,1928,6024,3976,8072,72,4168,2120,6216,1096,5192,3144,7240,584,4680,2632,6728,1608,5704,3656,7752,328,4424,2376,6472,1352,5448,3400,7496,840,4936,2888,6984,1864,5960,3912,8008,200,4296,2248,6344,1224,5320,3272,7368,712,4808,2760,6856,1736,5832,3784,7880,456,4552,2504,6600,1480,5576,3528,7624,968,5064,3016,7112,1992,6088,4040,8136,40,4136,2088,6184,1064,5160,3112,7208,552,4648,2600,6696,1576,5672,3624,7720,296,4392,2344,6440,1320,5416,3368,7464,808,4904,2856,6952,1832,5928,3880,7976,168,4264,2216,6312,1192,5288,3240,7336,680,4776,2728,6824,1704,5800,3752,7848,424,4520,2472,6568,1448,5544,3496,7592,936,5032,2984,7080,1960,6056,4008,8104,104,4200,2152,6248,1128,5224,3176,7272,616,4712,2664,6760,1640,5736,3688,7784,360,4456,2408,6504,1384,5480,3432,7528,872,4968,2920,7016,1896,5992,3944,8040,232,4328,2280,6376,1256,5352,3304,7400,744,4840,2792,6888,1768,5864,3816,7912,488,4584,2536,6632,1512,5608,3560,7656,1000,5096,3048,7144,2024,6120,4072,8168,24,4120,2072,6168,1048,5144,3096,7192,536,4632,2584,6680,1560,5656,3608,7704,280,4376,2328,6424,1304,5400,3352,7448,792,4888,2840,6936,1816,5912,3864,7960,152,4248,2200,6296,1176,5272,3224,7320,664,4760,2712,6808,1688,5784,3736,7832,408,4504,2456,6552,1432,5528,3480,7576,920,5016,2968,7064,1944,6040,3992,8088,88,4184,2136,6232,1112,5208,3160,7256,600,4696,2648,6744,1624,5720,3672,7768,344,4440,2392,6488,1368,5464,3416,7512,856,4952,2904,7000,1880,5976,3928,8024,216,4312,2264,6360,1240,5336,3288,7384,728,4824,2776,6872,1752,5848,3800,7896,472,4568,2520,6616,1496,5592,3544,7640,984,5080,3032,7128,2008,6104,4056,8152,56,4152,2104,6200,1080,5176,3128,7224,568,4664,2616,6712,1592,5688,3640,7736,312,4408,2360,6456,1336,5432,3384,7480,824,4920,2872,6968,1848,5944,3896,7992,184,4280,2232,6328,1208,5304,3256,7352,696,4792,2744,6840,1720,5816,3768,7864,440,4536,2488,6584,1464,5560,3512,7608,952,5048,3000,7096,1976,6072,4024,8120,120,4216,2168,6264,1144,5240,3192,7288,632,4728,2680,6776,1656,5752,3704,7800,376,4472,2424,6520,1400,5496,3448,7544,888,4984,2936,7032,1912,6008,3960,8056,248,4344,2296,6392,1272,5368,3320,7416,760,4856,2808,6904,1784,5880,3832,7928,504,4600,2552,6648,1528,5624,3576,7672,1016,5112,3064,7160,2040,6136,4088,8184,4,4100,2052,6148,1028,5124,3076,7172,516,4612,2564,6660,1540,5636,3588,7684,260,4356,2308,6404,1284,5380,3332,7428,772,4868,2820,6916,1796,5892,3844,7940,132,4228,2180,6276,1156,5252,3204,7300,644,4740,2692,6788,1668,5764,3716,7812,388,4484,2436,6532,1412,5508,3460,7556,900,4996,2948,7044,1924,6020,3972,8068,68,4164,2116,6212,1092,5188,3140,7236,580,4676,2628,6724,1604,5700,3652,7748,324,4420,2372,6468,1348,5444,3396,7492,836,4932,2884,6980,1860,5956,3908,8004,196,4292,2244,6340,1220,5316,3268,7364,708,4804,2756,6852,1732,5828,3780,7876,452,4548,2500,6596,1476,5572,3524,7620,964,5060,3012,7108,1988,6084,4036,8132,36,4132,2084,6180,1060,5156,3108,7204,548,4644,2596,6692,1572,5668,3620,7716,292,4388,2340,6436,1316,5412,3364,7460,804,4900,2852,6948,1828,5924,3876,7972,164,4260,2212,6308,1188,5284,3236,7332,676,4772,2724,6820,1700,5796,3748,7844,420,4516,2468,6564,1444,5540,3492,7588,932,5028,2980,7076,1956,6052,4004,8100,100,4196,2148,6244,1124,5220,3172,7268,612,4708,2660,6756,1636,5732,3684,7780,356,4452,2404,6500,1380,5476,3428,7524,868,4964,2916,7012,1892,5988,3940,8036,228,4324,2276,6372,1252,5348,3300,7396,740,4836,2788,6884,1764,5860,3812,7908,484,4580,2532,6628,1508,5604,3556,7652,996,5092,3044,7140,2020,6116,4068,8164,20,4116,2068,6164,1044,5140,3092,7188,532,4628,2580,6676,1556,5652,3604,7700,276,4372,2324,6420,1300,5396,3348,7444,788,4884,2836,6932,1812,5908,3860