/*******************************************************************************
   This file is part of LibTMCG.

     [CS00]  Ronald Cramer, Victor Shoup: 'Signature schemes based on the
              strong RSA assumption', ACM Transactions on Information and
             System Security, Vol.3(3), pp. 161--185, 2000

     [RS00]  Jean-Francois Raymond, Anton Stiglic: 'Security Issues in the
              Diffie-Hellman Key Agreement Protocol', ZKS technical report
             http://citeseer.ist.psu.edu/455251.html

      [HAC]  Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone:
              'Handbook of Applied Cryptography', CRC Press, 1996.

 Copyright (C) 2004, 2005, 2006, 
               2016, 2017, 2018, 2019  Heiko Stamer <HeikoStamer@gmx.net>

   LibTMCG is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.

   LibTMCG is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with LibTMCG; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*******************************************************************************/

// include headers
#ifdef HAVE_CONFIG_H
	#include "libTMCG_config.h"
#endif
#include "mpz_sprime.hh"

// additional headers
#include <cstdio>
#include <cassert>
#include <iostream>
#include <stdexcept>
#include "mpz_srandom.hh"

#define PRIMES 668
#define MPRIMES 7836
#define SIEVE_SIZE 16

unsigned long int primes[] = {
	3, 5, 7, 11, 13, 17, 19, 23, 
	29, 31, 37, 41, 43, 47, 53, 59, 
	61, 67, 71, 73, 79, 83, 89, 97, 
	101, 103, 107, 109, 113, 127, 131, 137, 
	139, 149, 151, 157, 163, 167, 173, 179, 
	181, 191, 193, 197, 199, 211, 223, 227, 
	229, 233, 239, 241, 251, 257, 263, 269, 
	271, 277, 281, 283, 293, 307, 311, 313, 
	317, 331, 337, 347, 349, 353, 359, 367, 
	373, 379, 383, 389, 397, 401, 409, 419, 
	421, 431, 433, 439, 443, 449, 457, 461, 
	463, 467, 479, 487, 491, 499, 503, 509, 
	521, 523, 541, 547, 557, 563, 569, 571, 
	577, 587, 593, 599, 601, 607, 613, 617, 
	619, 631, 641, 643, 647, 653, 659, 661, 
	673, 677, 683, 691, 701, 709, 719, 727, 
	733, 739, 743, 751, 757, 761, 769, 773, 
	787, 797, 809, 811, 821, 823, 827, 829, 
	839, 853, 857, 859, 863, 877, 881, 883, 
	887, 907, 911, 919, 929, 937, 941, 947, 
	953, 967, 971, 977, 983, 991, 997, 1009, 
	1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 
	1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 
	1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 
	1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 
	1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 
	1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 
	1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 
	1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 
	1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 
	1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 
	1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 
	1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 
	1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 
	1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 
	1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 
	1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 
	1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 
	2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 
	2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 
	2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 
	2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 
	2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 
	2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 
	2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 
	2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 
	2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 
	2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 
	2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 
	2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 
	2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 
	2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 
	2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 
	2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 
	3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 
	3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 
	3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 
	3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 
	3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 
	3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 
	3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 
	3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 
	3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 
	3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 
	3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 
	3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 
	3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 
	3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 
	3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 
	4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 
	4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 
	4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 
	4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 
	4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 
	4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 
	4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 
	4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 
	4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 
	4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 
	4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 
	4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 
	4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 
	4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 
	4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 
	5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 
	5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 
	5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 
	5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 
	5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 
	5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 
	5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 
	5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 
	5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 
	5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 
	5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 
	5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 
	5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 
	5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 
	6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 
	6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 
	6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 
	6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 
	6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 
	6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 
	6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 
	6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 
	6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 
	6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 
	6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 
	6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 
	6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 
	6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 
	6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 
	7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 
	7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 
	7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 
	7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 
	7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 
	7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 
	7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 
	7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 
	7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 
	7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 
	7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 
	7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 
	7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 
	8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 
	8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 
	8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 
	8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 
	8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 
	8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 
	8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 
	8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 
	8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 
	8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 
	8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 
	8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 
	8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 
	8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 
	9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 
	9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 
	9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 
	9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 
	9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 
	9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 
	9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 
	9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 
	9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 
	9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 
	9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 
	9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 
	9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 
	9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 
	10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 
	10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 
	10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 
	10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 
	10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 
	10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 
	10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 
	10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 
	10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 
	10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 
	10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 
	10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 
	10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 
	11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 
	11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 
	11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 
	11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 
	11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 
	11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 
	11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 
	11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 
	11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 
	11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 
	11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 
	11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 
	11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 
	12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 
	12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 
	12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 
	12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 
	12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 
	12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 
	12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 
	12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 
	12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 
	12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 
	12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 
	12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 
	12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 
	12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 
	13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 
	13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 
	13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 
	13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 
	13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 
	13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 
	13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 
	13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 
	13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 
	13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 
	13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 
	13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 
	13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 
	14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 
	14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 
	14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 
	14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 
	14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 
	14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 
	14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 
	14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 
	14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 
	14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 
	14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 
	14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 
	14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 
	15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 
	15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 
	15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 
	15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 
	15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 
	15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 
	15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 
	15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 
	15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 
	15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 
	15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 
	15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 
	15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 
	16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 
	16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 
	16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 
	16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 
	16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 
	16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 
	16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 
	16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 
	16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 
	16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 
	16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 
	16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 
	17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 
	17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 
	17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 
	17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 
	17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 
	17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 
	17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 
	17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 
	17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 
	17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 
	17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 
	17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 
	17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 
	18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 
	18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 
	18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 
	18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 
	18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 
	18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 
	18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 
	18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 
	18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 
	18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 
	18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 
	18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 
	19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 
	19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 
	19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 
	19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 
	19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 
	19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 
	19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 
	19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 
	19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 
	19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 
	19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 
	19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 
	19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 
	20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 
	20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 
	20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 
	20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 
	20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 
	20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 
	20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 
	20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 
	20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 
	20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 
	20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 
	20929, 20939, 20947, 20959, 20963, 20981, 20983, 21001, 
	21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 
	21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 
	21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 
	21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 
	21319, 21323, 21341, 21347, 21377, 21379, 21383, 21391, 
	21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 
	21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 
	21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 
	21601, 21611, 21613, 21617, 21647, 21649, 21661, 21673, 
	21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 
	21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 
	21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 
	21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 
	22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 
	22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129, 
	22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 
	22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 
	22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 
	22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 
	22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 
	22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 
	22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 
	22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777, 
	22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 
	22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 
	22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 
	23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 
	23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 
	23173, 23189, 23197, 23201, 23203, 23209, 23227, 23251, 
	23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 
	23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 
	23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 
	23549, 23557, 23561, 23563, 23567, 23581, 23593, 23599, 
	23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 
	23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, 
	23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 
	23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887, 
	23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 
	23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 
	24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 
	24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 
	24169, 24179, 24181, 24197, 24203, 24223, 24229, 24239, 
	24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 
	24373, 24379, 24391, 24407, 24413, 24419, 24421, 24439, 
	24443, 24469, 24473, 24481, 24499, 24509, 24517, 24527, 
	24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 
	24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 
	24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 
	24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 
	24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 
	24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 
	25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 
	25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 
	25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 
	25339, 25343, 25349, 25357, 25367, 25373, 25391, 25409, 
	25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 
	25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 
	25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 
	25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733, 
	25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 
	25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 
	25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 
	25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 
	26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 
	26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 
	26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 
	26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 
	26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 
	26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 
	26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 
	26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 
	26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 
	26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 
	26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 
	26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993, 
	27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 
	27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179, 
	27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 
	27277, 27281, 27283, 27299, 27329, 27337, 27361, 27367, 
	27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 
	27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 
	27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 
	27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 
	27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791, 
	27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 
	27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 
	27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 
	28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 
	28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 
	28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 
	28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 
	28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 
	28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 
	28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 
	28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 
	28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 
	28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 
	28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 
	28901, 28909, 28921, 28927, 28933, 28949, 28961, 28979, 
	29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 
	29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 
	29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 
	29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 
	29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 
	29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 
	29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 
	29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 
	29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 
	29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 
	29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 
	29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 
	30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 
	30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 
	30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 
	30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 
	30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 
	30469, 30491, 30493, 30497, 30509, 30517, 30529, 30539, 
	30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 
	30649, 30661, 30671, 30677, 30689, 30697, 30703, 30707, 
	30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 
	30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 
	30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 
	30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, 
	31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 
	31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189, 
	31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 
	31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 
	31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 
	31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 
	31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 
	31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 
	31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 
	31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 
	31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, 
	32009, 32027, 32029, 32051, 32057, 32059, 32063, 32069, 
	32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 
	32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 
	32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 
	32321, 32323, 32327, 32341, 32353, 32359, 32363, 32369, 
	32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 
	32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 
	32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 
	32587, 32603, 32609, 32611, 32621, 32633, 32647, 32653, 
	32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 
	32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, 
	32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 
	32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993, 
	32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 
	33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 
	33161, 33179, 33181, 33191, 33199, 33203, 33211, 33223, 
	33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 
	33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 
	33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 
	33493, 33503, 33521, 33529, 33533, 33547, 33563, 33569, 
	33577, 33581, 33587, 33589, 33599, 33601, 33613, 33617, 
	33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 
	33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 
	33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 
	33857, 33863, 33871, 33889, 33893, 33911, 33923, 33931, 
	33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 
	34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 
	34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 
	34253, 34259, 34261, 34267, 34273, 34283, 34297, 34301, 
	34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 
	34369, 34381, 34403, 34421, 34429, 34439, 34457, 34469, 
	34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 
	34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, 
	34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 
	34693, 34703, 34721, 34729, 34739, 34747, 34757, 34759, 
	34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 
	34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 
	34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059, 
	35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 
	35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221, 
	35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 
	35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 
	35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 
	35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 
	35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 
	35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771, 
	35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 
	35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 
	35951, 35963, 35969, 35977, 35983, 35993, 35999, 36007, 
	36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 
	36097, 36107, 36109, 36131, 36137, 36151, 36161, 36187, 
	36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 
	36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343, 
