function [ quasi, seed ] = i4_sobol ( dim_num, seed ) %% SOBOL generates a new quasirandom Sobol vector with each call. % % Discussion: % % The routine adapts the ideas of Antonov and Saleev. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 25 June 2008 % % Author: % % FORTRAN77 original version by Bennett Fox. % MATLAB version by John Burkardt % % Reference: % % IA Antonov, VM Saleev, % USSR Computational Mathematics and Mathematical Physics, % Volume 19, 1980, pages 252 - 256. % % Paul Bratley and Bennett Fox, % Algorithm 659: % Implementing Sobol's Quasirandom Sequence Generator, % ACM Transactions on Mathematical Software, % Volume 14, Number 1, pages 88-100, 1988. % % Bennett Fox, % Algorithm 647: % Implementation and Relative Efficiency of Quasirandom % Sequence Generators, % ACM Transactions on Mathematical Software, % Volume 12, Number 4, pages 362-376, 1986. % % Stephen Joe, Frances Kuo % Remark on Algorithm 659: % Implementing Sobol's Quasirandom Sequence Generator, % ACM Transactions on Mathematical Software, % Volume 29, Number 1, pages 49-57, March 2003. % % Ilya Sobol, % USSR Computational Mathematics and Mathematical Physics, % Volume 16, pages 236-242, 1977. % % Ilya Sobol, YL Levitan, % The Production of Points Uniformly Distributed in a Multidimensional % Cube (in Russian), % Preprint IPM Akad. Nauk SSSR, % Number 40, Moscow 1976. % % Parameters: % % Input, integer DIM_NUM, the number of spatial dimensions. % DIM_NUM must satisfy 2 <= DIM_NUM <= 1111. % % Input/output, integer SEED, the "seed" for the sequence. % This is essentially the index in the sequence of the quasirandom % value to be generated. On output, SEED has been set to the % appropriate next value, usually simply SEED+1. % If SEED is less than 0 on input, it is treated as though it were 0. % An input value of 0 requests the first (0-th) element of the sequence. % % Output, real QUASI(DIM_NUM), the next quasirandom vector. % persistent dim_num_save; persistent initialized; persistent lastq; persistent maxcol; persistent poly; persistent recipd; persistent seed_save; persistent v; dim_max = 1111; log_max = 30; if ( isempty ( initialized ) ) initialized = 1; dim_num_save = 0; seed_save = - 1; v = zeros(dim_max,log_max); % % Initialize (part of) V. % v(2:1111,1) = 1; v(3:401,2) = [ ... 1,3,1,3,1,3,3,1,3,1,3,1,3,1,1,3,1,3,1,3, ... 1,3,3,1,1,1,3,1,3,1,3,3,1,3,1,1,1,3,1,3,1,1,1,3,3,1,3,3,1,1, ... 3,3,1,3,3,3,1,3,1,3,1,1,3,3,1,1,1,1,3,1,1,3,1,1,1,3,3,1,3,3, ... 1,3,3,3,1,3,3,3,1,3,3,1,3,3,3,1,3,1,3,1,1,3,3,1,3,3,1,1,1,3, ... 3,1,3,3,1,3,1,1,3,3,3,1,1,1,3,1,1,3,1,1,3,3,1,3,1,3,3,3,3,1, ... 1,1,3,3,1,1,3,1,1,1,1,1,1,3,1,3,1,1,1,3,1,3,1,3,3,3,1,1,3,3, ... 1,3,1,3,1,1,3,1,3,1,3,1,3,1,1,1,3,3,1,3,3,1,3,1,1,1,3,1,3,1, ... 1,3,1,1,3,3,1,1,3,3,3,1,3,3,3,1,3,1,3,1,1,1,3,1,1,1,3,1,1,1, ... 1,1,3,3,3,1,1,1,1,3,3,3,1,3,3,1,1,1,1,3,1,1,3,1,3,3,1,1,3,3, ... 1,1,1,1,3,1,3,3,1,3,3,1,1,1,3,3,3,1,3,3,1,3,3,1,3,1,3,3,3,1, ... 3,1,1,3,1,3,1,1,1,3,3,3,1,1,3,1,3,1,1,1,1,1,1,3,1,1,3,1,3,3, ... 1,1,1,1,3,1,3,1,3,1,1,1,1,3,3,1,1,1,1,1,3,3,3,1,1,3,3,3,3,3, ... 1,3,3,1,3,3,3,3,1,1,1,1,1,1,3,1,1,3,1,1,1,3,1,1,1,3,3,3,1,3, ... 1,1,3,3,3,1,3,3,1,3,1,3,3,1,3,3,3,1,1]'; v(402:800,2) = [ ... 3,3,1,3,1,3,1,1,1,3,3,3,3,1,3,1,1,3,1, ... 3,1,1,1,3,1,3,1,3,1,3,3,3,3,3,3,3,3,1,3,3,3,3,3,1,3,1,3,3,3, ... 1,3,1,3,1,3,3,1,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,3,3,1,1,3,3,1, ... 1,1,3,3,1,1,3,3,3,3,1,1,3,1,3,3,1,3,3,1,1,1,3,3,3,1,1,3,3,3, ... 3,3,1,1,1,3,1,3,3,1,3,3,3,3,1,1,3,1,1,3,1,3,1,3,1,3,3,1,1,3, ... 3,1,3,3,1,3,3,1,1,3,1,3,3,1,1,3,1,3,1,3,1,1,3,3,1,1,1,3,3,1, ... 3,1,1,3,3,1,1,3,1,3,1,1,1,1,1,3,1,1,1,1,3,1,3,1,1,3,3,1,1,3, ... 1,3,1,3,3,3,1,3,3,3,1,1,3,3,3,1,1,1,1,3,1,3,1,3,1,1,3,3,1,1, ... 1,3,3,1,3,1,3,1,1,1,1,1,1,3,1,3,3,1,3,3,3,1,3,1,1,3,3,1,1,3, ... 3,1,1,1,3,1,3,3,1,1,3,1,1,3,1,3,1,1,1,3,3,3,3,1,1,3,3,1,1,1, ... 1,3,1,1,3,3,3,1,1,3,3,1,3,3,1,1,3,3,3,3,3,3,3,1,3,3,1,3,1,3, ... 1,1,3,3,1,1,1,3,1,3,3,1,3,3,1,3,1,1,3,3,3,1,1,1,3,1,1,1,3,3, ... 3,1,3,3,1,3,1,1,3,3,3,1,3,3,1,1,1,3,1,3,3,3,3,3,3,3,3,1,3,3, ... 1,3,1,1,3,3,3,1,3,3,3,3,3,1,3,3,3,1,1,1]'; v(801:1111,2) = [ ... 3,3,1,3,3,1,3,1,3,1,3,1,3,3,3,3,3,3, ... 1,1,3,1,3,1,1,1,1,1,3,1,1,1,3,1,3,1,1,3,3,3,1,3,1,3,1,1,3,1, ... 3,3,1,3,1,3,3,1,3,3,1,3,3,3,3,3,3,1,3,1,1,3,3,3,1,1,3,3,3,3, ... 3,3,3,1,3,3,3,3,1,3,1,3,3,3,1,3,1,3,1,1,1,3,3,1,3,1,1,3,3,1, ... 3,1,1,1,1,3,1,3,1,1,3,1,3,1,3,3,3,3,3,3,1,3,3,3,3,1,3,3,1,3, ... 3,3,3,3,1,1,1,1,3,3,3,1,3,3,1,1,3,3,1,1,3,3,1,3,1,1,3,1,3,3, ... 3,3,3,1,3,1,1,3,3,3,3,1,3,1,1,3,3,3,3,3,3,1,1,3,1,3,1,1,3,1, ... 1,1,1,3,3,1,1,3,1,1,1,3,1,3,1,1,3,3,1,3,1,1,3,3,3,3,3,1,3,1, ... 1,1,3,1,1,1,3,1,1,3,1,3,3,3,3,3,1,1,1,3,3,3,3,1,3,3,3,3,1,1, ... 3,3,3,1,3,1,1,3,3,1,3,3,1,1,1,1,1,3,1,1,3,3,1,1,1,3,1,1,3,3, ... 1,3,3,3,3,3,3,3,3,1,1,3,3,1,1,3,1,3,3,3,3,3,1]'; v(4:402,3) = [ ... 7,5,1,3,3,7,5,5,7,7,1,3,3,7,5,1,1,5,3,7, ... 1,7,5,1,3,7,7,1,1,1,5,7,7,5,1,3,3,7,5,5,5,3,3,3,1,1,5,1,1,5, ... 3,3,3,3,1,3,7,5,7,3,7,1,3,3,5,1,3,5,5,7,7,7,1,1,3,3,1,1,5,1, ... 5,7,5,1,7,5,3,3,1,5,7,1,7,5,1,7,3,1,7,1,7,3,3,5,7,3,3,5,1,3, ... 3,1,3,5,1,3,3,3,7,1,1,7,3,1,3,7,5,5,7,5,5,3,1,3,3,3,1,3,3,7, ... 3,3,1,7,5,1,7,7,5,7,5,1,3,1,7,3,7,3,5,7,3,1,3,3,3,1,5,7,3,3, ... 7,7,7,5,3,1,7,1,3,7,5,3,3,3,7,1,1,3,1,5,7,1,3,5,3,5,3,3,7,5, ... 5,3,3,1,3,7,7,7,1,5,7,1,3,1,1,7,1,3,1,7,1,5,3,5,3,1,1,5,5,3, ... 3,5,7,1,5,3,7,7,3,5,3,3,1,7,3,1,3,5,7,1,3,7,1,5,1,3,1,5,3,1, ... 7,1,5,5,5,3,7,1,1,7,3,1,1,7,5,7,5,7,7,3,7,1,3,7,7,3,5,1,1,7, ... 1,5,5,5,1,5,1,7,5,5,7,1,1,7,1,7,7,1,1,3,3,3,7,7,5,3,7,3,1,3, ... 7,5,3,3,5,7,1,1,5,5,7,7,1,1,1,1,5,5,5,7,5,7,1,1,3,5,1,3,3,7, ... 3,7,5,3,5,3,1,7,1,7,7,1,1,7,7,7,5,5,1,1,7,5,5,7,5,1,1,5,5,5, ... 5,5,5,1,3,1,5,7,3,3,5,7,3,7,1,7,7,1,3]'; v(403:801,3) = [ ... 5,1,5,5,3,7,3,7,7,5,7,5,7,1,1,5,3,5,1, ... 5,3,7,1,5,7,7,3,5,1,3,5,1,5,3,3,3,7,3,5,1,3,7,7,3,7,5,3,3,1, ... 7,5,1,1,3,7,1,7,1,7,3,7,3,5,7,3,5,3,1,1,1,5,7,7,3,3,1,1,1,5, ... 5,7,3,1,1,3,3,7,3,3,5,1,3,7,3,3,7,3,5,7,5,7,7,3,3,5,1,3,5,3, ... 1,3,5,1,1,3,7,7,1,5,1,3,7,3,7,3,5,1,7,1,1,3,5,3,7,1,5,5,1,1, ... 3,1,3,3,7,1,7,3,1,7,3,1,7,3,5,3,5,7,3,3,3,5,1,7,7,1,3,1,3,7, ... 7,1,3,7,3,1,5,3,1,1,1,5,3,3,7,1,5,3,5,1,3,1,3,1,5,7,7,1,1,5, ... 3,1,5,1,1,7,7,3,5,5,1,7,1,5,1,1,3,1,5,7,5,7,7,1,5,1,1,3,5,1, ... 5,5,3,1,3,1,5,5,3,3,3,3,1,1,3,1,3,5,5,7,5,5,7,5,7,1,3,7,7,3, ... 5,5,7,5,5,3,3,3,1,7,1,5,5,5,3,3,5,1,3,1,3,3,3,7,1,7,7,3,7,1, ... 1,5,7,1,7,1,7,7,1,3,7,5,1,3,5,5,5,1,1,7,1,7,1,7,7,3,1,1,5,1, ... 5,1,5,3,5,5,5,5,5,3,3,7,3,3,5,5,3,7,1,5,7,5,1,5,5,3,5,5,7,5, ... 3,5,5,5,1,5,5,5,5,1,3,5,3,1,7,5,5,7,1,5,3,3,1,5,3,7,1,7,5,1, ... 1,3,1,1,7,1,5,5,3,7,3,7,5,3,1,1,3,1,3,5]'; v(802:1111,3) = [ ... 5,7,5,3,7,7,7,3,7,3,7,1,3,1,7,7,1,7, ... 3,7,3,7,3,7,3,5,1,1,7,3,1,5,5,7,1,5,5,5,7,1,5,5,1,5,5,3,1,3, ... 1,7,3,1,3,5,7,7,7,1,1,7,3,1,5,5,5,1,1,1,1,1,5,3,5,1,3,5,3,1, ... 1,1,1,3,7,3,7,5,7,1,5,5,7,5,3,3,7,5,3,1,1,3,1,3,1,1,3,7,1,7, ... 1,1,5,1,7,5,3,7,3,5,3,1,1,5,5,1,7,7,3,7,3,7,1,5,1,5,3,7,3,5, ... 7,7,7,3,3,1,1,5,5,3,7,1,1,1,3,5,3,1,1,3,3,7,5,1,1,3,7,1,5,7, ... 3,7,5,5,7,3,5,3,1,5,3,1,1,7,5,1,7,3,7,5,1,7,1,7,7,1,1,7,1,5, ... 