,7956,148,4244,2196,6292,1172,5268,3220,7316,660,4756,2708,6804,1684,5780,3732,7828,404,4500,2452,6548,1428,5524,3476,7572,916,5012,2964,7060,1940,6036,3988,8084,84,4180,2132,6228,1108,5204,3156,7252,596,4692,2644,6740,1620,5716,3668,7764,340,4436,2388,6484,1364,5460,3412,7508,852,4948,2900,6996,1876,5972,3924,8020,212,4308,2260,6356,1236,5332,3284,7380,724,4820,2772,6868,1748,5844,3796,7892,468,4564,2516,6612,1492,5588,3540,7636,980,5076,3028,7124,2004,6100,4052,8148,52,4148,2100,6196,1076,5172,3124,7220,564,4660,2612,6708,1588,5684,3636,7732,308,4404,2356,6452,1332,5428,3380,7476,820,4916,2868,6964,1844,5940,3892,7988,180,4276,2228,6324,1204,5300,3252,7348,692,4788,2740,6836,1716,5812,3764,7860,436,4532,2484,6580,1460,5556,3508,7604,948,5044,2996,7092,1972,6068,4020,8116,116,4212,2164,6260,1140,5236,3188,7284,628,4724,2676,6772,1652,5748,3700,7796,372,4468,2420,6516,1396,5492,3444,7540,884,4980,2932,7028,1908,6004,3956,8052,244,4340,2292,6388,1268,5364,3316,7412,756,4852,2804,6900,1780,5876,3828,7924,500,4596,2548,6644,1524,5620,3572,7668,1012,5108,3060,7156,2036,6132,4084,8180,12,4108,2060,6156,1036,5132,3084,7180,524,4620,2572,6668,1548,5644,3596,7692,268,4364,2316,6412,1292,5388,3340,7436,780,4876,2828,6924,1804,5900,3852,7948,140,4236,2188,6284,1164,5260,3212,7308,652,4748,2700,6796,1676,5772,3724,7820,396,4492,2444,6540,1420,5516,3468,7564,908,5004,2956,7052,1932,6028,3980,8076,76,4172,2124,6220,1100,5196,3148,7244,588,4684,2636,6732,1612,5708,3660,7756,332,4428,2380,6476,1356,5452,3404,7500,844,4940,2892,6988,1868,5964,3916,8012,204,4300,2252,6348,1228,5324,3276,7372,716,4812,2764,6860,1740,5836,3788,7884,460,4556,2508,6604,1484,5580,3532,7628,972,5068,3020,7116,1996,6092,4044,8140,44,4140,2092,6188,1068,5164,3116,7212,556,4652,2604,6700,1580,5676,3628,7724,300,4396,2348,6444,1324,5420,3372,7468,812,4908,2860,6956,1836,5932,3884,7980,172,4268,2220,6316,1196,5292,3244,7340,684,4780,2732,6828,1708,5804,3756,7852,428,4524,2476,6572,1452,5548,3500,7596,940,5036,2988,7084,1964,6060,4012,8108,108,4204,2156,6252,1132,5228,3180,7276,620,4716,2668,6764,1644,5740,3692,7788,364,4460,2412,6508,1388,5484,3436,7532,876,4972,2924,7020,1900,5996,3948,8044,236,4332,2284,6380,1260,5356,3308,7404,748,4844,2796,6892,1772,5868,3820,7916,492,4588,2540,6636,1516,5612,3564,7660,1004,5100,3052,7148,2028,6124,4076,8172,28,4124,2076,6172,1052,5148,3100,7196,540,4636,2588,6684,1564,5660,3612,7708,284,4380,2332,6428,1308,5404,3356,7452,796,4892,2844,6940,1820,5916,3868,7964,156,4252,2204,6300,1180,5276,3228,7324,668,4764,2716,6812,1692,5788,3740,7836,412,4508,2460,6556,1436,5532,3484,7580,924,5020,2972,7068,1948,6044,3996,8092,92,4188,2140,6236,1116,5212,3164,7260,604,4700,2652,6748,1628,5724,3676,7772,348,4444,2396,6492,1372,5468,3420,7516,860,4956,2908,7004,1884,5980,3932,8028,220,4316,2268,6364,1244,5340,3292,7388,732,4828,2780,6876,1756,5852,3804,7900,476,4572,2524,6620,1500,5596,3548,7644,988,5084,3036,7132,2012,6108,4060,8156,60,4156,2108,6204,1084,5180,3132,7228,572,4668,2620,6716,1596,5692,3644,7740,316,4412,2364,6460,1340,5436,3388,7484,828,4924,2876,6972,1852,5948,3900,7996,188,4284,2236,6332,1212,5308,3260,7356,700,4796,2748,6844,1724,5820,3772,7868,444,4540,2492,6588,1468,5564,3516,7612,956,5052,3004,7100,1980,6076,4028,8124,124,4220,2172,6268,1148,5244,3196,7292,636,4732,2684,6780,1660,5756,3708,7804,380,4476,2428,6524,1404,5500,3452,7548,892,4988,2940,7036,1916,6012,3964,8060,252,4348,2300,6396,1276,5372,3324,7420,764,4860,2812,6908,1788,5884,3836,7932,508,4604,2556,6652,1532,5628,3580,7676,1020,5116,3068,7164,2044,6140,4092,8188]。