	36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 
	36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, 
	36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 
	36607, 36629, 36637, 36643, 36653, 36671, 36677, 36683, 
	36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 
	36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 
	36833, 36847, 36857, 36871, 36877, 36887, 36899, 36901, 
	36913, 36919, 36923, 36929, 36931, 36943, 36947, 36973, 
	36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 
	37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 
	37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 
	37253, 37273, 37277, 37307, 37309, 37313, 37321, 37337, 
	37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, 
	37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 
	37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 
	37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 
	37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 
	37717, 37747, 37781, 37783, 37799, 37811, 37813, 37831, 
	37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 
	37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997, 
	38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 
	38149, 38153, 38167, 38177, 38183, 38189, 38197, 38201, 
	38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287, 
	38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 
	38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 
	38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 
	38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 
	38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 
	38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 
	38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 
	38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 
	38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 
	39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 
	39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 
	39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 
	39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 
	39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 
	39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 
	39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 
	39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 
	39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827, 
	39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 
	39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 
	39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 
	40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 
	40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, 
	40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 
	40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459, 
	40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 
	40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 
	40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 
	40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 
	40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 
	40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 
	40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 
	41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 
	41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 
	41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 
	41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 
	41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 
	41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 
	41549, 41579, 41593, 41597, 41603, 41609, 41611, 41617, 
	41621, 41627, 41641, 41647, 41651, 41659, 41669, 41681, 
	41687, 41719, 41729, 41737, 41759, 41761, 41771, 41777, 
	41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 
	41887, 41893, 41897, 41903, 41911, 41927, 41941, 41947, 
	41953, 41957, 41959, 41969, 41981, 41983, 41999, 42013, 
	42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083, 
	42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 
	42187, 42193, 42197, 42209, 42221, 42223, 42227, 42239, 
	42257, 42281, 42283, 42293, 42299, 42307, 42323, 42331, 
	42337, 42349, 42359, 42373, 42379, 42391, 42397, 42403, 
	42407, 42409, 42433, 42437, 42443, 42451, 42457, 42461, 
	42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 
	42557, 42569, 42571, 42577, 42589, 42611, 42641, 42643, 
	42649, 42667, 42677, 42683, 42689, 42697, 42701, 42703, 
	42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773, 
	42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 
	42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 
	42953, 42961, 42967, 42979, 42989, 43003, 43013, 43019, 
	43037, 43049, 43051, 43063, 43067, 43093, 43103, 43117, 
	43133, 43151, 43159, 43177, 43189, 43201, 43207, 43223, 
	43237, 43261, 43271, 43283, 43291, 43313, 43319, 43321, 
	43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 
	43451, 43457, 43481, 43487, 43499, 43517, 43541, 43543, 
	43573, 43577, 43579, 43591, 43597, 43607, 43609, 43613, 
	43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 
	43717, 43721, 43753, 43759, 43777, 43781, 43783, 43787, 
	43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 
	43933, 43943, 43951, 43961, 43963, 43969, 43973, 43987, 
	43991, 43997, 44017, 44021, 44027, 44029, 44041, 44053, 
	44059, 44071, 44087, 44089, 44101, 44111, 44119, 44123, 
	44129, 44131, 44159, 44171, 44179, 44189, 44201, 44203, 
	44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 
	44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383, 
	44389, 44417, 44449, 44453, 44483, 44491, 44497, 44501, 
	44507, 44519, 44531, 44533, 44537, 44543, 44549, 44563, 
	44579, 44587, 44617, 44621, 44623, 44633, 44641, 44647, 
	44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 
	44741, 44753, 44771, 44773, 44777, 44789, 44797, 44809, 
	44819, 44839, 44843, 44851, 44867, 44879, 44887, 44893, 
	44909, 44917, 44927, 44939, 44953, 44959, 44963, 44971, 
	44983, 44987, 45007, 45013, 45053, 45061, 45077, 45083, 
	45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 
	45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 
	45289, 45293, 45307, 45317, 45319, 45329, 45337, 45341, 
	45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 
	45439, 45481, 45491, 45497, 45503, 45523, 45533, 45541, 
	45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 
	45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 
	45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 
	45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, 
	45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989, 
	46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 
	46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 
	46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 
	46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 
	46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 
	46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 
	46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 
	46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 
	46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 
	46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 
	46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 
	46993, 46997, 47017, 47041, 47051, 47057, 47059, 47087, 
	47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 
	47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 
	47279, 47287, 47293, 47297, 47303, 47309, 47317, 47339, 
	47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 
	47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 
	47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 
	47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 
	47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 
	47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 
	47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 
	47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 
	47981, 48017, 48023, 48029, 48049, 48073, 48079, 48091, 
	48109, 48119, 48121, 48131, 48157, 48163, 48179, 48187, 
	48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 
	48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383, 
	48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 
	48479, 48481, 48487, 48491, 48497, 48523, 48527, 48533, 
	48539, 48541, 48563, 48571, 48589, 48593, 48611, 48619, 
	48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 
	48733, 48751, 48757, 48761, 48767, 48779, 48781, 48787, 
	48799, 48809, 48817, 48821, 48823, 48847, 48857, 48859, 
	48869, 48871, 48883, 48889, 48907, 48947, 48953, 48973, 
	48989, 48991, 49003, 49009, 49019, 49031, 49033, 49037, 
	49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 
	49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 
	49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 
	49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 
	49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 
	49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 
	49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 
	49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 
	49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 
	49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 
	49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 
	49957, 49991, 49993, 49999, 50021, 50023, 50033, 50047, 
	50051, 50053, 50069, 50077, 50087, 50093, 50101, 50111, 
	50119, 50123, 50129, 50131, 50147, 50153, 50159, 50177, 
	50207, 50221, 50227, 50231, 50261, 50263, 50273, 50287, 
	50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 
	50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 
	50461, 50497, 50503, 50513, 50527, 50539, 50543, 50549, 
	50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, 
	50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 
	50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 
	50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 
	50957, 50969, 50971, 50989, 50993, 51001, 51031, 51043, 
	51047, 51059, 51061, 51071, 51109, 51131, 51133, 51137, 
	51151, 51157, 51169, 51193, 51197, 51199, 51203, 51217, 
	51229, 51239, 51241, 51257, 51263, 51283, 51287, 51307, 
	51329, 51341, 51343, 51347, 51349, 51361, 51383, 51407, 
	51413, 51419, 51421, 51427, 51431, 51437, 51439, 51449, 
	51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 
	51521, 51539, 51551, 51563, 51577, 51581, 51593, 51599, 
	51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 
	51683, 51691, 51713, 51719, 51721, 51749, 51767, 51769, 
	51787, 51797, 51803, 51817, 51827, 51829, 51839, 51853, 
	51859, 51869, 51871, 51893, 51899, 51907, 51913, 51929, 
	51941, 51949, 51971, 51973, 51977, 51991, 52009, 52021, 
	52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 
	52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 
	52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 
	52291, 52301, 52313, 52321, 52361, 52363, 52369, 52379, 
	52387, 52391, 52433, 52453, 52457, 52489, 52501, 52511, 
	52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 
	52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 
	52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747, 
	52757, 52769, 52783, 52807, 52813, 52817, 52837, 52859, 
	52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 
	52951, 52957, 52963, 52967, 52973, 52981, 52999, 53003, 
	53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 
	53101, 53113, 53117, 53129, 53147, 53149, 53161, 53171, 
	53173, 53189, 53197, 53201, 53231, 53233, 53239, 53267, 
	53269, 53279, 53281, 53299, 53309, 53323, 53327, 53353, 
	53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 
	53441, 53453, 53479, 53503, 53507, 53527, 53549, 53551, 
	53569, 53591, 53593, 53597, 53609, 53611, 53617, 53623, 
	53629, 53633, 53639, 53653, 53657, 53681, 53693, 53699, 
	53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791, 
	53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 
	53891, 53897, 53899, 53917, 53923, 53927, 53939, 53951, 
	53959, 53987, 53993, 54001, 54011, 54013, 54037, 54049, 
	54059, 54083, 54091, 54101, 54121, 54133, 54139, 54151, 
	54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 
	54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 
	54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 
	54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, 
	54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 
	54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 
	54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 
	54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 
	54851, 54869, 54877, 54881, 54907, 54917, 54919, 54941, 
	54949, 54959, 54973, 54979, 54983, 55001, 55009, 55021, 
	55049, 55051, 55057, 55061, 55073, 55079, 55103, 55109, 
	55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 
	55217, 55219, 55229, 55243, 55249, 55259, 55291, 55313, 
	55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 
	55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 
	55511, 55529, 55541, 55547, 55579, 55589, 55603, 55609, 
	55619, 55621, 55631, 55633, 55639, 55661, 55663, 55667, 
	55673, 55681, 55691, 55697, 55711, 55717, 55721, 55733, 
	55763, 55787, 55793, 55799, 55807, 55813, 55817, 55819, 
	55823, 55829, 55837, 55843, 55849, 55871, 55889, 55897, 
	55901, 55903, 55921, 55927, 55931, 55933, 55949, 55967, 
	55987, 55997, 56003, 56009, 56039, 56041, 56053, 56081, 
	56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149, 
	56167, 56171, 56179, 56197, 56207, 56209, 56237, 56239, 
	56249, 56263, 56267, 56269, 56299, 56311, 56333, 56359, 
	56369, 56377, 56383, 56393, 56401, 56417, 56431, 56437, 
	56443, 56453, 56467, 56473, 56477, 56479, 56489, 56501, 
	56503, 56509, 56519, 56527, 56531, 56533, 56543, 56569, 
	56591, 56597, 56599, 56611, 56629, 56633, 56659, 56663, 
	56671, 56681, 56687, 56701, 56711, 56713, 56731, 56737, 
	56747, 56767, 56773, 56779, 56783, 56807, 56809, 56813, 
	56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897, 
	56909, 56911, 56921, 56923, 56929, 56941, 56951, 56957, 
	56963, 56983, 56989, 56993, 56999, 57037, 57041, 57047, 
	57059, 57073, 57077, 57089, 57097, 57107, 57119, 57131, 
	57139, 57143, 57149, 57163, 57173, 57179, 57191, 57193, 
	57203, 57221, 57223, 57241, 57251, 57259, 57269, 57271, 
	57283, 57287, 57301, 57329, 57331, 57347, 57349, 57367, 
	57373, 57383, 57389, 57397, 57413, 57427, 57457, 57467, 
	57487, 57493, 57503, 57527, 57529, 57557, 57559, 57571, 
	57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667, 
	57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 
	57737, 57751, 57773, 57781, 57787, 57791, 57793, 57803, 
	57809, 57829, 57839, 57847, 57853, 57859, 57881, 57899, 
	57901, 57917, 57923, 57943, 57947, 57973, 57977, 57991, 
	58013, 58027, 58031, 58043, 58049, 58057, 58061, 58067, 
	58073, 58099, 58109, 58111, 58129, 58147, 58151, 58153, 
	58169, 58171, 58189, 58193, 58199, 58207, 58211, 58217, 
	58229, 58231, 58237, 58243, 58271, 58309, 58313, 58321, 
	58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403, 
	58411, 58417, 58427, 58439, 58441, 58451, 58453, 58477, 
	58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 
	58601, 58603, 58613, 58631, 58657, 58661, 58679, 58687, 
	58693, 58699, 58711, 58727, 58733, 58741, 58757, 58763, 
	58771, 58787, 58789, 58831, 58889, 58897, 58901, 58907, 
	58909, 58913, 58921, 58937, 58943, 58963, 58967, 58979, 
	58991, 58997, 59009, 59011, 59021, 59023, 59029, 59051, 
	59053, 59063, 59069, 59077, 59083, 59093, 59107, 59113, 
	59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197, 
	59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 
	59273, 59281, 59333, 59341, 59351, 59357, 59359, 59369, 
	59377, 59387, 59393, 59399, 59407, 59417, 59419, 59441, 
	59443, 59447, 59453, 59467, 59471, 59473, 59497, 59509, 
	59513, 59539, 59557, 59561, 59567, 59581, 59611, 59617, 
	59621, 59627, 59629, 59651, 59659, 59663, 59669, 59671, 
	59693, 59699, 59707, 59723, 59729, 59743, 59747, 59753, 
	59771, 59779, 59791, 59797, 59809, 59833, 59863, 59879, 
	59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999, 
	60013, 60017, 60029, 60037, 60041, 60077, 60083, 60089, 
	60091, 60101, 60103, 60107, 60127, 60133, 60139, 60149, 
	60161, 60167, 60169, 60209, 60217, 60223, 60251, 60257, 
	60259, 60271, 60289, 60293, 60317, 60331, 60337, 60343, 
	60353, 60373, 60383, 60397, 60413, 60427, 60443, 60449, 
	60457, 60493, 60497, 60509, 60521, 60527, 60539, 60589, 
	60601, 60607, 60611, 60617, 60623, 60631, 60637, 60647, 
	60649, 60659, 60661, 60679, 60689, 60703, 60719, 60727, 
	60733, 60737, 60757, 60761, 60763, 60773, 60779, 60793, 
	60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 
	60913, 60917, 60919, 60923, 60937, 60943, 60953, 60961, 
	61001, 61007, 61027, 61031, 61043, 61051, 61057, 61091, 
	61099, 61121, 61129, 61141, 61151, 61153, 61169, 61211, 
	61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 
	61333, 61339, 61343, 61357, 61363, 61379, 61381, 61403, 
	61409, 61417, 61441, 61463, 61469, 61471, 61483, 61487, 
	61493, 61507, 61511, 61519, 61543, 61547, 61553, 61559, 
	61561, 61583, 61603, 61609, 61613, 61627, 61631, 61637, 
	61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 
	61717, 61723, 61729, 61751, 61757, 61781, 61813, 61819, 
	61837, 61843, 61861, 61871, 61879, 61909, 61927, 61933, 
	61949, 61961, 61967, 61979, 61981, 61987, 61991, 62003, 
	62011, 62017, 62039, 62047, 62053, 62057, 62071, 62081, 
	62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, 
	62189, 62191, 62201, 62207, 62213, 62219, 62233, 62273, 
	62297, 62299, 62303, 62311, 62323, 62327, 62347, 62351, 
	62383, 62401, 62417, 62423, 62459, 62467, 62473, 62477, 
	62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 
	62581, 62591, 62597, 62603, 62617, 62627, 62633, 62639, 
	62653, 62659, 62683, 62687, 62701, 62723, 62731, 62743, 
	62753, 62761, 62773, 62791, 62801, 62819, 62827, 62851, 
	62861, 62869, 62873, 62897, 62903, 62921, 62927, 62929, 
	62939, 62969, 62971, 62981, 62983, 62987, 62989, 63029, 
	63031, 63059, 63067, 63073, 63079, 63097, 63103, 63113, 
	63127, 63131, 63149, 63179, 63197, 63199, 63211, 63241, 
	63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331, 
	63337, 63347, 63353, 63361, 63367, 63377, 63389, 63391, 
	63397, 63409, 63419, 63421, 63439, 63443, 63463, 63467, 
	63473, 63487, 63493, 63499, 63521, 63527, 63533, 63541, 
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	63617, 63629, 63647, 63649, 63659, 63667, 63671, 63689, 
	63691, 63697, 63703, 63709, 63719, 63727, 63737, 63743, 
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	63839, 63841, 63853, 63857, 63863, 63901, 63907, 63913, 
	63929, 63949, 63977, 63997, 64007, 64013, 64019, 64033, 
	64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, 
	64153, 64157, 64171, 64187, 64189, 64217, 64223, 64231, 
	64237, 64271, 64279, 64283, 64301, 64303, 64319, 64327, 
	64333, 64373, 64381, 64399, 64403, 64433, 64439, 64451, 
	64453, 64483, 64489, 64499, 64513, 64553, 64567, 64577, 
	64579, 64591, 64601, 64609, 64613, 64621, 64627, 64633, 
	64661, 64663, 64667, 64679, 64693, 64709, 64717, 64747, 
	64763, 64781, 64783, 64793, 64811, 64817, 64849, 64853, 
	64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 
	64937, 64951, 64969, 64997, 65003, 65011, 65027, 65029, 
	65033, 65053, 65063, 65071, 65089, 65099, 65101, 65111, 
	65119, 65123, 65129, 65141, 65147, 65167, 65171, 65173, 
	65179, 65183, 65203, 65213, 65239, 65257, 65267, 65269, 
	65287, 65293, 65309, 65323, 65327, 65353, 65357, 65371, 
	65381, 65393, 65407, 65413, 65419, 65423, 65437, 65447, 
	65449, 65479, 65497, 65519, 65521, 65537, 65539, 65543, 
	65551, 65557, 65563, 65579, 65581, 65587, 65599, 65609, 
	65617, 65629, 65633, 65647, 65651, 65657, 65677, 65687, 
	65699, 65701, 65707, 65713, 65717, 65719, 65729, 65731, 
	65761, 65777, 65789, 65809, 65827, 65831, 65837, 65839, 
	65843, 65851, 65867, 65881, 65899, 65921, 65927, 65929, 
	65951, 65957, 65963, 65981, 65983, 65993, 66029, 66037, 
	66041, 66047, 66067, 66071, 66083, 66089, 66103, 66107, 
	66109, 66137, 66161, 66169, 66173, 66179, 66191, 66221, 
	66239, 66271, 66293, 66301, 66337, 66343, 66347, 66359, 
	66361, 66373, 66377, 66383, 66403, 66413, 66431, 66449, 
	66457, 66463, 66467, 66491, 66499, 66509, 66523, 66529, 
	66533, 66541, 66553, 66569, 66571, 66587, 66593, 66601, 
	66617, 66629, 66643, 66653, 66683, 66697, 66701, 66713, 
	66721, 66733, 66739, 66749, 66751, 66763, 66791, 66797, 
	66809, 66821, 66841, 66851, 66853, 66863, 66877, 66883, 
	66889, 66919, 66923, 66931, 66943, 66947, 66949, 66959, 
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	67061, 67073, 67079, 67103, 67121, 67129, 67139, 67141, 
	67153, 67157, 67169, 67181, 67187, 67189, 67211, 67213, 
	67217, 67219, 67231, 67247, 67261, 67271, 67273, 67289, 
	67307, 67339, 67343, 67349, 67369, 67391, 67399, 67409, 
	67411, 67421, 67427, 67429, 67433, 67447, 67453, 67477, 
	67481, 67489, 67493, 67499, 67511, 67523, 67531, 67537, 
	67547, 67559, 67567, 67577, 67579, 67589, 67601, 67607, 
	67619, 67631, 67651, 67679, 67699, 67709, 67723, 67733, 
	67741, 67751, 67757, 67759, 67763, 67777, 67783, 67789, 
	67801, 67807, 67819, 67829, 67843, 67853, 67867, 67883, 
	67891, 67901, 67927, 67931, 67933, 67939, 67943, 67957, 
	67961, 67967, 67979, 67987, 67993, 68023, 68041, 68053, 
	68059, 68071, 68087, 68099, 68111, 68113, 68141, 68147, 
	68161, 68171, 68207, 68209, 68213, 68219, 68227, 68239, 
	68261, 68279, 68281, 68311, 68329, 68351, 68371, 68389, 
	68399, 68437, 68443, 68447, 68449, 68473, 68477, 68483, 
	68489, 68491, 68501, 68507, 68521, 68531, 68539, 68543, 
	68567, 68581, 68597, 68611, 68633, 68639, 68659, 68669, 
	68683, 68687, 68699, 68711, 68713, 68729, 68737, 68743, 
	68749, 68767, 68771, 68777, 68791, 68813, 68819, 68821, 
	68863, 68879, 68881, 68891, 68897, 68899, 68903, 68909, 
	68917, 68927, 68947, 68963, 68993, 69001, 69011, 69019, 
	69029, 69031, 69061, 69067, 69073, 69109, 69119, 69127, 
	69143, 69149, 69151, 69163, 69191, 69193, 69197, 69203, 
	69221, 69233, 69239, 69247, 69257, 69259, 69263, 69313, 
	69317, 69337, 69341, 69371, 69379, 69383, 69389, 69401, 
	69403, 69427, 69431, 69439, 69457, 69463, 69467, 69473, 
	69481, 69491, 69493, 69497, 69499, 69539, 69557, 69593, 
	69623, 69653, 69661, 69677, 69691, 69697, 69709, 69737, 
	69739, 69761, 69763, 69767, 69779, 69809, 69821, 69827, 
	69829, 69833, 69847, 69857, 69859, 69877, 69899, 69911, 
	69929, 69931, 69941, 69959, 69991, 69997, 70001, 70003, 
	70009, 70019, 70039, 70051, 70061, 70067, 70079, 70099, 
	70111, 70117, 70121, 70123, 70139, 70141, 70157, 70163, 
	70177, 70181, 70183, 70199, 70201, 70207, 70223, 70229, 
	70237, 70241, 70249, 70271, 70289, 70297, 70309, 70313, 
	70321, 70327, 70351, 70373, 70379, 70381, 70393, 70423, 
	70429, 70439, 70451, 70457, 70459, 70481, 70487, 70489, 
	70501, 70507, 70529, 70537, 70549, 70571, 70573, 70583, 
	70589, 70607, 70619, 70621, 70627, 70639, 70657, 70663, 
	70667, 70687, 70709, 70717, 70729, 70753, 70769, 70783, 
	70793, 70823, 70841, 70843, 70849, 70853, 70867, 70877, 
	70879, 70891, 70901, 70913, 70919, 70921, 70937, 70949, 
	70951, 70957, 70969, 70979, 70981, 70991, 70997, 70999, 
	71011, 71023, 71039, 71059, 71069, 71081, 71089, 71119, 
	71129, 71143, 71147, 71153, 71161, 71167, 71171, 71191, 
	71209, 71233, 71237, 71249, 71257, 71261, 71263, 71287, 
	71293, 71317, 71327, 71329, 71333, 71339, 71341, 71347, 
	71353, 71359, 71363, 71387, 71389, 71399, 71411, 71413, 
	71419, 71429, 71437, 71443, 71453, 71471, 71473, 71479, 
	71483, 71503, 71527, 71537, 71549, 71551, 71563, 71569, 
	71593, 71597, 71633, 71647, 71663, 71671, 71693, 71699, 
	71707, 71711, 71713, 71719, 71741, 71761, 71777, 71789, 
	71807, 71809, 71821, 71837, 71843, 71849, 71861, 71867, 
	71879, 71881, 71887, 71899, 71909, 71917, 71933, 71941, 
	71947, 71963, 71971, 71983, 71987, 71993, 71999, 72019, 
	72031, 72043, 72047, 72053, 72073, 72077, 72089, 72091, 
	72101, 72103, 72109, 72139, 72161, 72167, 72169, 72173, 
	72211, 72221, 72223, 72227, 72229, 72251, 72253, 72269, 
	72271, 72277, 72287, 72307, 72313, 72337, 72341, 72353, 
	72367, 72379, 72383, 72421, 72431, 72461, 72467, 72469, 
	72481, 72493, 72497, 72503, 72533, 72547, 72551, 72559, 
	72577, 72613, 72617, 72623, 72643, 72647, 72649, 72661, 
	72671, 72673, 72679, 72689, 72701, 72707, 72719, 72727, 
	72733, 72739, 72763, 72767, 72797, 72817, 72823, 72859, 
	72869, 72871, 72883, 72889, 72893, 72901, 72907, 72911, 
	72923, 72931, 72937, 72949, 72953, 72959, 72973, 72977, 
	72997, 73009, 73013, 73019, 73037, 73039, 73043, 73061, 
	73063, 73079, 73091, 73121, 73127, 73133, 73141, 73181, 
	73189, 73237, 73243, 73259, 73277, 73291, 73303, 73309, 
	73327, 73331, 73351, 73361, 73363, 73369, 73379, 73387, 
	73417, 73421, 73433, 73453, 73459, 73471, 73477, 73483, 
	73517, 73523, 73529, 73547, 73553, 73561, 73571, 73583, 
	73589, 73597, 73607, 73609, 73613, 73637, 73643, 73651, 
	73673, 73679, 73681, 73693, 73699, 73709, 73721, 73727, 
	73751, 73757, 73771, 73783, 73819, 73823, 73847, 73849, 
	73859, 73867, 73877, 73883, 73897, 73907, 73939, 73943, 
	73951, 73961, 73973, 73999, 74017, 74021, 74027, 74047, 
	74051, 74071, 74077, 74093, 74099, 74101, 74131, 74143, 
	74149, 74159, 74161, 74167, 74177, 74189, 74197, 74201, 
	74203, 74209, 74219, 74231, 74257, 74279, 74287, 74293, 
	74297, 74311, 74317, 74323, 74353, 74357, 74363, 74377, 
	74381, 74383, 74411, 74413, 74419, 74441, 74449, 74453, 
	74471, 74489, 74507, 74509, 74521, 74527, 74531, 74551, 
	74561, 74567, 74573, 74587, 74597, 74609, 74611, 74623, 
	74653, 74687, 74699, 74707, 74713, 74717, 74719, 74729, 
	74731, 74747, 74759, 74761, 74771, 74779, 74797, 74821, 
	74827, 74831, 74843, 74857, 74861, 74869, 74873, 74887, 
	74891, 74897, 74903, 74923, 74929, 74933, 74941, 74959, 
	75011, 75013, 75017, 75029, 75037, 75041, 75079, 75083, 
	75109, 75133, 75149, 75161, 75167, 75169, 75181, 75193, 
	75209, 75211, 75217, 75223, 75227, 75239, 75253, 75269, 
	75277, 75289, 75307, 75323, 75329, 75337, 75347, 75353, 
	75367, 75377, 75389, 75391, 75401, 75403, 75407, 75431, 
	75437, 75479, 75503, 75511, 75521, 75527, 75533, 75539, 
	75541, 75553, 75557, 75571, 75577, 75583, 75611, 75617, 
	75619, 75629, 75641, 75653, 75659, 75679, 75683, 75689, 
	75703, 75707, 75709, 75721, 75731, 75743, 75767, 75773, 
	75781, 75787, 75793, 75797, 75821, 75833, 75853, 75869, 
	75883, 75913, 75931, 75937, 75941, 75967, 75979, 75983, 
	75989, 75991, 75997, 76001, 76003, 76031, 76039, 76079, 
	76081, 76091, 76099, 76103, 76123, 76129, 76147, 76157, 
	76159, 76163, 76207, 76213, 76231, 76243, 76249, 76253, 
	76259, 76261, 76283, 76289, 76303, 76333, 76343, 76367, 
	76369, 76379, 76387, 76403, 76421, 76423, 76441, 76463, 
	76471, 76481, 76487, 76493, 76507, 76511, 76519, 76537, 
	76541, 76543, 76561, 76579, 76597, 76603, 76607, 76631, 
	76649, 76651, 76667, 76673, 76679, 76697, 76717, 76733, 
	76753, 76757, 76771, 76777, 76781, 76801, 76819, 76829, 
	76831, 76837, 76847, 76871, 76873, 76883, 76907, 76913, 
	76919, 76943, 76949, 76961, 76963, 76991, 77003, 77017, 
	77023, 77029, 77041, 77047, 77069, 77081, 77093, 77101, 
	77137, 77141, 77153, 77167, 77171, 77191, 77201, 77213, 
	77237, 77239, 77243, 77249, 77261, 77263, 77267, 77269, 
	77279, 77291, 77317, 77323, 77339, 77347, 77351, 77359, 
	77369, 77377, 77383, 77417, 77419, 77431, 77447, 77471, 
	77477, 77479, 77489, 77491, 77509, 77513, 77521, 77527, 
	77543, 77549, 77551, 77557, 77563, 77569, 77573, 77587, 
	77591, 77611, 77617, 77621, 77641, 77647, 77659, 77681, 
	77687, 77689, 77699, 77711, 77713, 77719, 77723, 77731, 
	77743, 77747, 77761, 77773, 77783, 77797, 77801, 77813, 
	77839, 77849, 77863, 77867, 77893, 77899, 77929, 77933, 
	77951, 77969, 77977, 77983, 77999, 78007, 78017, 78031, 
	78041, 78049, 78059, 78079, 78101, 78121, 78137, 78139, 
	78157, 78163, 78167, 78173, 78179, 78191, 78193, 78203, 
	78229, 78233, 78241, 78259, 78277, 78283, 78301, 78307, 
	78311, 78317, 78341, 78347, 78367, 78401, 78427, 78437, 
	78439, 78467, 78479, 78487, 78497, 78509, 78511, 78517, 
	78539, 78541, 78553, 78569, 78571, 78577, 78583, 78593, 
	78607, 78623, 78643, 78649, 78653, 78691, 78697, 78707, 
	78713, 78721, 78737, 78779, 78781, 78787, 78791, 78797, 
	78803, 78809, 78823, 78839, 78853, 78857, 78877, 78887, 
	78889, 78893, 78901, 78919, 78929, 78941, 78977, 78979, 
	78989, 79031, 79039, 79043, 79063, 79087, 79103, 79111, 
	79133, 79139, 79147, 79151, 79153, 79159, 79181, 79187, 
	79193, 79201, 79229, 79231, 79241, 79259, 79273, 79279, 
	79283, 79301, 79309, 79319, 79333, 79337, 79349, 79357, 
	79367, 79379, 79393, 79397, 79399, 79411, 79423, 79427, 
	79433, 79451, 79481, 79493, 79531, 79537, 79549, 79559, 
	79561, 79579, 79589, 79601, 79609, 79613, 79621, 79627, 
	79631, 79633, 79657, 79669, 79687, 79691, 79693, 79697, 
	79699, 79757, 79769, 79777, 79801, 79811, 79813, 79817, 
	79823, 79829, 79841, 79843, 79847, 79861, 79867, 79873, 
	79889, 79901, 79903, 79907, 79939, 79943, 79967, 79973, 
	79979, 79987, 79997, 79999, 0
}; // PRIMES_SIZE = 7836