5,1,1,7,5,7,1,5,3,5,3,3,7,1,5,1,1,5,5,3,3,7,5,5,1,1,1,3,1,5, ... 7,7,1,7,5,7,3,7,3,1,3,7,3,1,5,5,3,5,1,3,5,5,5,1,1,7,7,1,5,5, ... 1,3,5,1,5,3,5,3,3,7,5,7,3,7,3,1,3,7,7,3,3,1,1,3,3,3,3,3,5,5, ... 3,3,3,1,3,5,7,7,1,5,7,3,7,1,1,3,5,7,5,3,3,3]'; v(6:357,4) = [ ... 1,7,9,13,11,1,3,7,9,5,13,13,11,3,15,5,3, ... 15,7,9,13,9,1,11,7,5,15,1,15,11,5,11,1,7,9,7,7,1,15,15,15,13, ... 3,3,15,5,9,7,13,3,7,5,11,9,1,9,1,5,7,13,9,9,1,7,3,5,1,11,11, ... 13,7,7,9,9,1,1,3,9,15,1,5,13,1,9,9,9,9,9,13,11,3,5,11,11,13, ... 5,3,15,1,11,11,7,13,15,11,13,9,11,15,15,13,3,15,7,9,11,13,11, ... 9,9,5,13,9,1,13,7,7,7,7,7,5,9,7,13,11,9,11,15,3,13,11,1,11,3, ... 3,9,11,1,7,1,15,15,3,1,9,1,7,13,11,3,13,11,7,3,3,5,13,11,5, ... 11,1,3,9,7,15,7,5,13,7,9,13,15,13,9,7,15,7,9,5,11,11,13,13,9, ... 3,5,13,9,11,15,11,7,1,7,13,3,13,3,13,9,15,7,13,13,3,13,15,15, ... 11,9,13,9,15,1,1,15,11,11,7,1,11,13,9,13,3,5,11,13,9,9,13,1, ... 11,15,13,3,13,7,15,1,15,3,3,11,7,13,7,7,9,7,5,15,9,5,5,7,15, ... 13,15,5,15,5,3,1,11,7,1,5,7,9,3,11,1,15,1,3,15,11,13,5,13,1, ... 7,1,15,7,5,1,1,15,13,11,11,13,5,11,7,9,7,1,5,3,9,5,5,11,5,1, ... 7,1,11,7,9,13,15,13,3,1,11,13,15,1,1,11,9,13,3,13,11,15,13,9, ... 9,9,5,5,5,5,1,15,5,9]'; v(358:710,4) = [ ... 11,7,15,5,3,13,5,3,11,5,1,11,13,9,11, ... 3,7,13,15,1,7,11,1,13,1,15,1,9,7,3,9,11,1,9,13,13,3,11,7,9,1, ... 7,15,9,1,5,13,5,11,3,9,15,11,13,5,1,7,7,5,13,7,7,9,5,11,11,1, ... 1,15,3,13,9,13,9,9,11,5,5,13,15,3,9,15,3,11,11,15,15,3,11,15, ... 15,3,1,3,1,3,3,1,3,13,1,11,5,15,7,15,9,1,7,1,9,11,15,1,13,9, ... 13,11,7,3,7,3,13,7,9,7,7,3,3,9,9,7,5,11,13,13,7,7,15,9,5,5,3, ... 3,13,3,9,3,1,11,1,3,11,15,11,11,11,9,13,7,9,15,9,11,1,3,3,9, ... 7,15,13,13,7,15,9,13,9,15,13,15,9,13,1,11,7,11,3,13,5,1,7,15, ... 3,13,7,13,13,11,3,5,3,13,11,9,9,3,11,11,7,9,13,11,7,15,13,7, ... 5,3,1,5,15,15,3,11,1,7,3,15,11,5,5,3,5,5,1,15,5,1,5,3,7,5,11, ... 3,13,9,13,15,5,3,5,9,5,3,11,1,13,9,15,3,5,11,9,1,3,15,9,9,9, ... 11,7,5,13,1,15,3,13,9,13,5,1,5,1,13,13,7,7,1,9,5,11,9,11,13, ... 3,15,15,13,15,7,5,7,9,7,9,9,9,11,9,3,11,15,13,13,5,9,15,1,1, ... 9,5,13,3,13,15,3,1,3,11,13,1,15,9,9,3,1,9,1,9,1,13,11,15,7, ... 11,15,13,15,1,9,9,7]'; v(711:1065,4) = [ ... 3,5,11,7,3,9,5,15,7,5,3,13,7,1,1,9, ... 15,15,15,11,3,5,15,13,7,15,15,11,11,9,5,15,9,7,3,13,1,1,5,1, ... 3,1,7,1,1,5,1,11,11,9,9,5,13,7,7,7,1,1,9,9,11,11,15,7,5,5,3, ... 11,1,3,7,13,7,7,7,3,15,15,11,9,3,9,3,15,13,5,3,3,3,5,9,15,9, ... 9,1,5,9,9,15,5,15,7,9,1,9,9,5,11,5,15,15,11,7,7,7,1,1,11,11, ... 13,15,3,13,5,1,7,1,11,3,13,15,3,5,3,5,7,3,9,9,5,1,7,11,9,3,5, ... 11,13,13,13,9,15,5,7,1,15,11,9,15,15,13,13,13,1,11,9,15,9,5, ... 15,5,7,3,11,3,15,7,13,11,7,3,7,13,5,13,15,5,13,9,1,15,11,5,5, ... 1,11,3,3,7,1,9,7,15,9,9,3,11,15,7,1,3,1,1,1,9,1,5,15,15,7,5, ... 5,7,9,7,15,13,13,11,1,9,11,1,13,1,7,15,15,5,5,1,11,3,9,11,9, ... 9,9,1,9,3,5,15,1,1,9,7,3,3,1,9,9,11,9,9,13,13,3,13,11,13,5,1, ... 5,5,9,9,3,13,13,9,15,9,11,7,11,9,13,9,1,15,9,7,7,1,7,9,9,15, ... 1,11,1,13,13,15,9,13,7,15,3,9,3,1,13,7,5,9,3,1,7,1,1,13,3,3, ... 11,1,7,13,15,15,5,7,13,13,15,11,13,1,13,13,3,9,15,15,11,15,9, ... 15,1,13,15,1,1,5]'; v(1066:1111,4) = [ ... 11,5,1,11,11,5,3,9,1,3,5,13,9,7,7,1, ... 9,9,15,7,5,5,15,13,9,7,13,3,13,11,13,7,9,13,13,13,15,9,5,5,3, ... 3,3,1,3,15]'; v(8:331,5) = [ ... 9,3,27,15,29,21,23,19,11,25,7,13,17,1, ... 25,29,3,31,11,5,23,27,19,21,5,1,17,13,7,15,9,31,25,3,5,23,7, ... 3,17,23,3,3,21,25,25,23,11,19,3,11,31,7,9,5,17,23,17,17,25, ... 13,11,31,27,19,17,23,7,5,11,19,19,7,13,21,21,7,9,11,1,5,21, ... 11,13,25,9,7,7,27,15,25,15,21,17,19,19,21,5,11,3,5,29,31,29, ... 5,5,1,31,27,11,13,1,3,7,11,7,3,23,13,31,17,1,27,11,25,1,23, ... 29,17,25,7,25,27,17,13,17,23,5,17,5,13,11,21,5,11,5,9,31,19, ... 17,9,9,27,21,15,15,1,1,29,5,31,11,17,23,19,21,25,15,11,5,5,1, ... 19,19,19,7,13,21,17,17,25,23,19,23,15,13,5,19,25,9,7,3,21,17, ... 25,1,27,25,27,25,9,13,3,17,25,23,9,25,9,13,17,17,3,15,7,7,29, ... 3,19,29,29,19,29,13,15,25,27,1,3,9,9,13,31,29,31,5,15,29,1, ... 19,5,9,19,5,15,3,5,7,15,17,17,23,11,9,23,19,3,17,1,27,9,9,17, ... 13,25,29,23,29,11,31,25,21,29,19,27,31,3,5,3,3,13,21,9,29,3, ... 17,11,11,9,21,19,7,17,31,25,1,27,5,15,27,29,29,29,25,27,25,3, ... 21,17,25,13,15,17,13,23,9,3,11,7,9,9,7,17,7,1]'; v(332:654,5) = [ ... 27,1,9,5,31,21,25,25,21,11,1,23,19,27, ... 15,3,5,23,9,25,7,29,11,9,13,5,11,1,3,31,27,3,17,27,11,13,15, ... 29,15,1,15,23,25,13,21,15,3,29,29,5,25,17,11,7,15,5,21,7,31, ... 13,11,23,5,7,23,27,21,29,15,7,27,27,19,7,15,27,27,19,19,9,15, ... 1,3,29,29,5,27,31,9,1,7,3,19,19,29,9,3,21,31,29,25,1,3,9,27, ... 5,27,25,21,11,29,31,27,21,29,17,9,17,13,11,25,15,21,11,19,31, ... 3,19,5,3,3,9,13,13,3,29,7,5,9,23,13,21,23,21,31,11,7,7,3,23, ... 1,23,5,9,17,21,1,17,29,7,5,17,13,25,17,9,19,9,5,7,21,19,13,9, ... 7,3,9,3,15,31,29,29,25,13,9,21,9,31,7,15,5,31,7,15,27,25,19, ... 9,9,25,25,23,1,9,7,11,15,19,15,27,17,11,11,31,13,25,25,9,7, ... 13,29,19,5,19,31,25,13,25,15,5,9,29,31,9,29,27,25,27,11,17,5, ... 17,3,23,15,9,9,17,17,31,11,19,25,13,23,15,25,21,31,19,3,11, ... 25,7,15,19,7,5,3,13,13,1,23,5,25,11,25,15,13,21,11,23,29,5, ... 17,27,9,19,15,5,29,23,19,1,27,3,23,21,19,27,11,17,13,27,11, ... 31,23,5,9,21,31,29,11,21,17,15,7,15,7,9,21,27,25]'; v(655:975,5) = [ ... 29,11,3,21,13,23,19,27,17,29,25,17,9, ... 1,19,23,5,23,1,17,17,13,27,23,7,7,11,13,17,13,11,21,13,23,1, ... 27,13,9,7,1,27,29,5,13,25,21,3,31,15,13,3,19,13,1,27,15,17,1, ... 3,13,13,13,31,29,27,7,7,21,29,15,17,17,21,19,17,3,15,5,27,27, ... 3,31,31,7,21,3,13,11,17,27,25,1,9,7,29,27,21,23,13,25,29,15, ... 17,29,9,15,3,21,15,17,17,31,9,9,23,19,25,3,1,11,27,29,1,31, ... 29,25,29,1,23,29,25,13,3,31,25,5,5,11,3,21,9,23,7,11,23,11,1, ... 1,3,23,25,23,1,23,3,27,9,27,3,23,25,19,29,29,13,27,5,9,29,29, ... 13,17,3,23,19,7,13,3,19,23,5,29,29,13,13,5,19,5,17,9,11,11, ... 29,27,23,19,17,25,13,1,13,3,11,1,17,29,1,13,17,9,17,21,1,11, ... 1,1,25,5,7,29,29,19,19,1,29,13,3,1,31,15,13,3,1,11,19,5,29, ... 13,29,23,3,1,31,13,19,17,5,5,1,29,23,3,19,25,19,27,9,27,13, ... 15,29,23,13,25,25,17,19,17,15,27,3,25,17,27,3,27,31,23,13,31, ... 11,15,7,21,19,27,19,21,29,7,31,13,9,9,7,21,13,11,9,11,29,19, ... 11,19,21,5,29,13,7,19,19,27,23,31,1,27,21,7,3,7,11]'; v(976:1111,5) = [ ... 23,13,29,11,31,19,1,5,5,11,5,3,27,5, ... 7,11,31,1,27,31,31,23,5,21,27,9,25,3,15,19,1,19,9,5,25,21,15, ... 25,29,15,21,11,19,15,3,7,13,11,25,17,1,5,31,13,29,23,9,5,29, ... 7,17,27,7,17,31,9,31,9,9,7,21,3,3,3,9,11,21,11,31,9,25,5,1, ... 31,13,29,9,29,1,11,19,7,27,13,31,7,31,7,25,23,21,29,11,11,13, ... 11,27,1,23,31,21,23,21,19,31,5,31,25,25,19,17,11,25,7,13,1, ... 29,17,23,15,7,29,17,13,3,17]'; v(14:324,6) = [ ... 37,33,7,5,11,39,63,59,17,15,23,29,3,21, ... 13,31,25,9,49,33,19,29,11,19,27,15,25,63,55,17,63,49,19,41, ... 59,3,57,33,49,53,57,57,39,21,7,53,9,55,15,59,19,49,31,3,39,5, ... 5,41,9,19,9,57,25,1,15,51,11,19,61,53,29,19,11,9,21,19,43,13, ... 13,41,25,31,9,11,19,5,53,37,7,51,45,7,7,61,23,45,7,59,41,1, ... 29,61,37,27,47,15,31,35,31,17,51,13,25,45,5,5,33,39,5,47,29, ... 35,47,63,45,37,47,59,21,59,33,51,9,27,13,25,43,3,17,21,59,61, ... 