当N＝1024，

序列1d为：

Shorten_Q＝[0,512,256,768,128,640,384,896,64,576,320,832,192,704,448,960,32,544,288,800,160,672,416,928,96,608,352,864,224,736,480,992,16,528,272,784,144,656,400,912,80,592,336,848,208,720,464,976,48,560,304,816,176,688,432,944,112,624,368,880,240,752,496,1008,8,520,264,776,136,648,392,904,72,584,328,840,200,712,456,968,40,552,296,808,168,680,424,936,104,616,360,872,232,744,488,1000,24,536,280,792,152,664,408,920,88,600,344,856,216,728,472,984,56,568,312,824,184,696,440,952,120,632,376,888,248,760,504,1016,4,516,260,772,132,644,388,900,68,580,324,836,196,708,452,964,36,548,292,804,164,676,420,932,100,612,356,868,228,740,484,996,20,532,276,788,148,660,404,916,84,596,340,852,212,724,468,980,52,564,308,820,180,692,436,948,116,628,372,884,244,756,500,1012,12,524,268,780,140,652,396,908,76,588,332,844,204,716,460,972,44,556,300,812,172,684,428,940,108,620,364,876,236,748,492,1004,28,540,284,796,156,668,412,924,92,604,348,860,220,732,476,988,60,572,316,828,188,700,444,956,124,636,380,892,252,764,508,1020,2,514,258,770,130,642,386,898,66,578,322,834,194,706,450,962,34,546,290,802,162,674,418,930,98,610,354,866,226,738,482,994,18,530,274,786,146,658,402,914,82,594,338,850,210,722,466,978,50,562,306,818,178,690,434,946,114,626,370,882,242,754,498,1010,10,522,266,778,138,650,394,906,74,586,330,842,202,714,458,970,42,554,298,810,170,682,426,938,106,618,362,874,234,746,490,1002,26,538,282,794,154,666,410,922,90,602,346,858,218,730,474,986,58,570,314,826,186,698,442,954,122,634,378,890,250,762,506,1018,6,518,262,774,134,646,390,902,70,582,326,838,198,710,454,966,38,550,294,806,166,678,422,934,102,614,358,870,230,742,486,998,22,534,278,790,150,662,406,918,86,598,342,854,214,726,470,982,54,566,310,822,182,694,438,950,118,630,374,886,246,758,502,1014,14,526,270,782,142,654,398,910,78,590,334,846,206,718,462,974,46,558,302,814,174,686,430,942,110,622,366,878,238,750,494,1006,30,542,286,798,158,670,414,926,94,606,350,862,222,734,478,990,62,574,318,830,190,702,446,958,126,638,382,894,254,766,510,1022,1,513,257,769,129,641,385,897,65,577,321,833,193,705,449,961,33,545,289,801,161,673,417,929,97,609,353,865,225,737,481,993,17,529,273,785,145,657,401,913,81,593,337,849,209,721,465,977,49,561,305,817,177,689,433,945,113,625,369,881,241,753,497,1009,9,521,265,777,137,649,393,905,73,585,329,841,201,713,457,969,41,553,297,809,169,681,425,937,105,617,361,873,233,745,489,1001,25,537,281,793,153,665,409,921,89,601,345,857,217,729,473,985,57,569,313,825,185,697,441,953,121,633,377,889,249,761,505,1017,5,517,261,773,133,645,389,901,69,581,325,837,197,709,453,965,37,549,293,805,165,677,421,933,101,613,357,869,229,741,485,997,21,533,277,789,149,661,405,917,85,597,341,853,213,725,469,981,53,565,309,821,181,693,437,949,117,629,373,885,245,757,501,1013,13,525,269,781,141,653,397,909,77,589,333,845,205,717,461,973,45,557,301,813,173,685,429,941,109,621,365,877,237,749,493,1005,29,541,285,797,157,669,413,925,93,605,349,861,221,733,477,989,61,573,317,829,189,701,445,957,125,637,381,893,253,765,509,1021,3,515,259,771,131,643,387,899,67,579,323,835,195,707,451,963,35,547,291,803,163,675,419,931,99,611,355,867,227,739,483,995,19,531,275,787,147,659,403,915,83,595,339,851,211,723,467,979,51,563,307,819,179,691,435,947,115,627,371,883,243,755,499,1011,11,523,267,779,139,651,395,907,75,587,331,843,203,715,459,971,43,555,299,811,171,683,427,939,107,619,363,875,235,747,491,1003,27,539,283,795,155,667,411,923,91,603,347,859,219,731,475,987,59,571,315,827,187,699,443,955,123,635,379,891,251,763,507,1019,7,519,263,775,135,647,391,903,71,583,327,839,199,711,455,967,39,551,295,807,167,679,423,935,103,615,359,871,231,743,487,999,23,535,279,791,151,663,407,919,87,599,343,855,215,727,471,983,55,567,311,823,183,695,439,951,119,631,375,887,247,759,503,1015,15,527,271,783,143,655,399,911,79,591,335,847,207,719,463,975,47,559,303,815,175,687,431,943,111,623,367,879,239,751,495,1007,31,543,287,799,159,671,415,927,95,607,351,863,223,735,479,991,63,575,319,831,191,703,447,959,127,639,383,895,255,767,511,1023]。