unsigned long int primes_m1d2[] = {
	1, 2, 3, 5, 6, 8, 9, 11, 
	14, 15, 18, 20, 21, 23, 26, 29, 
	30, 33, 35, 36, 39, 41, 44, 48, 
	50, 51, 53, 54, 56, 63, 65, 68, 
	69, 74, 75, 78, 81, 83, 86, 89, 
	90, 95, 96, 98, 99, 105, 111, 113, 
	114, 116, 119, 120, 125, 128, 131, 134, 
	135, 138, 140, 141, 146, 153, 155, 156, 
	158, 165, 168, 173, 174, 176, 179, 183, 
	186, 189, 191, 194, 198, 200, 204, 209, 
	210, 215, 216, 219, 221, 224, 228, 230, 
	231, 233, 239, 243, 245, 249, 251, 254, 
	260, 261, 270, 273, 278, 281, 284, 285, 
	288, 293, 296, 299, 300, 303, 306, 308, 
	309, 315, 320, 321, 323, 326, 329, 330, 
	336, 338, 341, 345, 350, 354, 359, 363, 
	366, 369, 371, 375, 378, 380, 384, 386, 
	393, 398, 404, 405, 410, 411, 413, 414, 
	419, 426, 428, 429, 431, 438, 440, 441, 
	443, 453, 455, 459, 464, 468, 470, 473, 
	476, 483, 485, 488, 491, 495, 498, 504, 
	506, 509, 510, 515, 516, 519, 524, 525, 
	530, 531, 534, 543, 545, 546, 548, 551, 
	554, 558, 561, 564, 575, 576, 581, 585, 
	590, 593, 596, 600, 606, 608, 611, 614, 
	615, 618, 624, 629, 638, 639, 641, 644, 
	645, 648, 650, 651, 653, 659, 660, 663, 
	680, 683, 686, 690, 699, 704, 711, 713, 
	714, 716, 719, 723, 725, 726, 729, 735, 
	740, 741, 743, 744, 746, 749, 755, 761, 
	765, 771, 774, 776, 779, 783, 785, 789, 
	791, 798, 800, 803, 804, 806, 809, 810, 
	813, 818, 828, 831, 833, 834, 846, 848, 
	849, 854, 860, 861, 866, 870, 873, 876, 
	879, 888, 891, 893, 894, 900, 905, 911, 
	915, 923, 930, 933, 935, 936, 938, 939, 
	944, 950, 953, 956, 965, 966, 974, 975, 
	986, 989, 993, 996, 998, 999, 1001, 1005, 
	1008, 1013, 1014, 1019, 1026, 1031, 1034, 1040, 
	1041, 1043, 1044, 1049, 1055, 1056, 1064, 1065, 
	1068, 1070, 1071, 1076, 1080, 1089, 1101, 1103, 
	1106, 1110, 1118, 1119, 1121, 1125, 1133, 1134, 
	1136, 1140, 1143, 1146, 1148, 1154, 1155, 1166, 
	1169, 1170, 1173, 1175, 1178, 1185, 1188, 1190, 
	1191, 1194, 1196, 1199, 1205, 1208, 1211, 1218, 
	1220, 1223, 1229, 1233, 1236, 1238, 1251, 1260, 
	1265, 1269, 1271, 1274, 1275, 1278, 1289, 1295, 
	1296, 1304, 1308, 1310, 1316, 1323, 1328, 1329, 
	1331, 1335, 1338, 1341, 1343, 1344, 1346, 1349, 
	1353, 1355, 1356, 1359, 1364, 1365, 1370, 1374, 
	1376, 1383, 1388, 1394, 1395, 1398, 1400, 1401, 
	1409, 1416, 1418, 1421, 1425, 1428, 1430, 1439, 
	1443, 1448, 1451, 1454, 1458, 1463, 1469, 1476, 
	1478, 1481, 1484, 1485, 1499, 1500, 1505, 1509, 
	1511, 1518, 1520, 1524, 1530, 1533, 1539, 1541, 
	1544, 1554, 1559, 1560, 1568, 1581, 1583, 1584, 
	1590, 1593, 1595, 1601, 1604, 1608, 1610, 1614, 
	1625, 1626, 1628, 1629, 1635, 1649, 1650, 1653, 
	1656, 1659, 1661, 1664, 1665, 1671, 1673, 1679, 
	1680, 1685, 1686, 1694, 1695, 1703, 1706, 1716, 
	1724, 1728, 1730, 1731, 1733, 1734, 1745, 1749, 
	1755, 1758, 1763, 1764, 1766, 1769, 1770, 1773, 
	1778, 1779, 1785, 1790, 1791, 1796, 1803, 1806, 
	1808, 1811, 1815, 1818, 1821, 1829, 1835, 1836, 
	1838, 1845, 1848, 1850, 1854, 1859, 1863, 1866, 
	1869, 1880, 1883, 1884, 1889, 1896, 1898, 1901, 
	1910, 1911, 1916, 1923, 1925, 1926, 1931, 1938, 
	1940, 1944, 1953, 1955, 1958, 1959, 1961, 1964, 
	1965, 1971, 1973, 1983, 1994, 2000, 2001, 2003, 
	2006, 2009, 2010, 2013, 2024, 2025, 2028, 2036, 
	2039, 2045, 2046, 2049, 2055, 2063, 2064, 2066, 
	2069, 2076, 2078, 2079, 2088, 2100, 2105, 2108, 
	2109, 2114, 2115, 2120, 2121, 2126, 2129, 2130, 
	2135, 2136, 2141, 2144, 2148, 2163, 2168, 2169, 
	2174, 2178, 2181, 2186, 2195, 2198, 2204, 2210, 
	2211, 2220, 2223, 2225, 2228, 2231, 2240, 2241, 
	2246, 2253, 2256, 2258, 2259, 2261, 2273, 2274, 
	2280, 2283, 2291, 2295, 2298, 2301, 2310, 2318, 
	2319, 2321, 2324, 2325, 2328, 2331, 2336, 2339, 
	2345, 2351, 2360, 2361, 2364, 2366, 2375, 2379, 
	2391, 2393, 2394, 2396, 2399, 2400, 2406, 2408, 
	2415, 2430, 2435, 2438, 2444, 2451, 2454, 2459, 
	2465, 2466, 2468, 2471, 2475, 2478, 2483, 2484, 
	2486, 2493, 2496, 2499, 2501, 2504, 2505, 2510, 
	2511, 2519, 2525, 2529, 2538, 2540, 2543, 2549, 
	2550, 2553, 2556, 2559, 2573, 2576, 2583, 2585, 
	2589, 2594, 2598, 2604, 2613, 2615, 2616, 2618, 
	2630, 2636, 2639, 2640, 2648, 2651, 2654, 2661, 
	2666, 2673, 2675, 2690, 2693, 2696, 2699, 2703, 
	2706, 2708, 2709, 2715, 2718, 2720, 2721, 2724, 
	2735, 2738, 2739, 2741, 2750, 2751, 2753, 2759, 
	2760, 2763, 2765, 2778, 2781, 2784, 2786, 2790, 
	2795, 2811, 2819, 2820, 2823, 2825, 2826, 2828, 
	2829, 2834, 2841, 2844, 2846, 2850, 2855, 2858, 
	2868, 2870, 2871, 2874, 2889, 2891, 2895, 2900, 
	2903, 2906, 2910, 2913, 2919, 2921, 2924, 2925, 
	2928, 2930, 2933, 2934, 2939, 2940, 2948, 2951, 
	2961, 2963, 2969, 2976, 2990, 2993, 3003, 3005, 
	3014, 3018, 3021, 3023, 3026, 3033, 3036, 3039, 
	3044, 3045, 3050, 3056, 3060, 3065, 3066, 3071, 
	3075, 3081, 3086, 3098, 3099, 3101, 3105, 3108, 
	3110, 3114, 3123, 3128, 3131, 3134, 3135, 3138, 
	3143, 3149, 3150, 3155, 3158, 3161, 3164, 3168, 
	3171, 3176, 3179, 3180, 3183, 3186, 3189, 3194, 
	3198, 3210, 3213, 3224, 3225, 3234, 3236, 3240, 
	3245, 3260, 3264, 3273, 3275, 3276, 3281, 3284, 
	3285, 3288, 3290, 3299, 3303, 3309, 3318, 3326, 
	3329, 3330, 3336, 3339, 3344, 3345, 3350, 3351, 
	3354, 3359, 3366, 3368, 3380, 3381, 3389, 3390, 
	3395, 3396, 3401, 3411, 3413, 3414, 3416, 3420, 
	3428, 3431, 3434, 3435, 3441, 3449, 3453, 3455, 
	3458, 3473, 3474, 3479, 3480, 3483, 3485, 3488, 
	3491, 3495, 3498, 3500, 3506, 3509, 3513, 3519, 
	3521, 3528, 3534, 3539, 3551, 3554, 3560, 3563, 
	3564, 3575, 3579, 3588, 3593, 3596, 3603, 3605, 
	3606, 3609, 3614, 3618, 3621, 3623, 3626, 3641, 
	3648, 3653, 3654, 3660, 3665, 3666, 3674, 3675, 
	3684, 3696, 3705, 3708, 3716, 3725, 3728, 3729, 
	3738, 3740, 3743, 3744, 3749, 3753, 3758, 3761, 
	3764, 3768, 3770, 3773, 3774, 3779, 3780, 3786, 
	3788, 3791, 3794, 3795, 3801, 3803, 3810, 3819, 
	3821, 3824, 3834, 3836, 3840, 3843, 3845, 3849, 
	3851, 3858, 3861, 3863, 3870, 3876, 3878, 3879, 
	3894, 3896, 3908, 3911, 3914, 3920, 3926, 3933, 
	3936, 3938, 3939, 3941, 3950, 3953, 3959, 3963, 
	3966, 3968, 3974, 3975, 3981, 3996, 4004, 4005, 
	4008, 4019, 4026, 4029, 4034, 4040, 4043, 4044, 
	4046, 4050, 4055, 4058, 4061, 4073, 4080, 4083, 
	4085, 4089, 4095, 4104, 4109, 4110, 4115, 4116, 
	4118, 4121, 4131, 4134, 4136, 4143, 4145, 4146, 
	4148, 4155, 4158, 4164, 4176, 4181, 4184, 4188, 
	4193, 4194, 4209, 4211, 4214, 4215, 4221, 4223, 
	4230, 4233, 4250, 4256, 4260, 4263, 4268, 4269, 
	4271, 4281, 4286, 4290, 4298, 4299, 4304, 4311, 
	4313, 4314, 4320, 4323, 4331, 4334, 4338, 4340, 
	4344, 4346, 4349, 4353, 4356, 4359, 4365, 4368, 
	4370, 4373, 4376, 4380, 4389, 4391, 4401, 4403, 
	4409, 4410, 4415, 4418, 4419, 4424, 4430, 4431, 
	4433, 4443, 4446, 4461, 4464, 4466, 4470, 4475, 
	4481, 4484, 4485, 4499, 4500, 4503, 4505, 4506, 
	4514, 4520, 4521, 4524, 4529, 4533, 4545, 4551, 
	4554, 4563, 4566, 4568, 4575, 4578, 4580, 4586, 
	4590, 4593, 4599, 4601, 4604, 4610, 4613, 4619, 
	4620, 4628, 4638, 4640, 4641, 4646, 4655, 4659, 
	4661, 4668, 4670, 4671, 4674, 4685, 4688, 4695, 
	4698, 4701, 4706, 4709, 4710, 4715, 4716, 4718, 
	4719, 4730, 4731, 4733, 4736, 4739, 4745, 4748, 
	4755, 4760, 4766, 4769, 4773, 4775, 4793, 4800, 
	4806, 4809, 4811, 4814, 4815, 4821, 4824, 4830, 
	4838, 4839, 4844, 4848, 4859, 4860, 4866, 4869, 
	4871, 4874, 4883, 4884, 4890, 4893, 4895, 4901, 
	4905, 4908, 4914, 4916, 4919, 4925, 4928, 4929, 
	4935, 4941, 4943, 4950, 4953, 4961, 4964, 4965, 
	4970, 4974, 4983, 4986, 5003, 5004, 5018, 5019, 
	5030, 5033, 5034, 5039, 5045, 5046, 5049, 5051, 
	5055, 5066, 5069, 5070, 5075, 5079, 5081, 5084, 
	5088, 5090, 5096, 5105, 5111, 5121, 5123, 5126, 
	5129, 5133, 5135, 5136, 5144, 5150, 5151, 5156, 
	5160, 5165, 5166, 5168, 5171, 5178, 5184, 5195, 
	5199, 5213, 5214, 5216, 5226, 5228, 5229, 5231, 
	5238, 5243, 5249, 5250, 5256, 5264, 5265, 5279, 
	5283, 5294, 5298, 5300, 5303, 5306, 5313, 5315, 
	5319, 5325, 5328, 5331, 5333, 5343, 5345, 5354, 
	5355, 5361, 5364, 5366, 5369, 5376, 5385, 5390, 
	5394, 5399, 5415, 5418, 5423, 5426, 5429, 5430, 
	5433, 5441, 5444, 5445, 5451, 5454, 5468, 5469, 
	5474, 5478, 5486, 5489, 5493, 5496, 5501, 5513, 
	5523, 5528, 5529, 5534, 5535, 5541, 5543, 5546, 
	5556, 5558, 5559, 5565, 5574, 5579, 5580, 5585, 
	5586, 5588, 5598, 5606, 5619, 5621, 5625, 5628, 
	5630, 5636, 5639, 5643, 5649, 5655, 5658, 5660, 
	5664, 5675, 5676, 5684, 5691, 5696, 5699, 5705, 
	5711, 5718, 5721, 5723, 5733, 5735, 5741, 5744, 
	5745, 5748, 5751, 5759, 5763, 5774, 5775, 5789, 
	5793, 5796, 5798, 5808, 5810, 5816, 5828, 5838, 
	5840, 5844, 5849, 5850, 5858, 5859, 5865, 5871, 
	5888, 5889, 5891, 5894, 5900, 5903, 5906, 5910, 
	5913, 5915, 5916, 5919, 5931, 5933, 5943, 5948, 
	5951, 5954, 5961, 5963, 5966, 5969, 5970, 5976, 
	5979, 5984, 5985, 5990, 5993, 6003, 6005, 6018, 
	6020, 6021, 6024, 6035, 6036, 6048, 6050, 6053, 
	6054, 6056, 6059, 6071, 6074, 6078, 6080, 6081, 
	6098, 6101, 6105, 6113, 6119, 6120, 6125, 6126, 
	6131, 6134, 6138, 6140, 6144, 6150, 6161, 6164, 
	6171, 6173, 6186, 6188, 6189, 6195, 6200, 6204, 
	6206, 6210, 6216, 6218, 6225, 6228, 6236, 6239, 
	6243, 6245, 6248, 6251, 6255, 6258, 6263, 6269, 
	6270, 6273, 6276, 6284, 6288, 6291, 6294, 6300, 
	6305, 6306, 6309, 6318, 6320, 6323, 6326, 6329, 
	6335, 6344, 6348, 6351, 6356, 6360, 6369, 6371, 
	6378, 6381, 6390, 6395, 6399, 6404, 6410, 6411, 
	6414, 6420, 6426, 6444, 6446, 6449, 6453, 6455, 
	6458, 6459, 6461, 6470, 6476, 6479, 6483, 6486, 
	6489, 6491, 6500, 6501, 6503, 6504, 6516, 6518, 
	6521, 6524, 6531, 6546, 6549, 6551, 6554, 6560, 
	6563, 6573, 6575, 6579, 6581, 6585, 6588, 6591, 
	6593, 6608, 6609, 6614, 6620, 6624, 6629, 6633, 
	6645, 6648, 6654, 6656, 6663, 6665, 6668, 6669, 
	6683, 6690, 6698, 6699, 6705, 6708, 6710, 6720, 
	6725, 6728, 6731, 6734, 6738, 6743, 6749, 6756, 
	6761, 6768, 6776, 6783, 6788, 6795, 6798, 6806, 
	6809, 6813, 6816, 6824, 6834, 6839, 6840, 6843, 
	6845, 6846, 6848, 6854, 6855, 6860, 6861, 6864, 
	6875, 6878, 6879, 6881, 6890, 6894, 6899, 6903, 
	6914, 6915, 6920, 6929, 6936, 6938, 6939, 6941, 
	6950, 6951, 6953, 6956, 6960, 6965, 6966, 6981, 
	6983, 6998, 6999, 7004, 7005, 7014, 7016, 7025, 
	7028, 7035, 7040, 7041, 7043, 7053, 7071, 7074, 
	7076, 7079, 7086, 7088, 7098, 7103, 7110, 7121, 
	7124, 7125, 7140, 7146, 7151, 7160, 7161, 7163, 
	7170, 7173, 7184, 7193, 7194, 7200, 7203, 7205, 
	7209, 7211, 7215, 7218, 7223, 7224, 7230, 7239, 
	7244, 7251, 7259, 7266, 7268, 7271, 7274, 7275, 
	7278, 7280, 7281, 7295, 7296, 7310, 7313, 7314, 
	7316, 7319, 7326, 7328, 7334, 7341, 7349, 7356, 
	7358, 7361, 7365, 7368, 7370, 7373, 7376, 7379, 
	7383, 7385, 7389, 7391, 7398, 7406, 7410, 7413, 
	7415, 7421, 7425, 7433, 7434, 7439, 7443, 7445, 
	7448, 7461, 7464, 7469, 7473, 7475, 7478, 7484, 
	7491, 7506, 7508, 7515, 7526, 7530, 7536, 7538, 
	7541, 7545, 7550, 7553, 7560, 7565, 7568, 7569, 
	7574, 7580, 7586, 7593, 7596, 7599, 7608, 7613, 
	7616, 7620, 7629, 7631, 7634, 7635, 7638, 7643, 