27,47,57,11,17,39,1,63,21,59,17,13,31,3,31,7,9,27,37,23,31,9, ... 45,43,31,63,21,39,51,27,7,53,11,1,59,39,23,49,23,7,55,59,3, ... 19,35,13,9,13,15,23,9,7,43,55,3,19,9,27,33,27,49,23,47,19,7, ... 11,55,27,35,5,5,55,35,37,9,33,29,47,25,11,47,53,61,59,3,53, ... 47,5,19,59,5,47,23,45,53,3,49,61,47,39,29,17,57,5,17,31,23, ... 41,39,5,27,7,29,29,33,31,41,31,29,17,29,29,9,9,31,27,53,35,5, ... 61,1,49,13,57,29,5,21,43,25,57,49,37,27,11,61,37,49,5,63,63, ... 3,45,37,63,21,21,19,27,59,21,45,23,13,15,3,43,63,39,19]'; v(325:632,6) = [ ... 63,31,41,41,15,43,63,53,1,63,31,7,17, ... 11,61,31,51,37,29,59,25,63,59,47,15,27,19,29,45,35,55,39,19, ... 43,21,19,13,17,51,37,5,33,35,49,25,45,1,63,47,9,63,15,25,25, ... 15,41,13,3,19,51,49,37,25,49,13,53,47,23,35,29,33,21,35,23,3, ... 43,31,63,9,1,61,43,3,11,55,11,35,1,63,35,49,19,45,9,57,51,1, ... 47,41,9,11,37,19,55,23,55,55,13,7,47,37,11,43,17,3,25,19,55, ... 59,37,33,43,1,5,21,5,63,49,61,21,51,15,19,43,47,17,9,53,45, ... 11,51,25,11,25,47,47,1,43,29,17,31,15,59,27,63,11,41,51,29,7, ... 27,63,31,43,3,29,39,3,59,59,1,53,63,23,63,47,51,23,61,39,47, ... 21,39,15,3,9,57,61,39,37,21,51,1,23,43,27,25,11,13,21,43,7, ... 11,33,55,1,37,35,27,61,39,5,19,61,61,57,59,21,59,61,57,25,55, ... 27,31,41,33,63,19,57,35,13,63,35,17,11,11,49,41,55,5,45,17, ... 35,5,31,31,37,17,45,51,1,39,49,55,19,41,13,5,51,5,49,1,21,13, ... 17,59,51,11,3,61,1,33,37,33,61,25,27,59,7,49,13,63,3,33,3,15, ... 9,13,35,39,11,59,59,1,57,11,5,57,13,31,13,11,55,45,9,55,55]'; v(633:942,6) = [ ... 19,25,41,23,45,29,63,59,27,39,21,37,7, ... 61,49,35,39,9,29,7,25,23,57,5,19,15,33,49,37,25,17,45,29,15, ... 25,3,3,49,11,39,15,19,57,39,15,11,3,57,31,55,61,19,5,41,35, ... 59,61,39,41,53,53,63,31,9,59,13,35,55,41,49,5,41,25,27,43,5, ... 5,43,5,5,17,5,15,27,29,17,9,3,55,31,1,45,45,13,57,17,3,61,15, ... 49,15,47,9,37,45,9,51,61,21,33,11,21,63,63,47,57,61,49,9,59, ... 19,29,21,23,55,23,43,41,57,9,39,27,41,35,61,29,57,63,21,31, ... 59,35,49,3,49,47,49,33,21,19,21,35,11,17,37,23,59,13,37,35, ... 55,57,1,29,45,11,1,15,9,33,19,53,43,39,23,7,13,13,1,19,41,55, ... 1,13,15,59,55,15,3,57,37,31,17,1,3,21,29,25,55,9,37,33,53,41, ... 51,19,57,13,63,43,19,7,13,37,33,19,15,63,51,11,49,23,57,47, ... 51,15,53,41,1,15,37,61,11,35,29,33,23,55,11,59,19,61,61,45, ... 13,49,13,63,5,61,5,31,17,61,63,13,27,57,1,21,5,11,39,57,51, ... 53,39,25,41,39,37,23,31,25,33,17,57,29,27,23,47,41,29,19,47, ... 41,25,5,51,43,39,29,7,31,45,51,49,55,17,43,49,45,9,29,3,5,47, ... 9,15,19]'; v(943:1111,6) = [ ... 51,45,57,63,9,21,59,3,9,13,45,23,15, ... 31,21,15,51,35,9,11,61,23,53,29,51,45,31,29,5,35,29,53,35,17, ... 59,55,27,51,59,27,47,15,29,37,7,49,55,5,19,45,29,19,57,33,53, ... 45,21,9,3,35,29,43,31,39,3,45,1,41,29,5,59,41,33,35,27,19,13, ... 25,27,43,33,35,17,17,23,7,35,15,61,61,53,5,15,23,11,13,43,55, ... 47,25,43,15,57,45,1,49,63,57,15,31,31,7,53,27,15,47,23,7,29, ... 53,47,9,53,3,25,55,45,63,21,17,23,31,27,27,43,63,55,63,45,51, ... 15,27,5,37,43,11,27,5,27,59,21,7,39,27,63,35,47,55,17,17,17, ... 3,19,21,13,49,61,39,15]'; v(20:305,7) = [ ... 13,33,115,41,79,17,29,119,75,73,105,7, ... 59,65,21,3,113,61,89,45,107,21,71,79,19,71,61,41,57,121,87, ... 119,55,85,121,119,11,23,61,11,35,33,43,107,113,101,29,87,119, ... 97,29,17,89,5,127,89,119,117,103,105,41,83,25,41,55,69,117, ... 49,127,29,1,99,53,83,15,31,73,115,35,21,89,5,1,91,53,35,95, ... 83,19,85,55,51,101,33,41,55,45,95,61,27,37,89,75,57,61,15, ... 117,15,21,27,25,27,123,39,109,93,51,21,91,109,107,45,15,93, ... 127,3,53,81,79,107,79,87,35,109,73,35,83,107,1,51,7,59,33, ... 115,43,111,45,121,105,125,87,101,41,95,75,1,57,117,21,27,67, ... 29,53,117,63,1,77,89,115,49,127,15,79,81,29,65,103,33,73,79, ... 29,21,113,31,33,107,95,111,59,99,117,63,63,99,39,9,35,63,125, ... 99,45,93,33,93,9,105,75,51,115,11,37,17,41,21,43,73,19,93,7, ... 95,81,93,79,81,55,9,51,63,45,89,73,19,115,39,47,81,39,5,5,45, ... 53,65,49,17,105,13,107,5,5,19,73,59,43,83,97,115,27,1,69,103, ... 3,99,103,63,67,25,121,97,77,13,83,103,41,11,27,81,37,33,125, ... 71,41,41,59,41,87,123]'; v(306:589,7) = [ ... 43,101,63,45,39,21,97,15,97,111,21,49, ... 13,17,79,91,65,105,75,1,45,67,83,107,125,87,15,81,95,105,65, ... 45,59,103,23,103,99,67,99,47,117,71,89,35,53,73,9,115,49,37, ... 1,35,9,45,81,19,127,17,17,105,89,49,101,7,37,33,11,95,95,17, ... 111,105,41,115,5,69,101,27,27,101,103,53,9,21,43,79,91,65, ... 117,87,125,55,45,63,85,83,97,45,83,87,113,93,95,5,17,77,77, ... 127,123,45,81,85,121,119,27,85,41,49,15,107,21,51,119,11,87, ... 101,115,63,63,37,121,109,7,43,69,19,77,49,71,59,35,7,13,55, ... 101,127,103,85,109,29,61,67,21,111,67,23,57,75,71,101,123,41, ... 107,101,107,125,27,47,119,41,19,127,33,31,109,7,91,91,39,125, ... 105,47,125,123,91,9,103,45,23,117,9,125,73,11,37,61,79,21,5, ... 47,117,67,53,85,33,81,121,47,61,51,127,29,65,45,41,95,57,73, ... 33,117,61,111,59,123,65,47,105,23,29,107,37,81,67,29,115,119, ... 75,73,99,103,7,57,45,61,95,49,101,101,35,47,119,39,67,31,103, ... 7,61,127,87,3,35,29,73,95,103,71,75,51,87,57,97,11,105,87,41, ... 73,109,69,35,121,39,111,1,77]'; v(590:875,7) = [ ... 39,47,53,91,3,17,51,83,39,125,85,111, ... 21,69,85,29,55,11,117,1,47,17,65,63,47,117,17,115,51,25,33, ... 123,123,83,51,113,95,121,51,91,109,43,55,35,55,87,33,37,5,3, ... 45,21,105,127,35,17,35,37,97,97,21,77,123,17,89,53,105,75,25, ... 125,13,47,21,125,23,55,63,61,5,17,93,57,121,69,73,93,121,105, ... 75,91,67,95,75,9,69,97,99,93,11,53,19,73,5,33,79,107,65,69, ... 79,125,25,93,55,61,17,117,69,97,87,111,37,93,59,79,95,53,115, ... 53,85,85,65,59,23,75,21,67,27,99,79,27,3,95,27,69,19,75,47, ... 59,41,85,77,99,55,49,93,93,119,51,125,63,13,15,45,61,19,105, ... 115,17,83,7,7,11,61,37,63,89,95,119,113,67,123,91,33,37,99, ... 43,11,33,65,81,79,81,107,63,63,55,89,91,25,93,101,27,55,75, ... 121,79,43,125,73,27,109,35,21,71,113,89,59,95,41,45,113,119, ... 113,39,59,73,15,13,59,67,121,27,7,105,15,59,59,35,91,89,23, ... 125,97,53,41,91,111,29,31,3,103,61,71,35,7,119,29,45,49,111, ... 41,109,59,125,13,27,19,79,9,75,83,81,33,91,109,33,29,107,111, ... 101,107,109,65,59,43,37]'; v(876:1111,7) = [ ... 1,9,15,109,37,111,113,119,79,73,65, ... 71,93,17,101,87,97,43,23,75,109,41,49,53,31,97,105,109,119, ... 51,9,53,113,97,73,89,79,49,61,105,13,99,53,71,7,87,21,101,5, ... 71,31,123,121,121,73,79,115,13,39,101,19,37,51,83,97,55,81, ... 91,127,105,89,63,47,49,75,37,77,15,49,107,23,23,35,19,69,17, ... 59,63,73,29,125,61,65,95,101,81,57,69,83,37,11,37,95,1,73,27, ... 29,57,7,65,83,99,69,19,103,43,95,25,19,103,41,125,97,71,105, ... 83,83,61,39,9,45,117,63,31,5,117,67,125,41,117,43,77,97,15, ... 29,5,59,25,63,87,39,39,77,85,37,81,73,89,29,125,109,21,23, ... 119,105,43,93,97,15,125,29,51,69,37,45,31,75,109,119,53,5, ... 101,125,121,35,29,7,63,17,63,13,69,15,105,51,127,105,9,57,95, ... 59,109,35,49,23,33,107,55,33,57,79,73,69,59,107,55,11,63,95, ... 103,23,125,91,31,91,51,65,61,75,69,107,65,101,59,35,15]'; v(38:299,8) = [ ... 7,23,39,217,141,27,53,181,169,35,15, ... 207,45,247,185,117,41,81,223,151,81,189,61,95,185,23,73,113, ... 