序列2d为：

Shorten_Q_half＝[1,513,257,769,129,641,385,897,65,577,321,833,193,705,449,961,33,545,289,801,161,673,417,929,97,609,353,865,225,737,481,993,17,529,273,785,145,657,401,913,81,593,337,849,209,721,465,977,49,561,305,817,177,689,433,945,113,625,369,881,241,753,497,1009,9,521,265,777,137,649,393,905,73,585,329,841,201,713,457,969,41,553,297,809,169,681,425,937,105,617,361,873,233,745,489,1001,25,537,281,793,153,665,409,921,89,601,345,857,217,729,473,985,57,569,313,825,185,697,441,953,121,633,377,889,249,761,505,1017,5,517,261,773,133,645,389,901,69,581,325,837,197,709,453,965,37,549,293,805,165,677,421,933,101,613,357,869,229,741,485,997,21,533,277,789,149,661,405,917,85,597,341,853,213,725,469,981,53,565,309,821,181,693,437,949,117,629,373,885,245,757,501,1013,13,525,269,781,141,653,397,909,77,589,333,845,205,717,461,973,45,557,301,813,173,685,429,941,109,621,365,877,237,749,493,1005,29,541,285,797,157,669,413,925,93,605,349,861,221,733,477,989,61,573,317,829,189,701,445,957,125,637,381,893,253,765,509,1021,3,515,259,771,131,643,387,899,67,579,323,835,195,707,451,963,35,547,291,803,163,675,419,931,99,611,355,867,227,739,483,995,19,531,275,787,147,659,403,915,83,595,339,851,211,723,467,979,51,563,307,819,179,691,435,947,115,627,371,883,243,755,499,1011,11,523,267,779,139,651,395,907,75,587,331,843,203,715,459,971,43,555,299,811,171,683,427,939,107,619,363,875,235,747,491,1003,27,539,283,795,155,667,411,923,91,603,347,859,219,731,475,987,59,571,315,827,187,699,443,955,123,635,379,891,251,763,507,1019,7,519,263,775,135,647,391,903,71,583,327,839,199,711,455,967,39,551,295,807,167,679,423,935,103,615,359,871,231,743,487,999,23,535,279,791,151,663,407,919,87,599,343,855,215,727,471,983,55,567,311,823,183,695,439,951,119,631,375,887,247,759,503,1015,15,527,271,783,143,655,399,911,79,591,335,847,207,719,463,975,47,559,303,815,175,687,431,943,111,623,367,879,239,751,495,1007,31,543,287,799,159,671,415,927,95,607,351,863,223,735,479,991,63,575,319,831,191,703,447,959,127,639,383,895,255,767,511,1023]。