	7644, 7649, 7653, 7656, 7659, 7664, 7665, 7674, 
	7679, 7680, 7686, 7688, 7691, 7695, 7700, 7706, 
	7713, 7719, 7721, 7725, 7730, 7733, 7736, 7746, 
	7748, 7755, 7763, 7770, 7775, 7779, 7784, 7790, 
	7791, 7800, 7803, 7809, 7814, 7820, 7821, 7823, 
	7824, 7830, 7833, 7835, 7839, 7841, 7863, 7865, 
	7866, 7868, 7869, 7874, 7880, 7883, 7886, 7893, 
	7895, 7898, 7901, 7904, 7908, 7911, 7929, 7938, 
	7940, 7943, 7944, 7950, 7953, 7956, 7959, 7961, 
	7968, 7979, 7985, 7986, 7995, 8000, 8003, 8016, 
	8028, 8030, 8031, 8033, 8034, 8036, 8043, 8045, 
	8048, 8051, 8055, 8063, 8069, 8070, 8091, 8093, 
	8094, 8096, 8108, 8111, 8114, 8115, 8124, 8126, 
	8133, 8136, 8150, 8159, 8166, 8169, 8174, 8180, 
	8181, 8184, 8190, 8205, 8208, 8210, 8213, 8216, 
	8223, 8225, 8226, 8238, 8240, 8243, 8246, 8259, 
	8264, 8273, 8276, 8280, 8283, 8286, 8301, 8303, 
	8309, 8315, 8316, 8324, 8325, 8328, 8330, 8336, 
	8345, 8346, 8349, 8351, 8364, 8370, 8373, 8379, 
	8381, 8393, 8405, 8411, 8414, 8415, 8421, 8435, 
	8439, 8441, 8444, 8450, 8451, 8460, 8463, 8465, 
	8468, 8471, 8481, 8489, 8490, 8493, 8496, 8505, 
	8510, 8513, 8514, 8516, 8520, 8523, 8526, 8538, 
	8546, 8549, 8553, 8558, 8561, 8568, 8579, 8583, 
	8591, 8594, 8595, 8601, 8603, 8604, 8615, 8619, 
	8628, 8645, 8646, 8649, 8658, 8660, 8663, 8666, 
	8670, 8675, 8679, 8688, 8691, 8693, 8694, 8696, 
	8700, 8708, 8709, 8715, 8721, 8724, 8733, 8735, 
	8738, 8741, 8744, 8745, 8748, 8754, 8759, 8769, 
	8775, 8784, 8786, 8789, 8790, 8798, 8799, 8804, 
	8811, 8813, 8828, 8829, 8834, 8840, 8841, 8853, 
	8856, 8864, 8868, 8873, 8874, 8880, 8891, 8894, 
	8895, 8903, 8913, 8918, 8919, 8925, 8931, 8940, 
	8945, 8951, 8954, 8955, 8960, 8961, 8964, 8969, 
	8978, 8979, 8985, 8988, 8990, 8993, 8994, 9006, 
	9020, 9021, 9023, 9024, 9029, 9030, 9038, 9044, 
	9048, 9059, 9060, 9063, 9065, 9066, 9071, 9074, 
	9084, 9090, 9095, 9099, 9105, 9108, 9111, 9114, 
	9116, 9125, 9126, 9128, 9134, 9143, 9144, 9150, 
	9153, 9155, 9156, 9164, 9170, 9176, 9183, 9185, 
	9189, 9198, 9200, 9206, 9213, 9216, 9219, 9221, 
	9225, 9228, 9230, 9240, 9246, 9251, 9258, 9260, 
	9261, 9269, 9270, 9276, 9291, 9293, 9296, 9308, 
	9318, 9330, 9335, 9339, 9345, 9350, 9356, 9359, 
	9365, 9371, 9374, 9378, 9386, 9393, 9396, 9398, 
	9401, 9419, 9429, 9434, 9449, 9455, 9456, 9458, 
	9459, 9473, 9479, 9486, 9489, 9500, 9504, 9506, 
	9515, 9518, 9525, 9534, 9536, 9539, 9540, 9543, 
	9560, 9569, 9570, 9578, 9581, 9590, 9591, 9603, 
	9605, 9606, 9609, 9615, 9618, 9624, 9629, 9633, 
	9636, 9644, 9650, 9654, 9659, 9666, 9686, 9689, 
	9690, 9693, 9695, 9701, 9708, 9710, 9711, 9713, 
	9714, 9716, 9720, 9723, 9728, 9731, 9734, 9735, 
	9738, 9741, 9744, 9750, 9753, 9765, 9770, 9771, 
	9776, 9779, 9785, 9788, 9791, 9798, 9801, 9804, 
	9830, 9840, 9843, 9848, 9849, 9854, 9858, 9863, 
	9869, 9875, 9876, 9879, 9881, 9888, 9896, 9900, 
	9906, 9909, 9920, 9921, 9926, 9930, 9933, 9944, 
	9945, 9956, 9959, 9963, 9968, 9974, 9980, 9981, 
	9986, 9989, 9995, 9996, 9998, 10005, 10010, 10011, 
	10014, 10023, 10025, 10031, 10035, 10044, 10050, 10053, 
	10056, 10058, 10061, 10064, 10071, 10073, 10074, 10080, 
	10086, 10088, 10091, 10100, 10109, 10115, 10116, 10124, 
	10130, 10134, 10143, 10148, 10161, 10163, 10166, 10170, 
	10173, 10176, 10178, 10179, 10184, 10194, 10196, 10199, 
	10203, 10205, 10215, 10220, 10221, 10238, 10239, 10241, 
	10253, 10254, 10260, 10266, 10271, 10274, 10275, 10281, 
	10296, 10299, 10305, 10313, 10319, 10320, 10331, 10340, 
	10346, 10353, 10358, 10359, 10365, 10371, 10373, 10374, 
	10376, 10379, 10385, 10386, 10394, 10403, 10404, 10424, 
	10428, 10436, 10439, 10443, 10448, 10449, 10451, 10460, 
	10464, 10469, 10473, 10479, 10481, 10490, 10491, 10500, 
	10505, 10506, 10508, 10509, 10511, 10515, 10529, 10530, 
	10533, 10544, 10550, 10553, 10560, 10569, 10571, 10574, 
	10578, 10581, 10584, 10589, 10593, 10595, 10596, 10605, 
	10610, 10613, 10623, 10634, 10638, 10641, 10656, 10658, 
	10659, 10661, 10670, 10673, 10688, 10689, 10691, 10695, 
	10698, 10700, 10703, 10709, 10716, 10733, 10740, 10743, 
	10745, 10746, 10749, 10751, 10758, 10760, 10761, 10764, 
	10778, 10779, 10781, 10784, 10788, 10793, 10794, 10799, 
	10800, 10805, 10806, 10808, 10823, 10824, 10830, 10836, 
	10841, 10850, 10856, 10863, 10868, 10869, 10875, 10878, 
	10883, 10886, 10893, 10899, 10901, 10908, 10910, 10919, 
	10920, 10925, 10929, 10931, 10935, 10940, 10946, 10955, 
	10964, 10968, 10971, 10980, 10988, 10995, 10998, 11001, 
	11006, 11013, 11015, 11018, 11019, 11025, 11031, 11033, 
	11036, 11039, 11045, 11046, 11054, 11055, 11061, 11064, 
	11066, 11073, 11076, 11078, 11079, 11085, 11094, 11096, 
	11114, 11123, 11129, 11135, 11136, 11138, 11139, 11141, 
	11145, 11151, 11153, 11171, 11174, 11183, 11184, 11190, 
	11195, 11198, 11204, 11216, 11220, 11223, 11226, 11234, 
	11240, 11241, 11250, 11255, 11265, 11270, 11271, 11274, 
	11283, 11285, 11286, 11306, 11309, 11310, 11318, 11319, 
	11321, 11325, 11334, 11339, 11345, 11348, 11349, 11354, 
	11358, 11360, 11363, 11369, 11370, 11375, 11384, 11388, 
	11391, 11393, 11403, 11405, 11408, 11426, 11429, 11430, 
	11435, 11438, 11450, 11453, 11460, 11468, 11471, 11480, 
	11481, 11486, 11496, 11501, 11505, 11508, 11510, 11513, 
	11514, 11519, 11520, 11526, 11528, 11529, 11531, 11535, 
	11540, 11543, 11549, 11558, 11565, 11571, 11579, 11583, 
	11586, 11594, 11598, 11600, 11601, 11604, 11613, 11625, 
	11634, 11639, 11645, 11646, 11648, 11655, 11660, 11663, 
	11666, 11669, 11678, 11684, 11685, 11699, 11708, 11715, 
	11723, 11729, 11736, 11748, 11754, 11765, 11768, 11769, 
	11774, 11778, 11780, 11781, 11783, 11790, 11796, 11799, 
	11801, 11804, 11811, 11813, 11814, 11816, 11831, 11834, 
	11835, 11838, 11843, 11844, 11859, 11870, 11871, 11873, 
	11876, 11880, 11883, 11886, 11894, 11900, 11906, 11909, 
	11913, 11915, 11916, 11928, 11934, 11936, 11939, 11943, 
	11946, 11949, 11954, 11955, 11958, 11964, 11978, 11985, 
	11988, 11990, 11996, 12000, 12003, 12009, 12011, 12014, 
	12021, 12024, 12030, 12035, 12038, 12041, 12045, 12048, 
	12051, 12053, 12054, 12056, 12060, 12066, 12068, 12075, 
	12084, 12089, 12090, 12098, 12101, 12111, 12114, 12119, 
	12123, 12125, 12140, 12158, 12164, 12168, 12179, 12185, 
	12186, 12189, 12195, 12203, 12206, 12209, 12210, 12219, 
	12221, 12234, 12236, 12240, 12249, 12254, 12258, 12263, 
	12266, 12273, 12275, 12285, 12296, 12305, 12311, 12315, 
	12329, 12335, 12338, 12341, 12345, 12348, 12354, 12366, 
	12374, 12381, 12383, 12390, 12396, 12399, 12404, 12410, 
	12420, 12423, 12425, 12429, 12438, 12444, 12453, 12458, 
	12459, 12461, 12471, 12476, 12483, 12485, 12488, 12489, 
	12494, 12506, 12515, 12516, 12518, 12528, 12536, 12543, 
	12548, 12555, 12558, 12560, 12563, 12573, 12576, 12581, 
	12584, 12585, 12591, 12594, 12609, 12614, 12618, 12621, 
	12623, 12626, 12630, 12650, 12651, 12653, 12654, 12660, 
	12669, 12671, 12674, 12678, 12683, 12686, 12695, 12704, 
	12705, 12711, 12719, 12723, 12726, 12728, 12731, 12734, 
	12735, 12761, 12768, 12770, 12780, 12788, 12789, 12791, 
	12794, 12800, 12801, 12804, 12810, 12816, 12819, 12821, 
	12828, 12833, 12836, 12839, 12846, 12851, 12858, 12866, 
	12870, 12873, 12879, 12881, 12885, 12896, 12899, 12900, 
	12909, 12920, 12923, 12924, 12933, 12936, 12944, 12951, 
	12956, 12959, 12965, 12966, 12969, 12971, 12975, 12984, 
	12990, 12998, 12999, 13001, 13008, 13010, 13014, 13020, 
	13026, 13041, 13049, 13053, 13055, 13056, 13059, 13070, 
	13076, 13080, 13085, 13088, 13091, 13094, 13101, 13104, 
	13113, 13118, 13124, 13125, 13130, 13131, 13133, 13146, 
	13148, 13154, 13158, 13160, 13169, 13173, 13178, 13185, 
	13193, 13196, 13199, 13203, 13208, 13211, 13215, 13218, 
	13224, 13229, 13239, 13244, 13248, 13250, 13256, 13269, 
	13278, 13280, 13286, 13295, 13298, 13313, 13316, 13320, 
	13323, 13334, 13340, 13341, 13343, 13346, 13349, 13350, 
	13355, 13356, 13358, 13361, 13364, 13365, 13368, 13379, 
	13388, 13391, 13400, 13406, 13410, 13416, 13419, 13424, 
	13430, 13431, 13439, 13440, 13445, 13446, 13451, 13460, 
	13463, 13473, 13475, 13476, 13479, 13490, 13493, 13496, 
	13505, 13508, 13515, 13521, 13529, 13530, 13533, 13536, 
	13538, 13545, 13551, 13553, 13554, 13563, 13571, 13589, 
	13595, 13598, 13605, 13619, 13620, 13626, 13629, 13635, 
	13638, 13640, 13641, 13649, 13664, 13668, 13680, 13683, 
	13698, 13703, 13704, 13713, 13715, 13718, 13724, 13728, 
	13739, 13740, 13743, 13754, 13763, 13764, 13769, 13770, 
	13775, 13790, 13791, 13805, 13808, 13815, 13823, 13826, 
	13836, 13844, 13845, 13848, 13850, 13866, 13868, 13869, 
	13871, 13874, 13875, 13881, 13883, 13886, 13889, 13895, 
	13896, 13899, 13901, 13904, 13908, 13911, 13913, 13923, 
	13925, 13941, 13946, 13950, 13958, 13959, 13970, 13971, 
	13973, 13976, 13980, 13983, 13991, 13998, 14000, 14009, 
	14013, 14015, 14025, 14028, 14034, 14040, 14043, 14048, 
	14049, 14054, 14055, 14061, 14075, 14081, 14090, 14091, 
	14100, 14105, 14109, 14114, 14138, 14139, 14141, 14144, 
	14148, 14153, 14154, 14159, 14174, 14175, 14193, 14196, 
	14201, 14204, 14205, 14214, 14216, 14219, 14223, 14231, 
	14238, 14246, 14249, 14256, 14258, 14268, 14270, 14273, 
	14274, 14279, 14285, 14286, 14289, 14295, 14298, 14301, 
	14303, 14309, 14310, 14313, 14315, 14321, 14324, 14328, 
	14330, 14331, 14334, 14343, 14348, 14351, 14355, 14361, 
	14364, 14375, 14376, 14379, 14385, 14394, 14396, 14403, 
	14406, 14408, 14418, 14421, 14429, 14433, 14435, 14439, 
	14450, 14454, 14460, 14463, 14466, 14474, 14480, 14489, 
	14504, 14508, 14510, 14511, 14513, 14516, 14529, 14531, 
	14538, 14550, 14561, 14564, 14565, 14568, 14573, 14576, 
	14583, 14586, 14589, 14595, 14600, 14603, 14604, 14610, 
	14615, 14621, 14625, 14634, 14643, 14648, 14651, 14655, 
	14663, 14666, 14669, 14673, 14681, 14691, 14693, 14694, 
	14699, 14700, 14705, 14711, 14714, 14718, 14721, 14726, 
	14736, 14741, 14750, 14763, 14765, 14768, 14783, 14784, 
	14786, 14790, 14793, 14799, 14805, 14814, 14816, 14820, 
	14831, 14834, 14835, 14841, 14858, 14861, 14870, 14876, 
	14879, 14880, 14894, 14901, 14909, 14916, 14918, 14925, 
	14931, 14933, 14936, 14939, 14940, 14958, 14960, 14963, 
	14973, 14979, 14991, 14994, 15005, 15006, 15014, 15023, 
	15029, 15035, 15044, 15045, 15048, 15051, 15054, 15056, 
	15059, 15066, 15068, 15069, 15080, 15084, 15090, 15093, 
	15098, 15101, 15105, 15111, 15120, 15126, 15129, 15134, 
	15135, 15146, 15153, 15156, 15159, 15161, 15170, 15173, 
	15183, 15194, 15195, 15201, 15213, 15215, 15224, 15233, 
	15234, 15245, 15246, 15248, 15254, 15258, 15264, 15269, 
	15276, 15278, 15279, 15288, 15296, 15315, 15318, 15321, 
	15324, 15330, 15335, 15338, 15344, 15348, 15351, 15353, 
	15356, 15363, 15378, 15381, 15386, 15390, 15401, 15404, 
	15408, 15414, 15419, 15420, 15425, 15426, 15429, 15434, 
	15435, 15440, 15446, 15455, 15465, 15468, 15470, 15474, 
	15485, 15488, 15491, 15506, 15509, 15516, 15519, 15525, 
	15531, 15534, 15539, 15540, 15545, 15560, 15561, 15569, 