239,85,9,201,83,53,183,203,91,149,101,13,111,239,3,205,253, ... 247,121,189,169,179,197,175,217,249,195,95,63,19,7,5,75,217, ... 245,111,189,165,169,141,221,249,159,253,207,249,219,23,49, ... 127,237,5,25,177,37,103,65,167,81,87,119,45,79,143,57,79,187, ... 143,183,75,97,211,149,175,37,135,189,225,241,63,33,43,13,73, ... 213,57,239,183,117,21,29,115,43,205,223,15,3,159,51,101,127, ... 99,239,171,113,171,119,189,245,201,27,185,229,105,153,189,33, ... 35,137,77,97,17,181,55,197,201,155,37,197,137,223,25,179,91, ... 23,235,53,253,49,181,249,53,173,97,247,67,115,103,159,239,69, ... 173,217,95,221,247,97,91,123,223,213,129,181,87,239,85,89, ... 249,141,39,57,249,71,101,159,33,137,189,71,253,205,171,13, ... 249,109,131,199,189,179,31,99,113,41,173,23,189,197,3,135,9, ... 95,195,27,183,1,123,73,53,99,197,59,27,101,55,193,31,61,119, ... 11,7,255,233,53,157,193,97,83,65,81,239,167,69,71,109]'; v(300:559,8) = [ ... 97,137,71,193,189,115,79,205,37,227, ... 53,33,91,229,245,105,77,229,161,103,93,13,161,229,223,69,15, ... 25,23,233,93,25,217,247,61,75,27,9,223,213,55,197,145,89,199, ... 41,201,5,149,35,119,183,53,11,13,3,179,229,43,55,187,233,47, ... 133,91,47,71,93,105,145,45,255,221,115,175,19,129,5,209,197, ... 57,177,115,187,119,77,211,111,33,113,23,87,137,41,7,83,43, ... 121,145,5,219,27,11,111,207,55,97,63,229,53,33,149,23,187, ... 153,91,193,183,59,211,93,139,59,179,163,209,77,39,111,79,229, ... 85,237,199,137,147,25,73,121,129,83,87,93,205,167,53,107,229, ... 213,95,219,109,175,13,209,97,61,147,19,13,123,73,35,141,81, ... 19,171,255,111,107,233,113,133,89,9,231,95,69,33,1,253,219, ... 253,247,129,11,251,221,153,35,103,239,7,27,235,181,5,207,53, ... 149,155,225,165,137,155,201,97,245,203,47,39,35,105,239,49, ... 15,253,7,237,213,55,87,199,27,175,49,41,229,85,3,149,179,129, ... 185,249,197,15,97,197,139,203,63,33,251,217,199,199,99,249, ... 33,229,177,13,209,147,97,31,125,177,137]'; v(560:819,8) = [ ... 187,11,91,223,29,169,231,59,31,163,41, ... 57,87,247,25,127,101,207,187,73,61,105,27,91,171,243,33,3,1, ... 21,229,93,71,61,37,183,65,211,53,11,151,165,47,5,129,79,101, ... 147,169,181,19,95,77,139,197,219,97,239,183,143,9,13,209,23, ... 215,53,137,203,19,151,171,133,219,231,3,15,253,225,33,111, ... 183,213,169,119,111,15,201,123,121,225,113,113,225,161,165,1, ... 139,55,3,93,217,193,97,29,69,231,161,93,69,143,137,9,87,183, ... 113,183,73,215,137,89,251,163,41,227,145,57,81,57,11,135,145, ... 161,175,159,25,55,167,157,211,97,247,249,23,129,159,71,197, ... 127,141,219,5,233,131,217,101,131,33,157,173,69,207,239,81, ... 205,11,41,169,65,193,77,201,173,1,221,157,1,15,113,147,137, ... 205,225,73,45,49,149,113,253,99,17,119,105,117,129,243,75, ... 203,53,29,247,35,247,171,31,199,213,29,251,7,251,187,91,11, ... 149,13,205,37,249,137,139,9,7,113,183,205,187,39,3,79,155, ... 227,89,185,51,127,63,83,41,133,183,181,127,19,255,219,59,251, ... 3,187,57,217,115,217,229,181,185,149,83,115,11]'; v(820:1074,8) = [ ... 123,19,109,165,103,123,219,129,155, ... 207,177,9,49,181,231,33,233,67,155,41,9,95,123,65,117,249,85, ... 169,129,241,173,251,225,147,165,69,81,239,95,23,83,227,249, ... 143,171,193,9,21,57,73,97,57,29,239,151,159,191,47,51,1,223, ... 251,251,151,41,119,127,131,33,209,123,53,241,25,31,183,107, ... 25,115,39,11,213,239,219,109,185,35,133,123,185,27,55,245,61, ... 75,205,213,169,163,63,55,49,83,195,51,31,41,15,203,41,63,127, ... 161,5,143,7,199,251,95,75,101,15,43,237,197,117,167,155,21, ... 83,205,255,49,101,213,237,135,135,21,73,93,115,7,85,223,237, ... 79,89,5,57,239,67,65,201,155,71,85,195,89,181,119,135,147, ... 237,173,41,155,67,113,111,21,183,23,103,207,253,69,219,205, ... 195,43,197,229,139,177,129,69,97,201,163,189,11,99,91,253, ... 239,91,145,19,179,231,121,7,225,237,125,191,119,59,175,237, ... 131,79,43,45,205,199,251,153,207,37,179,113,255,107,217,61,7, ... 181,247,31,13,113,145,107,233,233,43,79,23,169,137,129,183, ... 53,91,55,103,223,87,177,157,79,213,139]'; v(1075:1111,8) = [ ... 183,231,205,143,129,243,205,93,59, ... 15,89,9,11,47,133,227,75,9,91,19,171,163,79,7,103,5,119,155, ... 75,11,71,95,17,13,243,207,187]'; v(54:299,9) = [ ... 235,307,495,417,57,151,19,119,375,451, ... 55,449,501,53,185,317,17,21,487,13,347,393,15,391,307,189, ... 381,71,163,99,467,167,433,337,257,179,47,385,23,117,369,425, ... 207,433,301,147,333,85,221,423,49,3,43,229,227,201,383,281, ... 229,207,21,343,251,397,173,507,421,443,399,53,345,77,385,317, ... 155,187,269,501,19,169,235,415,61,247,183,5,257,401,451,95, ... 455,49,489,75,459,377,87,463,155,233,115,429,211,419,143,487, ... 195,209,461,193,157,193,363,181,271,445,381,231,135,327,403, ... 171,197,181,343,113,313,393,311,415,267,247,425,233,289,55, ... 39,247,327,141,5,189,183,27,337,341,327,87,429,357,265,251, ... 437,201,29,339,257,377,17,53,327,47,375,393,369,403,125,429, ... 257,157,217,85,267,117,337,447,219,501,41,41,193,509,131,207, ... 505,421,149,111,177,167,223,291,91,29,305,151,177,337,183, ... 361,435,307,507,77,181,507,315,145,423,71,103,493,271,469, ... 339,237,437,483,31,219,61,131,391,233,219,69,57,459,225,421, ... 7,461,111,451,277,185,193,125,251,199,73,71,7,409,417,149]'; v(300:550,9) = [ ... 193,53,437,29,467,229,31,35,75,105, ... 503,75,317,401,367,131,365,441,433,93,377,405,465,259,283, ... 443,143,445,3,461,329,309,77,323,155,347,45,381,315,463,207, ... 321,157,109,479,313,345,167,439,307,235,473,79,101,245,19, ... 381,251,35,25,107,187,115,113,321,115,445,61,77,293,405,13, ... 53,17,171,299,41,79,3,485,331,13,257,59,201,497,81,451,199, ... 171,81,253,365,75,451,149,483,81,453,469,485,305,163,401,15, ... 91,3,129,35,239,355,211,387,101,299,67,375,405,357,267,363, ... 79,83,437,457,39,97,473,289,179,57,23,49,79,71,341,287,95, ... 229,271,475,49,241,261,495,353,381,13,291,37,251,105,399,81, ... 89,265,507,205,145,331,129,119,503,249,1,289,463,163,443,63, ... 123,361,261,49,429,137,355,175,507,59,277,391,25,185,381,197, ... 39,5,429,119,247,177,329,465,421,271,467,151,45,429,137,471, ... 11,17,409,347,199,463,177,11,51,361,95,497,163,351,127,395, ... 511,327,353,49,105,151,321,331,329,509,107,109,303,467,287, ... 161,45,385,289,363,331,265,407,37,433,315,343,63,51,185,71, ... 27,267]'; v(551:798,9) = [ ... 503,239,293,245,281,297,75,461,371, ... 129,189,189,339,287,111,111,379,93,27,185,347,337,247,507, ... 161,231,43,499,73,327,263,331,249,493,37,25,115,3,167,197, ... 127,357,497,103,125,191,165,55,101,95,79,351,341,43,125,135, ... 173,289,373,133,421,241,281,213,177,363,151,227,145,363,239, ... 431,81,397,241,67,291,255,405,421,399,75,399,105,329,41,425, ... 7,283,375,475,427,277,209,411,3,137,195,289,509,121,55,147, ... 275,251,19,129,285,415,487,491,193,219,403,23,97,65,285,75, ... 21,373,261,339,239,495,415,333,107,435,297,213,149,463,199, ... 323,45,19,301,121,499,187,229,63,425,99,281,35,125,349,87, ... 101,59,195,511,355,73,263,243,101,165,141,11,389,219,187,449, ... 447,393,477,305,221,51,355,209,499,479,265,377,145,411,173, ... 11,433,483,135,385,341,89,209,391,33,395,319,451,119,341,227, ... 