序列3d为；

Shorten_Z＝[0,4096,2048,6144,1024,5120,3072,7168,512,4608,2560,6656,1536,5632,3584,7680,256,4352,2304,6400,1280,5376,3328,7424,768,4864,2816,6912,1792,5888,3840,7936,128,4224,2176,6272,1152,5248,3200,7296,640,4736,2688,6784,1664,5760,3712,7808,384,4480,2432,6528,1408,5504,3456,7552,896,4992,2944,7040,1920,6016,3968,8064,64,4160,2112,6208,1088,5184,3136,7232,576,4672,2624,6720,1600,5696,3648,7744,320,4416,2368,6464,1344,5440,3392,7488,832,4928,2880,6976,1856,5952,3904,8000,192,4288,2240,6336,1216,5312,3264,7360,704,4800,2752,6848,1728,5824,3776,7872,448,4544,2496,6592,1472,5568,3520,7616,960,5056,3008,7104,1984,6080,4032,8128,32,4128,2080,6176,1056,5152,3104,7200,544,4640,2592,6688,1568,5664,3616,7712,288,4384,2336,6432,1312,5408,3360,7456,800,4896,2848,6944,1824,5920,3872,7968,160,4256,2208,6304,1184,5280,3232,7328,672,4768,2720,6816,1696,5792,3744,7840,416,4512,2464,6560,1440,5536,3488,7584,928,5024,2976,7072,1952,6048,4000,8096,96,4192,2144,6240,1120,5216,3168,7264,608,4704,2656,6752,1632,5728,3680,7776,352,4448,2400,6496,1376,5472,3424,7520,864,4960,2912,7008,1888,5984,3936,8032,224,4320,2272,6368,1248,5344,3296,7392,736,4832,2784,6880,1760,5856,3808,7904,480,4576,2528,6624,1504,5600,3552,7648,992,5088,3040,7136,2016,6112,4064,8160,16,4112,2064,6160,1040,5136,3088,7184,528,4624,2576,6672,1552,5648,3600,7696,272,4368,2320,6416,1296,5392,3344,7440,784,4880,2832,6928,1808,5904,3856,7952,144,4240,2192,6288,1168,5264,3216,7312,656,4752,2704,6800,1680,5776,3728,7824,400,4496,2448,6544,1424,5520,3472,7568,912,5008,2960,7056,1936,6032,3984,8080,80,4176,2128,6224,1104,5200,3152,7248,592,4688,2640,6736,1616,5712,3664,7760,336,4432,2384,6480,1360,5456,3408,7504,848,4944,2896,6992,1872,5968,3920,8016,208,4304,2256,6352,1232,5328,3280,7376,720,4816,2768,6864,1744,5840,3792,7888,464,4560,2512,6608,1488,5584,3536,7632,976,5072,3024,7120,2000,6096,4048,8144,48,4144,2096,6192,1072,5168,3120,7216,560,4656,2608,6704,1584,5680,3632,7728,304,4400,2352,6448,1328,5424,3376,7472,816,4912,2864,6960,1840,5936,3888,7984,176,4272,2224,6320,1200,5296,3248,7344,688,4784,2736,6832,1712,5808,3760,7856,432,4528,2480,6576,1456,5552,3504,7600,944,5040,2992,7088,1968,6064,4016,8112,112,4208,2160,6256,1136,5232,3184,7280,624,4720,2672,6768,1648,5744,3696,7792,368,4464,2416,6512,1392,5488,3440,7536,880,4976,2928,7024,1904,6000,3952,8048,240,4336,2288,6384,1264,5360,3312,7408,752,4848,2800,6896,1776,5872,3824,7920,496,4592,2544,6640,1520,5616,3568,7664,1008,5104,3056,7152,2032,6128,4080,8176,8,4104,2056,6152,1032,5128,3080,7176,520,4616,2568,6664,1544,5640,3592,7688,264,4360,2312,6408,1288,5384,3336,7432,776,4872,2824,6920,1800,5896,3848,7944,136,4232,2184,6280,1160,5256,3208,7304,648,4744,2696,6792,1672,5768,3720,7816,392,4488,2440,6536,1416,5512,3464,7560,904,5000,2952,7048,1928,6024,3976,8072,72,4168,2120,6216,1096,5192,3144,7240,584,4680,2632,6728,1608,5704,3656,7752,328,4424,2376,6472,1352,5448,3400,7496,840,4936,2888,6984,1864,5960,3912,8008,200,4296,2248,6344,1224,5320,3272,7368,712,4808,2760,6856,1736,5832,3784,7880,456,4552,2504,6600,1480,5576,3528,7624,968,5064,3016,7112,1992,6088,4040,8136,40,4136,2088,6184,1064,5160,3112,7208,552,4648,2600,6696,1576,5672,3624,7720,296,4392,2344,6440,1320,5416,3368,7464,808,4904,2856,6952,1832,5928,3880,7976,168,4264,2216,6312,1192,5288,3240,7336,680,4776,2728,6824,1704,5800,3752,7848,424,4520,2472,6568,1448,5544,3496,7592,936,5032,2984,7080,1960,6056,4008,8104,104,4200,2152,6248,1128,5224,3176,7272,616,4712,2664,6760,1640,5736,3688,7784,360,4456,2408,6504,1384,5480,3432,7528,872,4968,2920,7016,1896,5992,3944,8040,232,4328,2280,6376,1256,5352,3304,7400,744,4840,2792,6888,1768,5864,3816,7912,488,4584,2536,6632,1512,5608,3560,7656,1000,5096,3048,7144,2024,6120,4072,8168,24,4120,2072,6168,1048,5144,3096,7192,536,4632,2584,6680,1560,5656,3608,7704,280,4376,2328,6424,1304,5400,3352,7448,792,4888,2840,6936,1816,5912,3864,7960,152,4248,2200,6296,1176,5272,3224,7320,664,4760,2712,6808,1688,5784,3736,7832,408,4504,2456,6552,1432,5528,3480,7576,920,5016,2968,7064,1944,6040,3992,8088,88,4184,2136,6232,1112,5208,3160,7256,600,4696,2648,6744,1624,5720,3672,7768,344,4440,2392,6488,1368,5464,3416,7512,856,4952,2904,7000,1880,5976,3928,8024,216,4312,2264,6360,1240,5336,3288,7384,728,4824,2776,6872,1752,5848,3800,7896,472,4568,2520,6616,1496,5592,3544,7640,984,5080,3032,7128,2008,6104,4056,8152,56,4152,2104,6200,1080,5176,3128,7224,568,4664,2616,6712,1592,5688,3640,7736,312,4408,2360,6456,1336,5432,3384,7480,824,4920,2872,6968,1848,5944,3896,7992,184,4280,2232,6328,1208,5304,3256,7352,696,4792,2744,6840,1720,5816,3768,7864,440,4536,2488,6584,1464,5560,3512,7608,952,5048,3000,7096,1976,6072,4024,8120,120,4216,2168,6264,1144,5240,3192,7288,632,4728,2680,6776,1656,5752,3704,7800,376,4472,2424,6520,1400,5496,3448,7544,888,4984,2936,7032,1912,6008,3960,8056,248,4344,2296,6392,1272,5368,3320,7416,760,4856,2808,6904,1784,5880,3832,7928,504,4600,2552,6648,1528,5624,3576,7672,1016,5112,3064,7160,2040,6136,4088,8184]。