	15573, 15575, 15576, 15579, 15588, 15590, 15591, 15594, 
	15596, 15609, 15611, 15615, 15618, 15623, 15624, 15626, 
	15629, 15633, 15635, 15638, 15653, 15659, 15660, 15663, 
	15666, 15668, 15678, 15689, 15693, 15695, 15696, 15698, 
	15734, 15738, 15740, 15744, 15755, 15756, 15758, 15765, 
	15770, 15771, 15773, 15783, 15786, 15791, 15800, 15803, 
	15813, 15821, 15824, 15828, 15831, 15833, 15843, 15849, 
	15860, 15861, 15863, 15864, 15870, 15875, 15884, 15885, 
	15896, 15899, 15908, 15923, 15924, 15929, 15936, 15941, 
	15945, 15953, 15978, 15981, 15986, 15990, 15995, 16001, 
	16004, 16013, 16014, 16025, 16028, 16029, 16031, 16034, 
	16038, 16041, 16044, 16049, 16058, 16059, 16070, 16071, 
	16079, 16086, 16091, 16094, 16095, 16101, 16106, 16116, 
	16118, 16125, 16128, 16130, 16148, 16149, 16151, 16154, 
	16160, 16161, 16163, 16170, 16176, 16179, 16181, 16184, 
	16185, 16188, 16190, 16200, 16205, 16206, 16211, 16214, 
	16220, 16221, 16233, 16239, 16245, 16248, 16251, 16253, 
	16265, 16266, 16268, 16280, 16281, 16284, 16286, 16289, 
	16293, 16301, 16304, 16305, 16310, 16316, 16323, 16326, 
	16343, 16346, 16353, 16356, 16358, 16359, 16374, 16385, 
	16389, 16391, 16394, 16398, 16400, 16401, 16415, 16416, 
	16419, 16421, 16434, 16443, 16454, 16455, 16458, 16466, 
	16469, 16470, 16478, 16484, 16485, 16491, 16493, 16496, 
	16499, 16506, 16511, 16514, 16518, 16524, 16526, 16535, 
	16536, 16541, 16545, 16553, 16556, 16559, 16574, 16575, 
	16580, 16589, 16590, 16595, 16599, 16601, 16605, 16611, 
	16623, 16643, 16644, 16650, 16655, 16658, 16664, 16665, 
	16671, 16673, 16674, 16676, 16679, 16688, 16695, 16701, 
	16704, 16706, 16713, 16728, 16730, 16734, 16739, 16743, 
	16746, 16751, 16760, 16764, 16766, 16773, 16781, 16784, 
	16788, 16790, 16793, 16794, 16799, 16800, 16806, 16808, 
	16809, 16811, 16814, 16818, 16820, 16823, 16839, 16851, 
	16856, 16860, 16869, 16874, 16875, 16878, 16883, 16884, 
	16886, 16895, 16898, 16904, 16905, 16913, 16914, 16925, 
	16928, 16931, 16935, 16944, 16946, 16955, 16961, 16965, 
	16968, 16970, 16980, 16983, 16998, 17009, 17015, 17016, 
	17019, 17028, 17030, 17061, 17063, 17064, 17070, 17073, 
	17078, 17079, 17085, 17091, 17105, 17106, 17108, 17115, 
	17126, 17129, 17130, 17133, 17136, 17141, 17148, 17150, 
	17151, 17156, 17159, 17163, 17168, 17175, 17180, 17183, 
	17184, 17190, 17201, 17210, 17214, 17219, 17228, 17234, 
	17235, 17241, 17243, 17249, 17250, 17255, 17256, 17259, 
	17268, 17271, 17274, 17291, 17294, 17295, 17301, 17303, 
	17306, 17315, 17324, 17325, 17333, 17336, 17339, 17343, 
	17346, 17351, 17360, 17364, 17369, 17373, 17378, 17379, 
	17381, 17390, 17403, 17409, 17420, 17421, 17423, 17424, 
	17435, 17438, 17441, 17448, 17456, 17459, 17469, 17474, 
	17480, 17481, 17490, 17511, 17513, 17525, 17526, 17529, 
	17534, 17540, 17541, 17544, 17549, 17553, 17555, 17558, 
	17564, 17570, 17574, 17576, 17579, 17585, 17600, 17610, 
	17613, 17625, 17628, 17633, 17639, 17640, 17645, 17655, 
	17658, 17661, 17663, 17669, 17676, 17681, 17690, 17696, 
	17700, 17703, 17709, 17711, 17718, 17723, 17724, 17730, 
	17745, 17753, 17754, 17760, 17763, 17765, 17766, 17768, 
	17771, 17784, 17786, 17795, 17796, 17798, 17801, 17808, 
	17835, 17838, 17864, 17865, 17873, 17876, 17879, 17885, 
	17898, 17900, 17901, 17904, 17915, 17918, 17919, 17925, 
	17931, 17934, 17939, 17948, 17949, 17955, 17961, 17966, 
	17975, 17981, 17984, 17988, 17991, 17996, 17999, 18003, 
	18005, 18006, 18008, 18018, 18030, 18033, 18036, 18041, 
	18048, 18053, 18054, 18065, 18068, 18075, 18080, 18093, 
	18095, 18104, 18108, 18114, 18120, 18125, 18131, 18134, 
	18138, 18146, 18149, 18153, 18156, 18159, 18170, 18171, 
	18176, 18186, 18191, 18194, 18216, 18225, 18228, 18233, 
	18234, 18236, 18239, 18246, 18248, 18261, 18263, 18264, 
	18270, 18275, 18279, 18281, 18285, 18291, 18293, 18299, 
	18303, 18314, 18318, 18321, 18326, 18335, 18338, 18341, 
	18345, 18348, 18354, 18356, 18360, 18369, 18374, 18380, 
	18383, 18389, 18390, 18393, 18395, 18396, 18404, 18410, 
	18416, 18423, 18428, 18435, 18438, 18443, 18449, 18450, 
	18456, 18459, 18461, 18464, 18465, 18471, 18473, 18486, 
	18489, 18498, 18501, 18506, 18509, 18510, 18519, 18524, 
	18528, 18530, 18543, 18548, 18558, 18561, 18569, 18579, 
	18585, 18590, 18594, 18599, 18600, 18608, 18611, 18621, 
	18626, 18636, 18638, 18653, 18654, 18656, 18660, 18668, 
	18669, 18678, 18680, 18681, 18684, 18689, 18698, 18704, 
	18711, 18720, 18723, 18731, 18741, 18744, 18746, 18750, 
	18753, 18755, 18758, 18764, 18768, 18773, 18774, 18780, 
	18783, 18785, 18786, 18789, 18794, 18795, 18803, 18809, 
	18816, 18821, 18824, 18828, 18831, 18845, 18846, 18849, 
	18858, 18873, 18890, 18891, 18899, 18905, 18906, 18915, 
	18923, 18926, 18930, 18935, 18939, 18944, 18948, 18953, 
	18975, 18978, 18981, 18983, 18993, 18995, 18996, 18998, 
	19005, 19019, 19023, 19026, 19034, 19041, 19056, 19059, 
	19074, 19076, 19083, 19088, 19091, 19094, 19098, 19100, 
	19109, 19115, 19118, 19119, 19130, 19136, 19140, 19143, 
	19149, 19151, 19158, 19160, 19163, 19164, 19166, 19175, 
	19185, 19188, 19196, 19215, 19223, 19224, 19226, 19229, 
	19230, 19250, 19271, 19278, 19280, 19283, 19284, 19296, 
	19301, 19304, 19305, 19314, 19319, 19325, 19326, 19334, 
	19335, 19338, 19346, 19349, 19353, 19355, 19356, 19361, 
	19364, 19368, 19373, 19374, 19383, 19391, 19395, 19401, 
	19410, 19416, 19419, 19425, 19430, 19433, 19436, 19445, 
	19451, 19458, 19460, 19461, 19466, 19476, 19479, 19485, 
	19488, 19496, 19509, 19511, 19520, 19521, 19523, 19539, 
	19544, 19548, 19551, 19553, 19556, 19559, 19566, 19569, 
	19578, 19580, 19581, 19590, 19595, 19599, 19604, 19608, 
	19613, 19614, 19616, 19619, 19620, 19625, 19646, 19650, 
	19656, 19658, 19661, 19670, 19671, 19679, 19683, 19685, 
	19686, 19691, 19698, 19704, 19709, 19719, 19721, 19725, 
	19730, 19749, 19751, 19754, 19755, 19760, 19770, 19775, 
	19781, 19784, 19790, 19803, 19809, 19811, 19815, 19829, 
	19833, 19835, 19839, 19851, 19854, 19859, 19863, 19866, 
	19874, 19880, 19884, 19889, 19895, 19899, 19910, 19913, 
	19914, 19919, 19920, 19923, 19928, 19931, 19934, 19938, 
	19941, 19943, 19950, 19964, 19968, 19976, 19985, 19989, 
	19991, 19994, 20004, 20006, 20015, 20018, 20019, 20031, 
	20043, 20046, 20049, 20055, 20061, 20063, 20064, 20075, 
	20076, 20081, 20084, 20088, 20094, 20096, 20106, 20115, 
	20118, 20120, 20126, 20138, 20141, 20144, 20171, 20175, 
	20178, 20180, 20193, 20211, 20213, 20214, 20216, 20229, 
	20235, 20241, 20243, 20246, 20249, 20253, 20259, 20264, 
	20265, 20271, 20279, 20288, 20291, 20295, 20298, 20304, 
	20313, 20318, 20319, 20346, 20348, 20349, 20354, 20369, 
	20375, 20379, 20381, 20385, 20393, 20400, 20406, 20409, 
	20411, 20414, 20420, 20423, 20424, 20426, 20433, 20439, 
	20441, 20448, 20451, 20463, 20466, 20469, 20474, 20480, 
	20486, 20496, 20505, 20508, 20511, 20519, 20523, 20525, 
	20528, 20538, 20540, 20556, 20558, 20565, 20570, 20571, 
	20574, 20580, 20588, 20589, 20591, 20594, 20600, 20601, 
	20606, 20610, 20613, 20615, 20616, 20621, 20628, 20631, 
	20634, 20640, 20649, 20666, 20670, 20675, 20678, 20690, 
	20693, 20694, 20699, 20705, 20706, 20721, 20726, 20733, 
	20739, 20745, 20753, 20756, 20759, 20760, 20769, 20771, 
	20774, 20789, 20796, 20798, 20801, 20804, 20805, 20808, 
	20810, 20813, 20820, 20823, 20825, 20829, 20834, 20840, 
	20843, 20859, 20864, 20868, 20879, 20880, 20885, 20888, 
	20900, 20904, 20906, 20921, 20924, 20925, 20931, 20939, 
	20943, 20946, 20948, 20951, 20955, 20963, 20970, 20973, 
	20976, 20978, 20979, 20984, 20990, 20991, 20999, 21006, 
	21008, 21009, 21011, 21021, 21030, 21035, 21036, 21041, 
	21044, 21050, 21065, 21069, 21078, 21084, 21089, 21090, 
	21093, 21096, 21098, 21104, 21110, 21111, 21113, 21119, 
	21128, 21140, 21141, 21146, 21149, 21153, 21161, 21165, 
	21168, 21174, 21179, 21186, 21189, 21195, 21198, 21201, 
	21203, 21204, 21216, 21218, 21221, 21225, 21228, 21230, 
	21231, 21233, 21236, 21243, 21245, 21249, 21254, 21266, 
	21278, 21284, 21285, 21288, 21294, 21305, 21320, 21321, 
	21324, 21333, 21338, 21341, 21344, 21348, 21350, 21351, 
	21354, 21359, 21363, 21368, 21371, 21375, 21383, 21386, 
	21393, 21396, 21398, 21410, 21414, 21419, 21420, 21426, 
	21429, 21431, 21449, 21450, 21461, 21464, 21468, 21471, 
	21476, 21480, 21483, 21489, 21494, 21501, 21506, 21509, 
	21518, 21524, 21525, 21531, 21533, 21546, 21551, 21558, 
	21566, 21575, 21579, 21588, 21594, 21600, 21603, 21611, 
	21618, 21630, 21635, 21641, 21645, 21656, 21659, 21660, 
	21665, 21695, 21698, 21699, 21701, 21705, 21713, 21720, 
	21725, 21728, 21740, 21743, 21749, 21758, 21770, 21771, 
	21786, 21788, 21789, 21795, 21798, 21803, 21804, 21806, 
	21813, 21816, 21824, 21825, 21830, 21834, 21845, 21855, 
	21858, 21860, 21876, 21879, 21888, 21890, 21891, 21893, 
	21894, 21896, 21900, 21926, 21933, 21944, 21945, 21956, 
	21966, 21971, 21975, 21980, 21981, 21984, 21986, 21993, 
	21995, 21998, 22008, 22010, 22013, 22014, 22020, 22026, 
	22029, 22035, 22043, 22044, 22050, 22055, 22059, 22061, 
	22064, 22065, 22079, 22085, 22089, 22094, 22100, 22101, 
	22103, 22110, 22124, 22128, 22131, 22133, 22134, 22136, 
	22139, 22140, 22146, 22175, 22178, 22185, 22190, 22191, 
	22194, 22208, 22224, 22226, 22241, 22245, 22248, 22250, 
	22253, 22259, 22265, 22266, 22268, 22271, 22274, 22281, 
	22289, 22293, 22308, 22310, 22311, 22316, 22320, 22323, 
	22325, 22328, 22341, 22343, 22349, 22350, 22355, 22364, 
	22370, 22376, 22385, 22386, 22388, 22394, 22398, 22404, 
	22409, 22419, 22421, 22425, 22433, 22439, 22443, 22446, 
	22454, 22458, 22463, 22469, 22476, 22479, 22481, 22485, 
	22491, 22493, 22503, 22506, 22526, 22530, 22538, 22541, 
	22559, 22560, 22563, 22565, 22568, 22569, 22580, 22589, 
	22590, 22595, 22598, 22616, 22623, 22629, 22631, 22640, 
	22644, 22646, 22653, 22658, 22659, 22664, 22668, 22670, 
	22671, 22680, 22688, 22694, 22701, 22706, 22713, 22716, 
	22719, 22740, 22745, 22748, 22751, 22761, 22766, 22770, 
	22776, 22778, 22784, 22793, 22794, 22799, 22806, 22815, 
	22820, 22829, 22833, 22836, 22838, 22845, 22848, 22853, 
	22868, 22875, 22878, 22881, 22883, 22889, 22908, 22910, 
	22911, 22913, 22916, 22920, 22926, 22931, 22934, 22943, 
	22946, 22971, 22974, 22976, 22979, 22985, 22989, 22994, 
	23010, 23013, 23024, 23025, 23030, 23036, 23045, 23046, 
	23049, 23051, 23066, 23070, 23073, 23076, 23085, 23090, 
	23091, 23093, 23099, 23109, 23114, 23118, 23130, 23135, 
	23136, 23139, 23150, 23153, 23154, 23163, 23168, 23174, 
	23175, 23190, 23199, 23205, 23219, 23220, 23223, 23225, 
	23228, 23235, 23238, 23244, 23249, 23253, 23255, 23261, 
	23274, 23279, 23283, 23286, 23294, 23295, 23300, 23309, 
	23316, 23319, 23321, 23324, 23331, 23339, 23340, 23343, 
	23345, 23351, 23361, 23363, 23373, 23375, 23378, 23384, 
	23385, 23403, 23405, 23408, 23409, 23414, 23415, 23426, 
	23430, 23433, 23438, 23444, 23450, 23459, 23466, 23478, 