375,61,331,493,411,293,47,203,375,167,395,155,5,237,361,489, ... 127,21,345,101,371,233,431,109,119,277,125,263,73,135,123,83, ... 123,405,69,75,287,401,23,283,393,41,379,431,11,475,505,19, ... 365,265,271]'; v(799:1045,9) = [ ... 499,489,443,165,91,83,291,319,199, ... 107,245,389,143,137,89,125,281,381,215,131,299,249,375,455, ... 43,73,281,217,297,229,431,357,81,357,171,451,481,13,387,491, ... 489,439,385,487,177,393,33,71,375,443,129,407,395,127,65,333, ... 309,119,197,435,497,373,71,379,509,387,159,265,477,463,449, ... 47,353,249,335,505,89,141,55,235,187,87,363,93,363,101,67, ... 215,321,331,305,261,411,491,479,65,307,469,415,131,315,487, ... 83,455,19,113,163,503,99,499,251,239,81,167,391,255,317,363, ... 359,395,419,307,251,267,171,461,183,465,165,163,293,477,223, ... 403,389,97,335,357,297,19,469,501,249,85,213,311,265,379,297, ... 283,393,449,463,289,159,289,499,407,129,137,221,43,89,403, ... 271,75,83,445,453,389,149,143,423,499,317,445,157,137,453, ... 163,87,23,391,119,427,323,173,89,259,377,511,249,31,363,229, ... 353,329,493,427,57,205,389,91,83,13,219,439,45,35,371,441,17, ... 267,501,53,25,333,17,201,475,257,417,345,381,377,55,403,77, ... 389,347,363,211,413,419,5,167,219,201,285,425,11,77,269,489, ... 281,403,79]'; v(1046:1111,9) = [ ... 425,125,81,331,437,271,397,299,475, ... 271,249,413,233,261,495,171,69,27,409,21,421,367,81,483,255, ... 15,219,365,497,181,75,431,99,325,407,229,281,63,83,493,5,113, ... 15,271,37,87,451,299,83,451,311,441,47,455,47,253,13,109,369, ... 347,11,409,275,63,441,15]'; v(102:344,10) = [ ... 519,307,931,1023,517,771,151,1023, ... 539,725,45,927,707,29,125,371,275,279,817,389,453,989,1015, ... 29,169,743,99,923,981,181,693,309,227,111,219,897,377,425, ... 609,227,19,221,143,581,147,919,127,725,793,289,411,835,921, ... 957,443,349,813,5,105,457,393,539,101,197,697,27,343,515,69, ... 485,383,855,693,133,87,743,747,475,87,469,763,721,345,479, ... 965,527,121,271,353,467,177,245,627,113,357,7,691,725,355, ... 889,635,737,429,545,925,357,873,187,351,677,999,921,477,233, ... 765,495,81,953,479,89,173,473,131,961,411,291,967,65,511,13, ... 805,945,369,827,295,163,835,259,207,331,29,315,999,133,967, ... 41,117,677,471,717,881,755,351,723,259,879,455,721,289,149, ... 199,805,987,851,423,597,129,11,733,549,153,285,451,559,377, ... 109,357,143,693,615,677,701,475,767,85,229,509,547,151,389, ... 711,785,657,319,509,99,1007,775,359,697,677,85,497,105,615, ... 891,71,449,835,609,377,693,665,627,215,911,503,729,131,19, ... 895,199,161,239,633,1013,537,255,23,149,679,1021,595,199,557, ... 659,251,829,727,439,495,647,223]'; v(345:586,10) = [ ... 949,625,87,481,85,799,917,769,949, ... 739,115,499,945,547,225,1015,469,737,495,353,103,17,665,639, ... 525,75,447,185,43,729,577,863,735,317,99,17,477,893,537,519, ... 1017,375,297,325,999,353,343,729,135,489,859,267,141,831,141, ... 893,249,807,53,613,131,547,977,131,999,175,31,341,739,467, ... 675,241,645,247,391,583,183,973,433,367,131,467,571,309,385, ... 977,111,917,935,473,345,411,313,97,149,959,841,839,669,431, ... 51,41,301,247,1015,377,329,945,269,67,979,581,643,823,557,91, ... 405,117,801,509,347,893,303,227,783,555,867,99,703,111,797, ... 873,541,919,513,343,319,517,135,871,917,285,663,301,15,763, ... 89,323,757,317,807,309,1013,345,499,279,711,915,411,281,193, ... 739,365,315,375,809,469,487,621,857,975,537,939,585,129,625, ... 447,129,1017,133,83,3,415,661,53,115,903,49,79,55,385,261, ... 345,297,199,385,617,25,515,275,849,401,471,377,661,535,505, ... 939,465,225,929,219,955,659,441,117,527,427,515,287,191,33, ... 389,197,825,63,417,949,35,571,9,131,609,439,95,19,569,893, ... 451,397,971,801]'; v(587:824,10) = [ ... 125,471,187,257,67,949,621,453,411, ... 621,955,309,783,893,597,377,753,145,637,941,593,317,555,375, ... 575,175,403,571,555,109,377,931,499,649,653,329,279,271,647, ... 721,665,429,957,803,767,425,477,995,105,495,575,687,385,227, ... 923,563,723,481,717,111,633,113,369,955,253,321,409,909,367, ... 33,967,453,863,449,539,781,911,113,7,219,725,1015,971,1021, ... 525,785,873,191,893,297,507,215,21,153,645,913,755,371,881, ... 113,903,225,49,587,201,927,429,599,513,97,319,331,833,325, ... 887,139,927,399,163,307,803,169,1019,869,537,907,479,335,697, ... 479,353,769,787,1023,855,493,883,521,735,297,1011,991,879, ... 855,591,415,917,375,453,553,189,841,339,211,601,57,765,745, ... 621,209,875,639,7,595,971,263,1009,201,23,77,621,33,535,963, ... 661,523,263,917,103,623,231,47,301,549,337,675,189,357,1005, ... 789,189,319,721,1005,525,675,539,191,813,917,51,167,415,579, ... 755,605,721,837,529,31,327,799,961,279,409,847,649,241,285, ... 545,407,161,591,73,313,811,17,663,269,261,37,783,127,917,231, ... 577,975,793]'; v(825:1065,10) = [ ... 921,343,751,139,221,79,817,393,545, ... 11,781,71,1,699,767,917,9,107,341,587,903,965,599,507,843, ... 739,579,397,397,325,775,565,925,75,55,979,931,93,957,857,753, ... 965,795,67,5,87,909,97,995,271,875,671,613,33,351,69,811,669, ... 729,401,647,241,435,447,721,271,745,53,775,99,343,451,427, ... 593,339,845,243,345,17,573,421,517,971,499,435,769,75,203, ... 793,985,343,955,735,523,659,703,303,421,951,405,631,825,735, ... 433,841,485,49,749,107,669,211,497,143,99,57,277,969,107,397, ... 563,551,447,381,187,57,405,731,769,923,955,915,737,595,341, ... 253,823,197,321,315,181,885,497,159,571,981,899,785,947,217, ... 217,135,753,623,565,717,903,581,955,621,361,869,87,943,907, ... 853,353,335,197,771,433,743,195,91,1023,63,301,647,205,485, ... 927,1003,987,359,577,147,141,1017,701,273,89,589,487,859,343, ... 91,847,341,173,287,1003,289,639,983,685,697,35,701,645,911, ... 501,705,873,763,745,657,559,699,315,347,429,197,165,955,859, ... 167,303,833,531,473,635,641,195,589,821,205,3,635,371,891, ... 249,123]'; v(1066:1111,10) = [ ... 77,623,993,401,525,427,71,655,951, ... 357,851,899,535,493,323,1003,343,515,859,1017,5,423,315,1011, ... 703,41,777,163,95,831,79,975,235,633,723,297,589,317,679,981, ... 195,399,1003,121,501,155]'; v(162:376,11) = [ ... 7,2011,1001,49,825,415,1441,383,1581, ... 623,1621,1319,1387,619,839,217,75,1955,505,281,1629,1379,53, ... 1111,1399,301,209,49,155,1647,631,129,1569,335,67,1955,1611, ... 2021,1305,121,37,877,835,1457,669,1405,935,1735,665,551,789, ... 1543,1267,1027,1,1911,163,1929,67,1975,1681,1413,191,1711, ... 1307,401,725,1229,1403,1609,2035,917,921,1789,41,2003,187,67, ... 1635,717,1449,277,1903,1179,363,1211,1231,647,1261,1029,1485, ... 1309,1149,317,1335,171,243,271,1055,1601,1129,1653,205,1463, ... 1681,1621,197,951,573,1697,1265,1321,1805,1235,1853,1307,945, ... 1197,1411,833,273,1517,1747,1095,1345,869,57,1383,221,1713, ... 335,1751,1141,839,523,1861,1105,389,1177,1877,805,93,1591, ... 423,1835,99,1781,1515,1909,1011,303,385,1635,357,973,1781, ... 1707,1363,1053,649,1469,623,1429,1241,1151,1055,503,921,3, ... 349,1149,293,45,303,877,1565,1583,1001,663,1535,395,1141, ... 1481,1797,643,1507,465,2027,1695,367,937,719,545,1991,83,819, ... 239,1791,1461,1647,1501,1161,1629,139,1595,1921,1267,1415, ... 509,347,777,1083,363,269,1015]'; v(377:589,11) = [ ... 