当N＝512，

序列1e为：

Shorten_Q＝[0,256,128,384,64,320,192,448,32,288,160,416,96,352,224,480,16,272,144,400,80,336,208,464,48,304,176,432,112,368,240,496,8,264,136,392,72,328,200,456,40,296,168,424,104,360,232,488,24,280,152,408,88,344,216,472,56,312,184,440,120,376,248,504,4,260,132,388,68,324,196,452,36,292,164,420,100,356,228,484,20,276,148,404,84,340,212,468,52,308,180,436,116,372,244,500,12,268,140,396,76,332,204,460,44,300,172,428,108,364,236,492,28,284,156,412,92,348,220,476,60,316,188,444,124,380,252,508,2,258,130,386,66,322,194,450,34,290,162,418,98,354,226,482,18,274,146,402,82,338,210,466,50,306,178,434,114,370,242,498,10,266,138,394,74,330,202,458,42,298,170,426,106,362,234,490,26,282,154,410,90,346,218,474,58,314,186,442,122,378,250,506,6,262,134,390,70,326,198,454,38,294,166,422,102,358,230,486,22,278,150,406,86,342,214,470,54,310,182,438,118,374,246,502,14,270,142,398,78,334,206,462,46,302,174,430,110,366,238,494,30,286,158,414,94,350,222,478,62,318,190,446,126,382,254,510,1,257,129,385,65,321,193,449,33,289,161,417,97,353,225,481,17,273,145,401,81,337,209,465,49,305,177,433,113,369,241,497,9,265,137,393,73,329,201,457,41,297,169,425,105,361,233,489,25,281,153,409,89,345,217,473,57,313,185,441,121,377,249,505,5,261,133,389,69,325,197,453,37,293,165,421,101,357,229,485,21,277,149,405,85,341,213,469,53,309,181,437,117,373,245,501,13,269,141,397,77,333,205,461,45,301,173,429,109,365,237,493,29,285,157,413,93,349,221,477,61,317,189,445,125,381,253,509,3,259,131,387,67,323,195,451,35,291,163,419,99,355,227,483,19,275,147,403,83,339,211,467,51,307,179,435,115,371,243,499,11,267,139,395,75,331,203,459,43,299,171,427,107,363,235,491,27,283,155,411,91,347,219,475,59,315,187,443,123,379,251,507,7,263,135,391,71,327,199,455,39,295,167,423,103,359,231,487,23,279,151,407,87,343,215,471,55,311,183,439,119,375,247,503,15,271,143,399,79,335,207,463,47,303,175,431,111,367,239,495,31,287,159,415,95,351,223,479,63,319,191,447,127,383,255,511]。