	23496, 23498, 23508, 23520, 23525, 23528, 23529, 23543, 
	23546, 23555, 23559, 23561, 23564, 23568, 23571, 23573, 
	23574, 23580, 23594, 23603, 23610, 23618, 23625, 23634, 
	23639, 23643, 23646, 23648, 23651, 23654, 23658, 23669, 
	23675, 23676, 23681, 23690, 23693, 23694, 23703, 23708, 
	23709, 23715, 23720, 23729, 23745, 23748, 23750, 23753, 
	23756, 23760, 23763, 23766, 23771, 23781, 23784, 23790, 
	23795, 23799, 23804, 23811, 23814, 23819, 23826, 23828, 
	23829, 23840, 23849, 23850, 23855, 23856, 23858, 23868, 
	23870, 23871, 23888, 23889, 23895, 23898, 23903, 23904, 
	23909, 23918, 23921, 23928, 23934, 23940, 23951, 23955, 
	23958, 23966, 23969, 23973, 23975, 23981, 23984, 23988, 
	23990, 24008, 24011, 24014, 24024, 24036, 24039, 24045, 
	24054, 24059, 24060, 24065, 24078, 24081, 24089, 24093, 
	24096, 24098, 24110, 24119, 24123, 24129, 24135, 24140, 
	24149, 24155, 24156, 24168, 24170, 24176, 24185, 24191, 
	24198, 24203, 24204, 24206, 24218, 24224, 24231, 24236, 
	24239, 24240, 24243, 24245, 24248, 24261, 24263, 24266, 
	24269, 24270, 24281, 24285, 24294, 24296, 24305, 24309, 
	24311, 24323, 24324, 24330, 24336, 24338, 24339, 24365, 
	24366, 24375, 24378, 24380, 24383, 24389, 24390, 24393, 
	24399, 24404, 24408, 24410, 24411, 24423, 24428, 24429, 
	24434, 24435, 24441, 24444, 24453, 24473, 24476, 24486, 
	24494, 24495, 24501, 24504, 24509, 24515, 24516, 24518, 
	24521, 24528, 24534, 24540, 24551, 24554, 24558, 24560, 
	24561, 24569, 24578, 24584, 24585, 24588, 24596, 24599, 
	24600, 24603, 24605, 24611, 24626, 24630, 24638, 24639, 
	24648, 24653, 24665, 24666, 24669, 24681, 24683, 24684, 
	24695, 24696, 24704, 24705, 24708, 24714, 24716, 24725, 
	24729, 24731, 24738, 24740, 24749, 24761, 24764, 24765, 
	24768, 24773, 24774, 24779, 24798, 24801, 24806, 24813, 
	24816, 24819, 24831, 24833, 24834, 24840, 24848, 24855, 
	24863, 24869, 24870, 24873, 24878, 24891, 24893, 24894, 
	24900, 24903, 24905, 24911, 24915, 24921, 24926, 24935, 
	24938, 24945, 24959, 24960, 24963, 24968, 24969, 24971, 
	24978, 24995, 24996, 24999, 25010, 25011, 25016, 25023, 
	25025, 25026, 25034, 25038, 25043, 25046, 25050, 25055, 
	25059, 25061, 25064, 25065, 25073, 25076, 25079, 25088, 
	25103, 25110, 25113, 25115, 25130, 25131, 25136, 25143, 
	25145, 25155, 25160, 25164, 25166, 25170, 25179, 25181, 
	25188, 25191, 25193, 25205, 25208, 25211, 25220, 25229, 
	25230, 25248, 25251, 25256, 25263, 25269, 25271, 25274, 
	25275, 25290, 25293, 25295, 25296, 25299, 25313, 25323, 
	25325, 25335, 25341, 25353, 25361, 25370, 25376, 25383, 
	25386, 25388, 25394, 25410, 25416, 25419, 25424, 25428, 
	25433, 25436, 25445, 25446, 25454, 25461, 25464, 25475, 
	25478, 25484, 25485, 25494, 25496, 25500, 25515, 25521, 
	25523, 25529, 25530, 25535, 25554, 25565, 25566, 25568, 
	25575, 25578, 25584, 25596, 25598, 25599, 25601, 25608, 
	25614, 25619, 25620, 25628, 25631, 25641, 25643, 25653, 
	25664, 25670, 25671, 25673, 25674, 25680, 25691, 25703, 
	25706, 25709, 25710, 25713, 25715, 25718, 25719, 25724, 
	25730, 25736, 25739, 25740, 25743, 25751, 25755, 25758, 
	25760, 25769, 25775, 25781, 25788, 25790, 25796, 25799, 
	25803, 25806, 25815, 25818, 25823, 25829, 25836, 25839, 
	25841, 25845, 25856, 25859, 25860, 25874, 25883, 25884, 
	25893, 25898, 25901, 25908, 25913, 25914, 25919, 25926, 
	25929, 25934, 25935, 25946, 25949, 25953, 25956, 25964, 
	25970, 25974, 25985, 25986, 25988, 25995, 26004, 26010, 
	26013, 26025, 26028, 26033, 26034, 26040, 26051, 26060, 
	26063, 26073, 26076, 26081, 26088, 26090, 26091, 26094, 
	26100, 26111, 26118, 26124, 26126, 26129, 26133, 26144, 
	26145, 26150, 26156, 26160, 26180, 26181, 26184, 26189, 
	26193, 26195, 26216, 26226, 26228, 26244, 26250, 26255, 
	26258, 26264, 26270, 26271, 26276, 26280, 26283, 26285, 
	26289, 26291, 26304, 26313, 26315, 26319, 26333, 26336, 
	26345, 26348, 26354, 26355, 26360, 26363, 26366, 26373, 
	26378, 26384, 26391, 26403, 26406, 26408, 26418, 26429, 
	26430, 26439, 26441, 26444, 26450, 26451, 26459, 26468, 
	26475, 26478, 26481, 26483, 26486, 26490, 26499, 26501, 
	26508, 26523, 26525, 26534, 26538, 26543, 26544, 26546, 
	26550, 26556, 26558, 26564, 26573, 26574, 26580, 26585, 
	26586, 26594, 26598, 26600, 26615, 26616, 26619, 26633, 
	26634, 26639, 26640, 26649, 26654, 26661, 26663, 26676, 
	26679, 26688, 26690, 26700, 26703, 26705, 26709, 26718, 
	26720, 26726, 26739, 26751, 26753, 26763, 26774, 26775, 
	26784, 26795, 26796, 26798, 26804, 26805, 26808, 26811, 
	26814, 26816, 26819, 26826, 26828, 26840, 26846, 26849, 
	26858, 26859, 26865, 26879, 26886, 26888, 26891, 26895, 
	26906, 26909, 26915, 26924, 26928, 26930, 26940, 26943, 
	26945, 26948, 26949, 26958, 26961, 26963, 26969, 26975, 
	26979, 26993, 26996, 27000, 27005, 27006, 27018, 27024, 
	27029, 27041, 27045, 27050, 27060, 27066, 27069, 27075, 
	27081, 27083, 27090, 27096, 27108, 27125, 27134, 27138, 
	27143, 27146, 27155, 27159, 27161, 27165, 27173, 27180, 
	27183, 27185, 27188, 27200, 27201, 27204, 27206, 27209, 
	27210, 27218, 27221, 27224, 27234, 27246, 27248, 27249, 
	27251, 27258, 27260, 27269, 27270, 27273, 27279, 27281, 
	27288, 27290, 27291, 27300, 27308, 27311, 27314, 27315, 
	27323, 27333, 27336, 27339, 27354, 27356, 27360, 27363, 
	27375, 27383, 27386, 27389, 27393, 27399, 27414, 27416, 
	27425, 27434, 27438, 27440, 27453, 27458, 27459, 27470, 
	27474, 27479, 27486, 27489, 27491, 27500, 27504, 27510, 
	27524, 27525, 27528, 27530, 27536, 27539, 27551, 27554, 
	27558, 27563, 27573, 27581, 27585, 27600, 27603, 27606, 
	27608, 27609, 27614, 27621, 27624, 27629, 27645, 27656, 
	27665, 27666, 27668, 27669, 27671, 27675, 27686, 27690, 
	27699, 27705, 27719, 27720, 27728, 27734, 27743, 27750, 
	27755, 27764, 27770, 27773, 27789, 27794, 27801, 27804, 
	27809, 27810, 27815, 27816, 27819, 27830, 27831, 27833, 
	27836, 27840, 27845, 27848, 27855, 27858, 27860, 27866, 
	27881, 27893, 27896, 27899, 27903, 27906, 27908, 27909, 
	27911, 27914, 27918, 27921, 27924, 27935, 27944, 27948, 
	27950, 27951, 27960, 27963, 27965, 27966, 27974, 27983, 
	27993, 27998, 28001, 28004, 28019, 28020, 28026, 28040, 
	28043, 28046, 28049, 28050, 28056, 28061, 28065, 28074, 
	28083, 28085, 28089, 28098, 28103, 28104, 28118, 28119, 
	28124, 28131, 28133, 28134, 28149, 28155, 28166, 28179, 
	28184, 28188, 28191, 28196, 28200, 28208, 28215, 28218, 
	28221, 28226, 28233, 28236, 28238, 28239, 28244, 28250, 
	28251, 28254, 28259, 28263, 28265, 28266, 28271, 28284, 
	28295, 28298, 28299, 28305, 28314, 28316, 28329, 28331, 
	28335, 28340, 28343, 28350, 28355, 28356, 28365, 28368, 
	28373, 28383, 28386, 28389, 28391, 28403, 28404, 28406, 
	28410, 28413, 28421, 28428, 28436, 28445, 28446, 28448, 
	28454, 28455, 28460, 28461, 28464, 28470, 28475, 28478, 
	28481, 28491, 28494, 28496, 28499, 28518, 28520, 28523, 
	28529, 28536, 28538, 28544, 28548, 28553, 28559, 28565, 
	28569, 28571, 28574, 28581, 28586, 28589, 28595, 28596, 
	28601, 28610, 28611, 28620, 28625, 28629, 28634, 28635, 
	28641, 28643, 28650, 28664, 28665, 28673, 28674, 28683, 
	28686, 28691, 28694, 28698, 28706, 28713, 28728, 28733, 
	28743, 28746, 28751, 28763, 28764, 28778, 28779, 28785, 
	28793, 28796, 28800, 28818, 28820, 28824, 28826, 28833, 
	28839, 28844, 28848, 28854, 28856, 28859, 28863, 28865, 
	28868, 28875, 28886, 28890, 28893, 28895, 28896, 28901, 
	28904, 28914, 28919, 28923, 28926, 28929, 28940, 28949, 
	28950, 28958, 28961, 28971, 28973, 28986, 28988, 28995, 
	29006, 29013, 29015, 29021, 29024, 29028, 29030, 29033, 
	29036, 29049, 29054, 29055, 29064, 29073, 29075, 29076, 
	29084, 29085, 29094, 29096, 29099, 29103, 29105, 29108, 
	29114, 29115, 29118, 29121, 29135, 29154, 29156, 29160, 
	29168, 29181, 29183, 29184, 29189, 29195, 29196, 29201, 
	29205, 29208, 29213, 29219, 29220, 29225, 29226, 29238, 
	29240, 29255, 29268, 29271, 29274, 29283, 29286, 29289, 
	29300, 29301, 29306, 29315, 29328, 29330, 29339, 29343, 
	29346, 29349, 29355, 29363, 29366, 29370, 29378, 29381, 
	29385, 29393, 29394, 29415, 29444, 29448, 29450, 29453, 
	29454, 29456, 29460, 29468, 29471, 29481, 29483, 29489, 
	29495, 29498, 29504, 29505, 29510, 29511, 29514, 29525, 
	29526, 29531, 29534, 29538, 29541, 29546, 29553, 29556, 
	29559, 29561, 29570, 29574, 29579, 29583, 29591, 29598, 
	29603, 29604, 29609, 29610, 29616, 29619, 29621, 29631, 
	29636, 29640, 29666, 29670, 29675, 29678, 29679, 29684, 
	29688, 29693, 29696, 29699, 29703, 29708, 29709, 29720, 
	29721, 29723, 29726, 29733, 29735, 29736, 29748, 29754, 
	29756, 29769, 29778, 29780, 29783, 29790, 29805, 29808, 
	29810, 29813, 29814, 29825, 29829, 29831, 29834, 29835, 
	29846, 29849, 29853, 29861, 29864, 29871, 29873, 29876, 
	29885, 29889, 29895, 29898, 29904, 29916, 29931, 29939, 
	29943, 29960, 29964, 29975, 29978, 29985, 29990, 29999, 
	30006, 30008, 30014, 30018, 30020, 30038, 30041, 30044, 
	30045, 30050, 30051, 30053, 30063, 30066, 30069, 30074, 
	30080, 30083, 30084, 30104, 30108, 30111, 30125, 30128, 
	30129, 30135, 30144, 30146, 30158, 30165, 30168, 30171, 
	30176, 30186, 30191, 30198, 30206, 30213, 30221, 30224, 
	30228, 30246, 30248, 30254, 30260, 30263, 30269, 30294, 
	30300, 30303, 30305, 30308, 30311, 30315, 30318, 30323, 
	30324, 30329, 30330, 30339, 30344, 30351, 30359, 30363, 
	30366, 30368, 30378, 30380, 30381, 30386, 30389, 30396, 
	30405, 30410, 30429, 30434, 30443, 30444, 30449, 30450, 
	30456, 30458, 30459, 30461, 30468, 30471, 30476, 30480, 
	30500, 30503, 30513, 30515, 30521, 30525, 30528, 30545, 
	30549, 30560, 30564, 30570, 30575, 30576, 30584, 30605, 
	30611, 30615, 30626, 30630, 30641, 30645, 30648, 30665, 
	30666, 30669, 30671, 30678, 30681, 30689, 30690, 30701, 
	30704, 30708, 30720, 30731, 30734, 30735, 30741, 30743, 
	30746, 30753, 30755, 30759, 30771, 30773, 30776, 30779, 
	30780, 30791, 30801, 30804, 30806, 30813, 30815, 30818, 
	30821, 30825, 30828, 30833, 30836, 30840, 30843, 30851, 
	30858, 30861, 30864, 30875, 30878, 30890, 30906, 30909, 
	30918, 30921, 30930, 30935, 30939, 30954, 30963, 30966, 
	30974, 30980, 30983, 30989, 30990, 30993, 30995, 31001, 
	31005, 31008, 31019, 31023, 31026, 31028, 31035, 31040, 
	31049, 31059, 31064, 31065, 31068, 31070, 31071, 31085, 
	31094, 31095, 31100, 31103, 31106, 31109, 31116, 31136, 
	31148, 31149, 31151, 31155, 31161, 31163, 31173, 31175, 
	31191, 31200, 31208, 31211, 31229, 31233, 31236, 31238, 
	31241, 31248, 31250, 31253, 31266, 31269, 31274, 31281, 
	31290, 31295, 31298, 31301, 31308, 31313, 31316, 31319, 
	31326, 31329, 31341, 31343, 31350, 31361, 31365, 31371, 
	31376, 31380, 31386, 31395, 31400, 31409, 31413, 31425, 
	31430, 31434, 31436, 31448, 31451, 31460, 31463, 31464, 
	31469, 31484, 31485, 31490, 31491, 31493, 31494, 31514, 
	31515, 31529, 31533, 31536, 31539, 31548, 31551, 31556, 
	31563, 31565, 31574, 31589, 31598, 31599, 31605, 31620, 
	31623, 31638, 31640, 31649, 31655, 31656, 31658, 31665, 