1809,1105,1429,1471,2019,381,2025, ... 1223,827,1733,887,1321,803,1951,1297,1995,833,1107,1135,1181, ... 1251,983,1389,1565,273,137,71,735,1005,933,67,1471,551,457, ... 1667,1729,919,285,1629,1815,653,1919,1039,531,393,1411,359, ... 221,699,1485,471,1357,1715,595,1677,153,1903,1281,215,781, ... 543,293,1807,965,1695,443,1985,321,879,1227,1915,839,1945, ... 1993,1165,51,557,723,1491,817,1237,947,1215,1911,1225,1965, ... 1889,1503,1177,73,1767,303,177,1897,1401,321,921,217,1779, ... 327,1889,333,615,1665,1825,1639,237,1205,361,129,1655,983, ... 1089,1171,401,677,643,749,303,1407,1873,1579,1491,1393,1247, ... 789,763,49,5,1607,1891,735,1557,1909,1765,1777,1127,813,695, ... 97,731,1503,1751,333,769,865,693,377,1919,957,1359,1627,1039, ... 1783,1065,1665,1917,1947,991,1997,841,459,221,327,1595,1881, ... 1269,1007,129,1413,475,1105,791,1983,1359,503,691,659,691, ... 343,1375,1919,263,1373,603,1383,297,781,145,285,767,1739, ... 1715,715,317,1333,85,831,1615,81,1667,1467,1457,1453,1825, ... 109,387,1207,2039,213,1351,1329,1173]'; v(590:802,11) = [ ... 57,1769,951,183,23,451,1155,1551, ... 2037,811,635,1671,1451,863,1499,1673,363,1029,1077,1525,277, ... 1023,655,665,1869,1255,965,277,1601,329,1603,1901,395,65, ... 1307,2029,21,1321,543,1569,1185,1905,1701,413,2041,1697,725, ... 1417,1847,411,211,915,1891,17,1877,1699,687,1089,1973,1809, ... 851,1495,1257,63,1323,1307,609,881,1543,177,617,1505,1747, ... 1537,925,183,77,1723,1877,1703,397,459,521,257,1177,389,1947, ... 1553,1583,1831,261,485,289,1281,1543,1591,1123,573,821,1065, ... 1933,1373,2005,905,207,173,1573,1597,573,1883,1795,1499,1743, ... 553,335,333,1645,791,871,1157,969,557,141,223,1129,1685,423, ... 1069,391,99,95,1847,531,1859,1833,1833,341,237,1997,1799,409, ... 431,1917,363,335,1039,1085,1657,1975,1527,1111,659,389,899, ... 595,1439,1861,1979,1569,1087,1009,165,1895,1481,1583,29,1193, ... 1673,1075,301,1081,1377,1747,1497,1103,1789,887,739,1577,313, ... 1367,1299,1801,1131,1837,73,1865,1065,843,635,55,1655,913, ... 1037,223,1871,1161,461,479,511,1721,1107,389,151,35,375,1099, ... 937,1185,1701,769,639,1633]'; v(803:1018,11) = [ ... 1609,379,1613,2031,685,289,975,671, ... 1599,1447,871,647,99,139,1427,959,89,117,841,891,1959,223, ... 1697,1145,499,1435,1809,1413,1445,1675,171,1073,1349,1545, ... 2039,1027,1563,859,215,1673,1919,1633,779,411,1845,1477,1489, ... 447,1545,351,1989,495,183,1639,1385,1805,1097,1249,1431,1571, ... 591,697,1509,709,31,1563,165,513,1425,1299,1081,145,1841, ... 1211,941,609,845,1169,1865,1593,347,293,1277,157,211,93,1679, ... 1799,527,41,473,563,187,1525,575,1579,857,703,1211,647,709, ... 981,285,697,163,981,153,1515,47,1553,599,225,1147,381,135, ... 821,1965,609,1033,983,503,1117,327,453,2005,1257,343,1649, ... 1199,599,1877,569,695,1587,1475,187,973,233,511,51,1083,665, ... 1321,531,1875,1939,859,1507,1979,1203,1965,737,921,1565,1943, ... 819,223,365,167,1705,413,1577,745,1573,655,1633,1003,91,1123, ... 477,1741,1663,35,715,37,1513,815,941,1379,263,1831,1735,1111, ... 1449,353,1941,1655,1349,877,285,1723,125,1753,985,723,175, ... 439,791,1051,1261,717,1555,1757,1777,577,1583,1957,873,331, ... 1163,313,1,1963,963,1905,821]'; v(1019:1111,11) = [ ... 1677,185,709,545,1723,215,1885, ... 1249,583,1803,839,885,485,413,1767,425,129,1035,329,1263, ... 1881,1779,1565,359,367,453,707,1419,831,1889,887,1871,1869, ... 747,223,1547,1799,433,1441,553,2021,1303,1505,1735,1619,1065, ... 1161,2047,347,867,881,1447,329,781,1065,219,589,645,1257, ... 1833,749,1841,1733,1179,1191,1025,1639,1955,1423,1685,1711, ... 493,549,783,1653,397,895,233,759,1505,677,1449,1573,1297, ... 1821,1691,791,289,1187,867,1535,575,183]'; v(338:545,12) = [ ... 3915,97,3047,937,2897,953,127,1201, ... 3819,193,2053,3061,3759,1553,2007,2493,603,3343,3751,1059, ... 783,1789,1589,283,1093,3919,2747,277,2605,2169,2905,721,4069, ... 233,261,1137,3993,3619,2881,1275,3865,1299,3757,1193,733,993, ... 1153,2945,3163,3179,437,271,3493,3971,1005,2615,2253,1131, ... 585,2775,2171,2383,2937,2447,1745,663,1515,3767,2709,1767, ... 3185,3017,2815,1829,87,3341,793,2627,2169,1875,3745,367,3783, ... 783,827,3253,2639,2955,3539,1579,2109,379,2939,3019,1999, ... 2253,2911,3733,481,1767,1055,4019,4085,105,1829,2097,2379, ... 1567,2713,737,3423,3941,2659,3961,1755,3613,1937,1559,2287, ... 2743,67,2859,325,2601,1149,3259,2403,3947,2011,175,3389,3915, ... 1315,2447,141,359,3609,3933,729,2051,1755,2149,2107,1741, ... 1051,3681,471,1055,845,257,1559,1061,2803,2219,1315,1369, ... 3211,4027,105,11,1077,2857,337,3553,3503,3917,2665,3823,3403, ... 3711,2085,1103,1641,701,4095,2883,1435,653,2363,1597,767,869, ... 1825,1117,1297,501,505,149,873,2673,551,1499,2793,3277,2143, ... 3663,533,3991,575,1877,1009,3929,473,3009,2595,3249,675,3593]'; v(546:752,12) = [ ... 2453,1567,973,595,1335,1715,589,85, ... 2265,3069,461,1659,2627,1307,1731,1501,1699,3545,3803,2157, ... 453,2813,2047,2999,3841,2361,1079,573,69,1363,1597,3427,2899, ... 2771,1327,1117,1523,3521,2393,2537,1979,3179,683,2453,453, ... 1227,779,671,3483,2135,3139,3381,3945,57,1541,3405,3381,2371, ... 2879,1985,987,3017,3031,3839,1401,3749,2977,681,1175,1519, ... 3355,907,117,771,3741,3337,1743,1227,3335,2755,1909,3603, ... 2397,653,87,2025,2617,3257,287,3051,3809,897,2215,63,2043, ... 1757,3671,297,3131,1305,293,3865,3173,3397,2269,3673,717, ... 3041,3341,3595,3819,2871,3973,1129,513,871,1485,3977,2473, ... 1171,1143,3063,3547,2183,3993,133,2529,2699,233,2355,231, ... 3241,611,1309,3829,1839,1495,301,1169,1613,2673,243,3601, ... 3669,2813,2671,2679,3463,2477,1795,617,2317,1855,1057,1703, ... 1761,2515,801,1205,1311,473,3963,697,1221,251,381,3887,1761, ... 3093,3721,2079,4085,379,3601,3845,433,1781,29,1897,1599,2163, ... 75,3475,3957,1641,3911,2959,2833,1279,1099,403,799,2183,2699, ... 1711,2037,727,289,1785,1575,3633,2367,1261,3953,1735,171, ... 1959]'; v(753:960,12) = [ ... 2867,859,2951,3211,15,1279,1323,599, ... 1651,3951,1011,315,3513,3351,1725,3793,2399,287,4017,3571, ... 1007,541,3115,429,1585,1285,755,1211,3047,915,3611,2697,2129, ... 3669,81,3939,2437,915,779,3567,3701,2479,3807,1893,3927,2619, ... 2543,3633,2007,3857,3837,487,1769,3759,3105,2727,3155,2479, ... 1341,1657,2767,2541,577,2105,799,17,2871,3637,953,65,69,2897, ... 3841,3559,4067,2335,3409,1087,425,2813,1705,1701,1237,821, ... 1375,3673,2693,3925,1541,1871,2285,847,4035,1101,2029,855, ... 2733,2503,121,2855,1069,3463,3505,1539,607,1349,575,2301, ... 2321,1101,333,291,2171,4085,2173,2541,1195,925,4039,1379,699, ... 1979,275,953,1755,1643,325,101,2263,3329,3673,3413,1977,2727, ... 2313,1419,887,609,2475,591,2613,2081,3805,3435,2409,111,3557, ... 3607,903,231,3059,473,2959,2925,3861,2043,3887,351,2865,369, ... 1377,2639,1261,3625,3279,2201,2949,3049,449,1297,897,1891, ... 411,2773,749,2753,1825,853,2775,3547,3923,3923,987,3723,2189, ... 3877,3577,297,2763,1845,3083,2951,483,2169,3985,245,3655, ... 3441,1023,235,835,3693,3585,327,1003,543,3059,2637]'; v(961:1111,12) = [ ... 2923,87,3617,1031,1043,903,2913, ... 