序列2e为：

Shorten_Q_half＝[1,257,129,385,65,321,193,449,33,289,161,417,97,353,225,481,17,273,145,401,81,337,209,465,49,305,177,433,113,369,241,497,9,265,137,393,73,329,201,457,41,297,169,425,105,361,233,489,25,281,153,409,89,345,217,473,57,313,185,441,121,377,249,505,5,261,133,389,69,325,197,453,37,293,165,421,101,357,229,485,21,277,149,405,85,341,213,469,53,309,181,437,117,373,245,501,13,269,141,397,77,333,205,461,45,301,173,429,109,365,237,493,29,285,157,413,93,349,221,477,61,317,189,445,125,381,253,509,3,259,131,387,67,323,195,451,35,291,163,419,99,355,227,483,19,275,147,403,83,339,211,467,51,307,179,435,115,371,243,499,11,267,139,395,75,331,203,459,43,299,171,427,107,363,235,491,27,283,155,411,91,347,219,475,59,315,187,443,123,379,251,507,7,263,135,391,71,327,199,455,39,295,167,423,103,359,231,487,23,279,151,407,87,343,215,471,55,311,183,439,119,375,247,503,15,271,143,399,79,335,207,463,47,303,175,431,111,367,239,495,31,287,159,415,95,351,223,479,63,319,191,447,127,383,255,511]。

序列3e为：

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Claims (25)

1.一种极化码编码的速率匹配方法，其特征在于，包括：

获取K个待编码比特、目标码长M、母码长度N，N＝2ⁿ，M、K、n和N为正整数；

根据所述母码长度N对所述K个待编码比特进行极化编码，得到编码后的比特序列；

根据速率匹配序列对所述编码后的比特序列进行速率匹配，获取速率匹配后的序列；

输出所述速率匹配后的序列。

2.一种极化码解码的解速率匹配方法，其特征在于，包括：

获取包括M个比特的待解码信息序列，其中包括K个待解码比特；

确定母码长度N，母码长度N，N＝2ⁿ，M、K、n和N为正整数；

根据所述母码长度N和速率匹配序列对所述待解码信息序列进行解速率匹配和解码，获取解码结果；

输出所述解码结果。

3.如权利要求1或2所述的方法，其特征在于，

所述速率匹配序列为第一序列的子序列，所述第一序列为附录一中的序列1或序列2或序列3，其中所述序列1包括N₂个极化子信道号，所述序列2包括N₂/2个极化子信道号，所述序列3中包括N₂个大小不同的值，所述极化子信道号由0开始，N₂大于或等于N。

4.如权利要求1～3中任意一项所述的方法，其特征在于，

当N＝8192，所述速率匹配序列为说明书中的序列1a或序列2a或序列3a；或者

当N＝4096，所述速率匹配序列为说明书中的序列1b或2b或3b；或者

当N＝2048，所述速率匹配序列为说明书中的序列1c或2c或3c；或者

当N＝1024，所述速率匹配序列为说明书中的序列1d或2d或3d；或者

当N＝512，所述速率匹配序列为说明书中的序列1e或2e或3e；

其中所述序列1a、所述序列1b、所述序列1c、所述序列1d、所述序列1e为所述序列1的子序列；

所述序列2a、所述序列2b、所述序列2c、所述序列2d、所述序列2e为所述序列2的子序列；

所述序列3a、所述序列3b、所述序列3c、所述序列3d、所述序列3e为所述序列3的子序列。

5.如权利要求3或4所述的方法，其特征在于，所述速率匹配的方式为打孔操作，

若所述第一序列为所述序列1，所述打孔操作为：根据所述目标码长M取所述速率匹配序列中后M个极化子信道号对应子信道承载的比特或根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列2，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列3，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中最小的N-M个值所在的极化子信道承载的比特或根据所述目标码长M取所述速率匹配序列中最大的M个值所在的极化子信道承载的比特。

6.如权利要求1～5中任意一项所述的方法，其特征在于，所述K个比特中，包括循环冗余校验比特。

7.如权利要求1～6中任意一项所述的方法，其特征在于，所述K个比特中，包括奇偶校验比特。

8.如权利要求1、3～7中任意一项所述的方法，其特征在于，所述根据所述母码长度N对所述K个待编码比特进行极化编码为：所述K个待编码比特映射到M-P个非打孔的极化子信道中可靠度较高的K个极化子信道，使得K个待编码比特所在的极化子信道的可靠度高于其余M-P-K个极化子信道的可靠度，P为预冻结的极化子信道的数目，P大于或等于0。

9.如权利要求1、3～8中任意一项所述的方法，其特征在于，所述根据速率匹配序列对所述编码后的比特序列进行速率匹配获取速率匹配后的序列之前，对所述编码后的比特序列进行交织。