	31668, 31673, 31676, 31680, 31683, 31688, 31694, 31695, 
	31698, 31704, 31709, 31710, 31719, 31721, 31731, 31733, 
	31736, 31743, 31746, 31749, 31760, 31763, 31766, 31770, 
	31779, 31788, 31793, 31794, 31799, 31800, 31803, 31805, 
	31808, 31814, 31823, 31824, 31829, 31833, 31835, 31844, 
	31845, 31848, 31851, 31854, 31859, 31863, 31868, 31871, 
	31880, 31886, 31890, 31896, 31899, 31901, 31904, 31911, 
	31919, 31920, 31926, 31928, 31931, 31950, 31953, 31956, 
	31964, 31974, 31988, 31998, 32003, 32006, 32009, 32016, 
	32018, 32031, 32033, 32040, 32045, 32054, 32061, 32075, 
	32076, 32078, 32085, 32093, 32094, 32108, 32111, 32115, 
	32118, 32135, 32139, 32141, 32150, 32151, 32159, 32163, 
	32166, 32186, 32190, 32199, 32201, 32216, 32219, 32225, 
	32226, 32241, 32244, 32249, 32256, 32276, 32283, 32288, 
	32289, 32295, 32300, 32304, 32306, 32310, 32313, 32316, 
	32330, 32331, 32333, 32339, 32346, 32354, 32358, 32373, 
	32381, 32390, 32391, 32396, 32405, 32408, 32424, 32426, 
	32435, 32438, 32439, 32445, 32450, 32459, 32460, 32463, 
	32468, 32475, 32484, 32498, 32501, 32505, 32513, 32514, 
	32516, 32526, 32531, 32535, 32544, 32549, 32550, 32555, 
	32559, 32561, 32564, 32570, 32573, 32583, 32585, 32586, 
	32589, 32591, 32601, 32606, 32619, 32628, 32633, 32634, 
	32643, 32646, 32654, 32661, 32663, 32676, 32678, 32685, 
	32690, 32696, 32703, 32706, 32709, 32711, 32718, 32723, 
	32724, 32739, 32748, 32759, 32760, 32768, 32769, 32771, 
	32775, 32778, 32781, 32789, 32790, 32793, 32799, 32804, 
	32808, 32814, 32816, 32823, 32825, 32828, 32838, 32843, 
	32849, 32850, 32853, 32856, 32858, 32859, 32864, 32865, 
	32880, 32888, 32894, 32904, 32913, 32915, 32918, 32919, 
	32921, 32925, 32933, 32940, 32949, 32960, 32963, 32964, 
	32975, 32978, 32981, 32990, 32991, 32996, 33014, 33018, 
	33020, 33023, 33033, 33035, 33041, 33044, 33051, 33053, 
	33054, 33068, 33080, 33084, 33086, 33089, 33095, 33110, 
	33119, 33135, 33146, 33150, 33168, 33171, 33173, 33179, 
	33180, 33186, 33188, 33191, 33201, 33206, 33215, 33224, 
	33228, 33231, 33233, 33245, 33249, 33254, 33261, 33264, 
	33266, 33270, 33276, 33284, 33285, 33293, 33296, 33300, 
	33308, 33314, 33321, 33326, 33341, 33348, 33350, 33356, 
	33360, 33366, 33369, 33374, 33375, 33381, 33395, 33398, 
	33404, 33410, 33420, 33425, 33426, 33431, 33438, 33441, 
	33444, 33459, 33461, 33465, 33471, 33473, 33474, 33479, 
	33486, 33488, 33501, 33510, 33516, 33521, 33524, 33528, 
	33530, 33536, 33539, 33551, 33560, 33564, 33569, 33570, 
	33576, 33578, 33584, 33590, 33593, 33594, 33605, 33606, 
	33608, 33609, 33615, 33623, 33630, 33635, 33636, 33644, 
	33653, 33669, 33671, 33674, 33684, 33695, 33699, 33704, 
	33705, 33710, 33713, 33714, 33716, 33723, 33726, 33738, 
	33740, 33744, 33746, 33749, 33755, 33761, 33765, 33768, 
	33773, 33779, 33783, 33788, 33789, 33794, 33800, 33803, 
	33809, 33815, 33825, 33839, 33849, 33854, 33861, 33866, 
	33870, 33875, 33878, 33879, 33881, 33888, 33891, 33894, 
	33900, 33903, 33909, 33914, 33921, 33926, 33933, 33941, 
	33945, 33950, 33963, 33965, 33966, 33969, 33971, 33978, 
	33980, 33983, 33989, 33993, 33996, 34011, 34020, 34026, 
	34029, 34035, 34043, 34049, 34055, 34056, 34070, 34073, 
	34080, 34085, 34103, 34104, 34106, 34109, 34113, 34119, 
	34130, 34139, 34140, 34155, 34164, 34175, 34185, 34194, 
	34199, 34218, 34221, 34223, 34224, 34236, 34238, 34241, 
	34244, 34245, 34250, 34253, 34260, 34265, 34269, 34271, 
	34283, 34290, 34298, 34305, 34316, 34319, 34329, 34334, 
	34341, 34343, 34349, 34355, 34356, 34364, 34368, 34371, 
	34374, 34383, 34385, 34388, 34395, 34406, 34409, 34410, 
	34431, 34439, 34440, 34445, 34448, 34449, 34451, 34454, 
	34458, 34463, 34473, 34481, 34496, 34500, 34505, 34509, 
	34514, 34515, 34530, 34533, 34536, 34554, 34559, 34563, 
	34571, 34574, 34575, 34581, 34595, 34596, 34598, 34601, 
	34610, 34616, 34619, 34623, 34628, 34629, 34631, 34656, 
	34658, 34668, 34670, 34685, 34689, 34691, 34694, 34700, 
	34701, 34713, 34715, 34719, 34728, 34731, 34733, 34736, 
	34740, 34745, 34746, 34748, 34749, 34769, 34778, 34796, 
	34811, 34826, 34830, 34838, 34845, 34848, 34854, 34868, 
	34869, 34880, 34881, 34883, 34889, 34904, 34910, 34913, 
	34914, 34916, 34923, 34928, 34929, 34938, 34949, 34955, 
	34964, 34965, 34970, 34979, 34995, 34998, 35000, 35001, 
	35004, 35009, 35019, 35025, 35030, 35033, 35039, 35049, 
	35055, 35058, 35060, 35061, 35069, 35070, 35078, 35081, 
	35088, 35090, 35091, 35099, 35100, 35103, 35111, 35114, 
	35118, 35120, 35124, 35135, 35144, 35148, 35154, 35156, 
	35160, 35163, 35175, 35186, 35189, 35190, 35196, 35211, 
	35214, 35219, 35225, 35228, 35229, 35240, 35243, 35244, 
	35250, 35253, 35264, 35268, 35274, 35285, 35286, 35291, 
	35294, 35303, 35309, 35310, 35313, 35319, 35328, 35331, 
	35333, 35343, 35354, 35358, 35364, 35376, 35384, 35391, 
	35396, 35411, 35420, 35421, 35424, 35426, 35433, 35438, 
	35439, 35445, 35450, 35456, 35459, 35460, 35468, 35474, 
	35475, 35478, 35484, 35489, 35490, 35495, 35498, 35499, 
	35505, 35511, 35519, 35529, 35534, 35540, 35544, 35559, 
	35564, 35571, 35573, 35576, 35580, 35583, 35585, 35595, 
	35604, 35616, 35618, 35624, 35628, 35630, 35631, 35643, 
	35646, 35658, 35663, 35664, 35666, 35669, 35670, 35673, 
	35676, 35679, 35681, 35693, 35694, 35699, 35705, 35706, 
	35709, 35714, 35718, 35721, 35726, 35735, 35736, 35739, 
	35741, 35751, 35763, 35768, 35774, 35775, 35781, 35784, 
	35796, 35798, 35816, 35823, 35831, 35835, 35846, 35849, 
	35853, 35855, 35856, 35859, 35870, 35880, 35888, 35894, 
	35903, 35904, 35910, 35918, 35921, 35924, 35930, 35933, 
	35939, 35940, 35943, 35949, 35954, 35958, 35966, 35970, 
	35973, 35981, 35985, 35991, 35993, 35996, 35999, 36009, 
	36015, 36021, 36023, 36026, 36036, 36038, 36044, 36045, 
	36050, 36051, 36054, 36069, 36080, 36083, 36084, 36086, 
	36105, 36110, 36111, 36113, 36114, 36125, 36126, 36134, 
	36135, 36138, 36143, 36153, 36156, 36168, 36170, 36176, 
	36183, 36189, 36191, 36210, 36215, 36230, 36233, 36234, 
	36240, 36246, 36248, 36251, 36266, 36273, 36275, 36279, 
	36288, 36306, 36308, 36311, 36321, 36323, 36324, 36330, 
	36335, 36336, 36339, 36344, 36350, 36353, 36359, 36363, 
	36366, 36369, 36381, 36383, 36398, 36408, 36411, 36429, 
	36434, 36435, 36441, 36444, 36446, 36450, 36453, 36455, 
	36461, 36465, 36468, 36474, 36476, 36479, 36486, 36488, 
	36498, 36504, 36506, 36509, 36518, 36519, 36521, 36530, 
	36531, 36539, 36545, 36560, 36563, 36566, 36570, 36590, 
	36594, 36618, 36621, 36629, 36638, 36645, 36651, 36654, 
	36663, 36665, 36675, 36680, 36681, 36684, 36689, 36693, 
	36708, 36710, 36716, 36726, 36729, 36735, 36738, 36741, 
	36758, 36761, 36764, 36773, 36776, 36780, 36785, 36791, 
	36794, 36798, 36803, 36804, 36806, 36818, 36821, 36825, 
	36836, 36839, 36840, 36846, 36849, 36854, 36860, 36863, 
	36875, 36878, 36885, 36891, 36909, 36911, 36923, 36924, 
	36929, 36933, 36938, 36941, 36948, 36953, 36969, 36971, 
	36975, 36980, 36986, 36999, 37008, 37010, 37013, 37023, 
	37025, 37035, 37038, 37046, 37049, 37050, 37065, 37071, 
	37074, 37079, 37080, 37083, 37088, 37094, 37098, 37100, 
	37101, 37104, 37109, 37115, 37128, 37139, 37143, 37146, 
	37148, 37155, 37158, 37161, 37176, 37178, 37181, 37188, 
	37190, 37191, 37205, 37206, 37209, 37220, 37224, 37226, 
	37235, 37244, 37253, 37254, 37260, 37263, 37265, 37275, 
	37280, 37283, 37286, 37293, 37298, 37304, 37305, 37311, 
	37326, 37343, 37349, 37353, 37356, 37358, 37359, 37364, 
	37365, 37373, 37379, 37380, 37385, 37389, 37398, 37410, 
	37413, 37415, 37421, 37428, 37430, 37434, 37436, 37443, 
	37445, 37448, 37451, 37461, 37464, 37466, 37470, 37479, 
	37505, 37506, 37508, 37514, 37518, 37520, 37539, 37541, 
	37554, 37566, 37574, 37580, 37583, 37584, 37590, 37596, 
	37604, 37605, 37608, 37611, 37613, 37619, 37626, 37634, 
	37638, 37644, 37653, 37661, 37664, 37668, 37673, 37676, 
	37683, 37688, 37694, 37695, 37700, 37701, 37703, 37715, 
	37718, 37739, 37751, 37755, 37760, 37763, 37766, 37769, 
	37770, 37776, 37778, 37785, 37788, 37791, 37805, 37808, 
	37809, 37814, 37820, 37826, 37829, 37839, 37841, 37844, 
	37851, 37853, 37854, 37860, 37865, 37871, 37883, 37886, 
	37890, 37893, 37896, 37898, 37910, 37916, 37926, 37934, 
	37941, 37956, 37965, 37968, 37970, 37983, 37989, 37991, 
	37994, 37995, 37998, 38000, 38001, 38015, 38019, 38039, 
	38040, 38045, 38049, 38051, 38061, 38064, 38073, 38078, 
	38079, 38081, 38103, 38106, 38115, 38121, 38124, 38126, 
	38129, 38130, 38141, 38144, 38151, 38166, 38171, 38183, 
	38184, 38189, 38193, 38201, 38210, 38211, 38220, 38231, 
	38235, 38240, 38243, 38246, 38253, 38255, 38259, 38268, 
	38270, 38271, 38280, 38289, 38298, 38301, 38303, 38315, 
	38324, 38325, 38333, 38336, 38339, 38348, 38358, 38366, 
	38376, 38378, 38385, 38388, 38390, 38400, 38409, 38414, 
	38415, 38418, 38423, 38435, 38436, 38441, 38453, 38456, 
	38459, 38471, 38474, 38480, 38481, 38495, 38501, 38508, 
	38511, 38514, 38520, 38523, 38534, 38540, 38546, 38550, 
	38568, 38570, 38576, 38583, 38585, 38595, 38600, 38606, 
	38618, 38619, 38621, 38624, 38630, 38631, 38633, 38634, 
	38639, 38645, 38658, 38661, 38669, 38673, 38675, 38679, 
	38684, 38688, 38691, 38708, 38709, 38715, 38723, 38735, 
	38738, 38739, 38744, 38745, 38754, 38756, 38760, 38763, 
	38771, 38774, 38775, 38778, 38781, 38784, 38786, 38793, 
	38795, 38805, 38808, 38810, 38820, 38823, 38829, 38840, 
	38843, 38844, 38849, 38855, 38856, 38859, 38861, 38865, 
	38871, 38873, 38880, 38886, 38891, 38898, 38900, 38906, 
	38919, 38924, 38931, 38933, 38946, 38949, 38964, 38966, 
	38975, 38984, 38988, 38991, 38999, 39003, 39008, 39015, 
	39020, 39024, 39029, 39039, 39050, 39060, 39068, 39069, 
	39078, 39081, 39083, 39086, 39089, 39095, 39096, 39101, 
	39114, 39116, 39120, 39129, 39138, 39141, 39150, 39153, 
	39155, 39158, 39170, 39173, 39183, 39200, 39213, 39218, 
	39219, 39233, 39239, 39243, 39248, 39254, 39255, 39258, 
	39269, 39270, 39276, 39284, 39285, 39288, 39291, 39296, 
	39303, 39311, 39321, 39324, 39326, 39345, 39348, 39353, 
	39356, 39360, 39368, 39389, 39390, 39393, 39395, 39398, 
	39401, 39404, 39411, 39419, 39426, 39428, 39438, 39443, 
	39444, 39446, 39450, 39459, 39464, 39470, 39488, 39489, 
	39494, 39515, 39519, 39521, 39531, 39543, 39551, 39555, 
	39566, 39569, 39573, 39575, 39576, 39579, 39590, 39593, 
	39596, 39600, 39614, 39615, 39620, 39629, 39636, 39639, 
	39641, 39650, 39654, 39659, 39666, 39668, 39674, 39678, 
	39683, 39689, 39696, 39698, 39699, 39705, 39711, 39713, 
	39716, 39725, 39740, 39746, 39765, 39768, 39774, 39779, 
	39780, 39789, 39794, 39800, 39804, 39806, 39810, 39813, 
	39815, 39816, 39828, 39834, 39843, 39845, 39846, 39848, 
	39849, 39878, 39884, 39888, 39900, 39905, 39906, 39908, 
	39911, 39914, 39920, 39921, 39923, 39930, 39933, 39936, 
	39944, 39950, 39951, 39953, 39969, 39971, 39983, 39986, 
	39989, 39993, 39998, 39999, 0
};