2177,2641,3279,389,2009,525,4085,3299,987,2409,813,2683,373, ... 2695,3775,2375,1119,2791,223,325,587,1379,2877,2867,3793,655, ... 831,3425,1663,1681,2657,1865,3943,2977,1979,2271,3247,1267, ... 1747,811,159,429,2001,1195,3065,553,1499,3529,1081,2877,3077, ... 845,1793,2409,3995,2559,4081,1195,2955,1117,1409,785,287, ... 1521,1607,85,3055,3123,2533,2329,3477,799,3683,3715,337,3139, ... 3311,431,3511,2299,365,2941,3067,1331,1081,1097,2853,2299, ... 495,1745,749,3819,619,1059,3559,183,3743,723,949,3501,733, ... 2599,3983,3961,911,1899,985,2493,1795,653,157,433,2361,3093, ... 3119,3679,2367,1701,1445,1321,2397,1241,3305,3985,2349,4067, ... 3805,3073,2837,1567,3783,451,2441,1181,487,543,1201,3735, ... 2517,733,1535,2175,3613,3019]'; v(482:680,13) = [ ... 2319,653,1379,1675,1951,7075,2087, ... 7147,1427,893,171,2019,7235,5697,3615,1961,7517,6849,2893, ... 1883,2863,2173,4543,73,381,3893,6045,1643,7669,1027,1549, ... 3983,1985,6589,7497,2745,2375,7047,1117,1171,1975,5199,3915, ... 3695,8113,4303,3773,7705,6855,1675,2245,2817,1719,569,1021, ... 2077,5945,1833,2631,4851,6371,833,7987,331,1899,8093,6719, ... 6903,5903,5657,5007,2689,6637,2675,1645,1819,689,6709,7717, ... 6295,7013,7695,3705,7069,2621,3631,6571,6259,7261,3397,7645, ... 1115,4753,2047,7579,2271,5403,4911,7629,4225,1209,6955,6951, ... 1829,5579,5231,1783,4285,7425,599,5785,3275,5643,2263,657, ... 6769,6261,1251,3249,4447,4111,3991,1215,131,4397,3487,7585, ... 5565,7199,3573,7105,7409,1671,949,3889,5971,3333,225,3647, ... 5403,3409,7459,6879,5789,6567,5581,4919,1927,4407,8085,4691, ... 611,3005,591,753,589,171,5729,5891,1033,3049,6567,5257,8003, ... 1757,4489,4923,6379,5171,1757,689,3081,1389,4113,455,2761, ... 847,7575,5829,633,6629,1103,7635,803,6175,6587,2711,3879,67, ... 1179,4761,7281,1557,3379,2459,4273,4127,7147,35]'; v(681:877,13) = [ ... 3549,395,3735,5787,4179,5889,5057, ... 7473,4713,2133,2897,1841,2125,1029,1695,6523,1143,5105,7133, ... 3351,2775,3971,4503,7589,5155,4305,1641,4717,2427,5617,1267, ... 399,5831,4305,4241,3395,3045,4899,1713,171,411,7099,5473, ... 5209,1195,1077,1309,2953,7343,4887,3229,6759,6721,6775,675, ... 4039,2493,7511,3269,4199,6625,7943,2013,4145,667,513,2303, ... 4591,7941,2741,987,8061,3161,5951,1431,831,5559,7405,1357, ... 4319,4235,5421,2559,4415,2439,823,1725,6219,4903,6699,5451, ... 349,7703,2927,7809,6179,1417,5987,3017,4983,3479,4525,4643, ... 4911,227,5475,2287,5581,6817,1937,1421,4415,7977,1789,3907, ... 6815,6789,6003,5609,4507,337,7427,7943,3075,6427,1019,7121, ... 4763,81,3587,2929,1795,8067,2415,1265,4025,5599,4771,3025, ... 2313,6129,7611,6881,5253,4413,7869,105,3173,1629,2537,1023, ... 4409,7209,4413,7107,7469,33,1955,2881,5167,6451,4211,179, ... 5573,7879,3387,7759,5455,7157,1891,5683,5689,6535,3109,6555, ... 6873,1249,4251,6437,49,2745,1201,7327,4179,6783,623,2779, ... 5963,2585,6927,5333,4033,285,7467,4443,4917,3]'; v(878:1070,13) = [ ... 4319,5517,3449,813,5499,2515,5771, ... 3357,2073,4395,4925,2643,7215,5817,1199,1597,1619,7535,4833, ... 609,4797,8171,6847,793,6757,8165,3371,2431,5235,4739,7703, ... 7223,6525,5891,5605,4433,3533,5267,5125,5037,225,6717,1121, ... 5741,2013,4327,4839,569,5227,7677,4315,2391,5551,859,3627, ... 6377,3903,4311,6527,7573,4905,7731,1909,1555,3279,1949,1887, ... 6675,5509,2033,5473,3539,5033,5935,6095,4761,1771,1271,1717, ... 4415,5083,6277,3147,7695,2461,4783,4539,5833,5583,651,1419, ... 2605,5511,3913,5795,2333,2329,4431,3725,6069,2699,7055,6879, ... 1017,3121,2547,4603,2385,6915,6103,5669,7833,2001,4287,6619, ... 955,2761,5711,6291,3415,3909,2841,5627,4939,7671,6059,6275, ... 6517,1931,4583,7301,1267,7509,1435,2169,6939,3515,2985,2787, ... 2123,1969,3307,353,4359,7059,5273,5873,6657,6765,6229,3179, ... 1583,6237,2155,371,273,7491,3309,6805,3015,6831,7819,713, ... 4747,3935,4109,1311,709,3089,7059,4247,2989,1509,4919,1841, ... 3045,3821,6929,4655,1333,6429,6649,2131,5265,1051,261,8057, ... 3379,2179,1993,5655,3063,6381]'; v(1071:1111,13) = [ ... 3587,7417,1579,1541,2107,5085,2873, ... 6141,955,3537,2157,841,1999,1465,5171,5651,1535,7235,4349, ... 1263,1453,1005,6893,2919,1947,1635,3963,397,969,4569,655, ... 6737,2995,7235,7713,973,4821,2377,1673,1,6541]'; % % Set POLY. % poly(1:1111)= [ ... 1, 3, 7, 11, 13, 19, 25, 37, 59, 47,... 61, 55, 41, 67, 97, 91, 109, 103, 115, 131,... 193, 137, 145, 143, 241, 157, 185, 167, 229, 171,... 213, 191, 253, 203, 211, 239, 247, 285, 369, 299,... 301, 333, 351, 355, 357, 361, 391, 397, 425, 451,... 463, 487, 501, 529, 539, 545, 557, 563, 601, 607,... 617, 623, 631, 637, 647, 661, 675, 677, 687, 695, ... 701, 719, 721, 731, 757, 761, 787, 789, 799, 803,... 817, 827, 847, 859, 865, 875, 877, 883, 895, 901,... 911, 949, 953, 967, 971, 973, 981, 985, 995, 1001,... 1019, 1033, 1051, 1063, 1069, 1125, 1135, 1153, 1163, 1221,... 1239, 1255, 1267, 1279, 1293, 1305, 1315, 1329, 1341, 1347,... 1367, 1387, 1413, 1423, 1431, 1441, 1479, 1509, 1527, 1531,... 1555, 1557, 1573, 1591, 1603, 1615, 1627, 1657, 1663, 1673, ... 1717, 1729, 1747, 1759, 1789, 1815, 1821, 1825, 1849, 1863,... 1869, 1877, 1881, 1891, 1917, 1933, 1939, 1969, 2011, 2035,... 2041, 2053, 2071, 2091, 2093, 2119, 2147, 2149, 2161, 2171,... 2189, 2197, 2207, 2217, 2225, 2255, 2257, 2273, 2279, 2283,... 2293, 2317, 2323, 2341, 2345, 2363, 2365, 2373, 2377, 2385,... 2395, 2419, 2421, 2431, 2435, 2447, 2475, 2477, 2489, 2503, ... 2521, 2533, 2551, 2561, 2567, 2579, 2581, 2601, 2633, 2657,... 2669, 2681, 2687, 2693, 2705, 2717, 2727, 2731, 2739, 2741,... 2773, 2783, 2793, 2799, 2801, 2811, 2819, 2825, 2833, 2867,... 2879, 2881, 2891, 2905, 2911, 2917, 2927, 2941, 2951, 2955,... 2963, 2965, 2991, 2999, 3005, 3017, 3035, 3037, 3047, 3053,... 3083, 3085, 3097, 3103, 3159, 3169, 3179, 3187, 3205, 3209,... 3223, 3227, 3229, 3251, 3263, 3271, 3277, 3283, 3285, 3299,... 3305, 3319, 3331, 3343, 3357, 3367, 3373, 3393, 3399, 3413,... 3417, 3427, 3439, 3441, 3475, 3487, 3497, 3515, 3517, 3529,... 3543, 3547, 3553, 3559, 3573, 3589, 3613, 3617, 3623, 3627,... 3635, 3641, 3655, 3659, 3669, 3679, 3697, 3707, 3709, 3713,... 3731, 3743, 3747, 3771, 3791, 3805, 3827, 3833, 3851, 3865,... 3889, 3895, 3933, 3947, 3949, 3957, 3971, 3985, 3991, 3995,... 4007, 4013, 4021, 4045, 4051, 4069, 4073, 4179, 4201, 4219,... 4221, 4249, 4305, 4331, 4359, 4383, 4387, 4411, 4431, 4439,... 4449, 4459, 4485, 4531, 4569, 4575, 4621, 4663, 4669, 4711,... 4723, 4735, 4793, 4801, 4811, 4879, 4893, 4897, 4921, 4927,... 4941, 4977, 5017, 5027, 5033, 5127, 5169, 5175, 5199, 5213,... 5223, 5237, 5287, 5293, 5331, 5391, 5405, 5453, 5523, 5573,... 5591, 5597, 5611, 5641, 5703, 5717, 5721, 5797, 5821, 5909,... 5913, 5955, 5957, 6005, 6025, 6061, 6067, 6079, 6081, 6231,... 6237, 6289, 6295, 6329, 6383, 6427, 6453, 6465, 6501, 6523,... 6539, 6577, 6589, 6601, 6607, 6631, 6683, 6699, 6707, 6761,... 6795, 6865, 6881, 6901, 6923, 6931, 6943, 6999, 7057, 7079,... 7103, 7105, 7123, 7173, 7185, 7191, 7207, 7245, 7303, 7327, ... 7333, 7355, 7365, 7369, 7375, 7411, 7431, 7459, 7491, 7505, ... 