10.一种极化Polar码速率匹配装置，其特征在于，包括：

获取单元，K个待编码比特、目标码长M，所述K为正整数；

编码单元，用于确定母码长度N，根据所述母码长度N对所述K个待编码比特进行极化编码，得到编码后的比特序列，N＝2ⁿ，n为正整数，K≤N；以及

速率匹配单元，用于根据速率匹配序列对所述编码后的比特序列进行速率匹配，获取长度为M的速率匹配后的比特序列。

11.一种Polar码解速率匹配装置，其特征在于，包括：

获取单元1001，用于获取待解码信息序列；

处理单元1002，用于确定母码长度N，根据母码长度N和速率匹配序列对所述待解码信息序列序列进行解速率匹配的操作和解码解调操作，从而得到并输出解码结果。

12.如权利要求10或11所述的装置，其特征在于，所述速率匹配序列为第一序列的子序列，所述第一序列为附录一中的序列1或序列2或序列3，其中所述序列1包括N₂个极化子信道号，所述序列2包括N₂/2个极化子信道号，所述序列3中包括N₂个大小不同的值，所述极化子信道号由0开始，N₂大于或等于N。

13.如权利要求10～12中任意一项所述的装置，其特征在于，

当N＝8192，所述速率匹配序列为说明书中的序列1a或序列2a或序列3a；或者

当N＝4096，所述速率匹配序列为说明书中的序列1b或2b或3b；或者

当N＝2048，所述速率匹配序列为说明书中的序列1c或2c或3c；或者

当N＝1024，所述速率匹配序列为说明书中的序列1d或2d或3d；或者

当N＝512，所述速率匹配序列为说明书中的序列1e或2e或3e；

其中所述序列1a、所述序列1b、所述序列1c、所述序列1d、所述序列1e为所述序列1的子序列；

所述序列2a、所述序列2b、所述序列2c、所述序列2d、所述序列2e为所述序列2的子序列；

所述序列3a、所述序列3b、所述序列3c、所述序列3d、所述序列3e为所述序列3的子序列。

14.如权利要求12或13所述的装置，其特征在于，所述速率匹配的方式为打孔操作，

若所述第一序列为所述序列1，所述打孔操作为：根据所述目标码长M取所述速率匹配序列中后M个极化子信道号对应子信道承载的比特或根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列2，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中前N-M个极化子信道号对应的子信道承载的比特；或者

若所述第一序列为所述序列3，所述打孔操作为：根据所述目标码长M删除所述速率匹配序列中取值最小的N-M个值所在的极化子信道承载的比特或根据所述目标码长M取所述速率匹配序列中取值最大的M个值所在的极化子信道承载的比特。

15.如权利要求10～14中任意一项所述的装置，其特征在于，所述K个比特中包括循环冗余校验比特。

16.如权利要求10～15中任意一项所述的装置，其特征在于，所述K个比特中包括奇偶校验比特。

17.如权利要求10、12～16中任意一项所述的装置，其特征在于，所述根据所述母码长度N对所述K个待编码比特进行极化编码为：所述K个待编码比特映射到M-P个非打孔的极化子信道中可靠度较高的K个极化子信道，使得K个待编码比特所在的极化子信道的可靠度高于其余M-P-K个极化子信道的可靠度，P为预冻结的极化子信道的数目，P大于或等于0。

18.如权利要求10、12～17中任意一项所述的装置，其特征在于，所述根据速率匹配序列对所述编码后的比特序列进行速率匹配获取长度为M的速率匹配后的比特序列之前，对所述编码后的比特序列进行交织。

19.一种极化Polar码速率匹配装置，其特征在于，包括：处理器，用于执行如权利要求1、3～8任一项所述的方法。

20.如权利要求19所述的装置，其特征在于，还包括：存储器，用于存储由所述处理器执行如权利要求1、3～8中任一项所述的方法时所用的程序指令。

21.一种Polar码速率匹配装置，其特征在于，包括：

输入接口电路，用于获取K个待编码比特；

逻辑电路，用于基于所述K个待编码比特按照如权利要求1、3～8中任意一项所述的方法得到速率匹配后的序列；

输出接口电路，用于输出所述速率匹配后的序列。

22.一种极化Polar码解速率匹配装置，其特征在于，包括：处理器，用于执行如权利要求2～7任一项所述的方法。

23.如权利要求19所述的装置，其特征在于，还包括：存储器，用于存储由所述处理器执行如权利要求2～7中任一项所述的方法时所用的程序指令。

24.一种Polar码解速率匹配装置，其特征在于，包括：

输入接口电路，用于获取待解码信息序列；

逻辑电路，用于按照如权利要求2～7中任意一项所述的方法对所述待解码信息序列序列进行解速率匹配的操作和解码解调操作，从而得到解码结果；

输出接口电路，用于输出所述解码结果。

25.一种计算机可读介质，其特征在于，存储有计算机程序指令，当所述计算机程序指令由计算机执行时，使得如权利要求1-9中任意一项所述的方法被执行。

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