7515, 7541, 7557, 7561, 7701, 7705, 7727, 7749, 7761, 7783,... 7795, 7823, 7907, 7953, 7963, 7975, 8049, 8089, 8123, 8125,... 8137, 8219, 8231, 8245, 8275, 8293, 8303, 8331, 8333, 8351,... 8357, 8367, 8379, 8381, 8387, 8393, 8417, 8435, 8461, 8469,... 8489, 8495, 8507, 8515, 8551, 8555, 8569, 8585, 8599, 8605,... 8639, 8641, 8647, 8653, 8671, 8675, 8689, 8699, 8729, 8741,... 8759, 8765, 8771, 8795, 8797, 8825, 8831, 8841, 8855, 8859,... 8883, 8895, 8909, 8943, 8951, 8955, 8965, 8999, 9003, 9031,... 9045, 9049, 9071, 9073, 9085, 9095, 9101, 9109, 9123, 9129,... 9137, 9143, 9147, 9185, 9197, 9209, 9227, 9235, 9247, 9253,... 9257, 9277, 9297, 9303, 9313, 9325, 9343, 9347, 9371, 9373,... 9397, 9407, 9409, 9415, 9419, 9443, 9481, 9495, 9501, 9505,... 9517, 9529, 9555, 9557, 9571, 9585, 9591, 9607, 9611, 9621,... 9625, 9631, 9647, 9661, 9669, 9679, 9687, 9707, 9731, 9733,... 9745, 9773, 9791, 9803, 9811, 9817, 9833, 9847, 9851, 9863,... 9875, 9881, 9905, 9911, 9917, 9923, 9963, 9973,10003,10025,... 10043,10063,10071,10077,10091,10099,10105,10115,10129,10145,... 10169,10183,10187,10207,10223,10225,10247,10265,10271,10275,... 10289,10299,10301,10309,10343,10357,10373,10411,10413,10431,... 10445,10453,10463,10467,10473,10491,10505,10511,10513,10523,... 10539,10549,10559,10561,10571,10581,10615,10621,10625,10643,... 10655,10671,10679,10685,10691,10711,10739,10741,10755,10767,... 10781,10785,10803,10805,10829,10857,10863,10865,10875,10877,... 10917,10921,10929,10949,10967,10971,10987,10995,11009,11029,... 11043,11045,11055,11063,11075,11081,11117,11135,11141,11159,... 11163,11181,11187,11225,11237,11261,11279,11297,11307,11309,... 11327,11329,11341,11377,11403,11405,11413,11427,11439,11453,... 11461,11473,11479,11489,11495,11499,11533,11545,11561,11567,... 11575,11579,11589,11611,11623,11637,11657,11663,11687,11691,... 11701,11747,11761,11773,11783,11795,11797,11817,11849,11855,... 11867,11869,11873,11883,11919,11921,11927,11933,11947,11955,... 11961,11999,12027,12029,12037,12041,12049,12055,12095,12097,... 12107,12109,12121,12127,12133,12137,12181,12197,12207,12209,... 12239,12253,12263,12269,12277,12287,12295,12309,12313,12335,... 12361,12367,12391,12409,12415,12433,12449,12469,12479,12481,... 12499,12505,12517,12527,12549,12559,12597,12615,12621,12639,... 12643,12657,12667,12707,12713,12727,12741,12745,12763,12769,... 12779,12781,12787,12799,12809,12815,12829,12839,12857,12875,... 12883,12889,12901,12929,12947,12953,12959,12969,12983,12987,... 12995,13015,13019,13031,13063,13077,13103,13137,13149,13173,... 13207,13211,13227,13241,13249,13255,13269,13283,13285,13303,... 13307,13321,13339,13351,13377,13389,13407,13417,13431,13435,... 13447,13459,13465,13477,13501,13513,13531,13543,13561,13581,... 13599,13605,13617,13623,13637,13647,13661,13677,13683,13695,... 13725,13729,13753,13773,13781,13785,13795,13801,13807,13825,... 13835,13855,13861,13871,13883,13897,13905,13915,13939,13941,... 13969,13979,13981,13997,14027,14035,14037,14051,14063,14085,... 14095,14107,14113,14125,14137,14145,14151,14163,14193,14199,... 14219,14229,14233,14243,14277,14287,14289,14295,14301,14305,... 14323,14339,14341,14359,14365,14375,14387,14411,14425,14441,... 14449,14499,14513,14523,14537,14543,14561,14579,14585,14593,... 14599,14603,14611,14641,14671,14695,14701,14723,14725,14743,... 14753,14759,14765,14795,14797,14803,14831,14839,14845,14855,... 14889,14895,14909,14929,14941,14945,14951,14963,14965,14985,... 15033,15039,15053,15059,15061,15071,15077,15081,15099,15121,... 15147,15149,15157,15167,15187,15193,15203,15205,15215,15217,... 15223,15243,15257,15269,15273,15287,15291,15313,15335,15347,... 15359,15373,15379,15381,15391,15395,15397,15419,15439,15453,... 15469,15491,15503,15517,15527,15531,15545,15559,15593,15611,... 15613,15619,15639,15643,15649,15661,15667,15669,15681,15693,... 15717,15721,15741,15745,15765,15793,15799,15811,15825,15835,... 15847,15851,15865,15877,15881,15887,15899,15915,15935,15937,... 15955,15973,15977,16011,16035,16061,16069,16087,16093,16097,... 16121,16141,16153,16159,16165,16183,16189,16195,16197,16201,... 16209,16215,16225,16259,16265,16273,16299,16309,16355,16375,... 16381 ]; end if ( dim_num ~= dim_num_save ) % % Check parameters. % if ( dim_num < 2 | dim_max < dim_num ) fprintf ( 1, '\n' ); fprintf ( 1, 'I4_SOBOL - Fatal error!\n' ); fprintf ( 1, ' The spatial dimension DIM_NUM should satisfy:\n' ); fprintf ( 1, ' 2 <= DIM_NUM <= %d\n', dim_max ); fprintf ( 1, ' But this input value is DIM_NUM = %d\n', dim_num ); return end dim_num_save = dim_num; % % Set ATMOST = 2**LOG_MAX - 1. % atmost = 0; for i = 1 : log_max atmost = 2 * atmost + 1; end % % Find the highest 1 bit in ATMOST. % maxcol = i4_bit_hi1 ( atmost ); % % Initialize row 1 of V. % v(1,1:maxcol) = 1; % % Initialize the remaining rows of V. % for i = 2 : dim_num % % The bit pattern of the integer POLY(I) gives the form % of polynomial I. % % Find the degree of polynomial I from binary encoding. % j = poly(i); m = 0; while ( 1 ) j = floor ( j / 2 ); if ( j <= 0 ) break; end m = m + 1; end % % We expand this bit pattern to separate components of the % logical array INCLUD. % j = poly(i); for k = m : -1 : 1 j2 = floor ( j / 2 ); includ(k) = ( j ~= 2 * j2 ); j = j2; end % % Calculate the remaining elements of row I as explained % in Bratley and Fox, section 2. % for j = m + 1 : maxcol newv = v(i,j-m); l = 1; for k = 1 : m l = 2 * l; if ( includ(k) ) newv = i4_xor ( newv, l * v(i,j-k) ); % newv = bitxor ( newv, l * v(i,j-k) ); end end v(i,j) = newv; end end % % Multiply columns of V by appropriate power of 2. % l = 1; for j = maxcol-1 : -1 : 1 l = 2 * l; v(1:dim_num,j) = v(1:dim_num,j) * l; end % % RECIPD is 1/(common denominator of the elements in V). % recipd = 1.0 / ( 2 * l ); end seed = floor ( seed ); if ( seed < 0 ) seed = 0; end if ( seed == 0 ) l = 1; lastq(1:dim_num) = 0; elseif ( seed == seed_save + 1 ) % % Find the position of the right-hand zero in SEED. % l = i4_bit_lo0 ( seed ); elseif ( seed <= seed_save ) seed_save = 0; l = 1; lastq(1:dim_num) = 0; for seed_temp = seed_save : seed-1 l = i4_bit_lo0 ( seed_temp ); for i = 1 : dim_num lastq(i) = i4_xor ( lastq(i), v(i,l) ); % lastq(i) = bitxor ( lastq(i), v(i,l) ); end end l = i4_bit_lo0 ( seed ); elseif ( seed_save + 1 < seed ) for seed_temp = seed_save + 1 : seed-1 l = i4_bit_lo0 ( seed_temp ); for i = 1 : dim_num lastq(i) = i4_xor ( lastq(i), v(i,l) ); % lastq(i) = bitxor ( lastq(i), v(i,l) ); end end l = i4_bit_lo0 ( seed ); end % % Check that the user is not calling too many times! % if ( maxcol < l ) fprintf ( 1, '\n' ); fprintf ( 1, 'I4_SOBOL - Fatal error!\n' ); fprintf ( 1, ' Too many calls!\n' ); fprintf ( 1, ' MAXCOL = %d\n', maxcol ); fprintf ( 1, ' L = %d\n', l ); return end % % Calculate the new components of QUASI. % quasi(1:dim_num) = lastq(1:dim_num) * recipd; for i = 1 : dim_num lastq(i) = i4_xor ( lastq(i), v(i,l) ); % lastq(i) = bitxor ( lastq(i), v(i,l) ); end seed_save = seed; seed = seed + 1; return end