int notest
	(mpz_ptr p, mpz_ptr q)
{
	assert((p == q) || (p != q)); // dummy to supress compiler warning
	return 1;
}

int test7mod8
	(mpz_ptr p, mpz_ptr q)
{
	assert((p == q) || (p != q)); // dummy to supress compiler warning
	return mpz_congruent_ui_p(p, 7L, 8L);
}

int test3mod4
	(mpz_ptr p, mpz_ptr q)
{
	assert((p == q) || (p != q)); // dummy to supress compiler warning
	return mpz_congruent_ui_p(p, 3L, 4L);
}

/** Miller-Rabin witness test, basically algorithm 4.24 [HAC], for a
    fixed base.

    @returns 1, if the number @a base is a Miller-Rabin witness to the
                compositness of @a n.
    @returns 0, otherwise. */

int tmcg_mpz_mr_witness
	(mpz_srcptr n, mpz_srcptr base)
{
	int result = 1;
	mpz_t y, r, nm1;
	
	mpz_init(y), mpz_init(nm1), mpz_init(r);
	
	// 1. Write $\mathtt{n} - 1 = 2^s r$ such that $r$ is odd.
	mpz_sub_ui(nm1, n, 1L);
	unsigned long int s = mpz_scan1(nm1, 0L);
	mpz_tdiv_q_2exp(r, nm1, s);
	if (mpz_odd_p(r))
	{
		// 2.2 Compute $y = \mathtt{base}^r \bmod \mathtt{n}$.
		mpz_powm(y, base, r, n);
		result = 0;
		
		// 2.3 If $y \neq 1$ and $y \neq \mathtt{n} - 1$ then do the following:
		if ((mpz_cmp_ui(y, 1L) != 0) && (mpz_cmp(y, nm1) != 0))
		{
			for (unsigned long int j = 1; j < s; j++)
			{
				mpz_mul(y, y, y);
				mpz_mod(y, y, n);
				if (mpz_cmp_ui(y, 1L) == 0)
				{
					result = 1;
					break;
				}
				if (mpz_cmp(y, nm1) == 0)
					break;
			}
			// strong witness?
			if (mpz_cmp(y, nm1) != 0)
				result = 1;
		}
	}
	
	mpz_clear(y), mpz_clear(nm1), mpz_clear(r);
	return result;
}

bool tmcg_mpz_mr_witness_fast
	(mpz_srcptr n, mpz_srcptr base, mpz_ptr y, mpz_srcptr nm1, mpz_ptr r)
{
	// 1. Write $\mathtt{n} - 1 = 2^s r$ such that $r$ is odd.
	unsigned long int s = mpz_scan1(nm1, 0L);
	mpz_tdiv_q_2exp(r, nm1, s);
	if (mpz_even_p(r))
		return true;
	
	// 2.2 Compute $y = \mathtt{base}^r \bmod \mathtt{n}$.
	mpz_powm(y, base, r, n);

	// 2.3 If $y \neq 1$ and $y \neq \mathtt{n} - 1$ then do the following:
	if ((mpz_cmp_ui(y, 1L) != 0) && (mpz_cmp(y, nm1) != 0))
	{
		for (unsigned long int j = 1; j < s; j++)
		{
			mpz_mul(y, y, y);
			mpz_mod(y, y, n);
			if (mpz_cmp_ui(y, 1L) == 0)
				return true;
			if (mpz_cmp(y, nm1) == 0)
				break;
		}
		// strong witness?
		if (mpz_cmp(y, nm1) != 0)
			return true;
	}
	return false;
}

/** The fast generation of safe primes is implemented according to [CS00]
    and M.J. Wiener's "Safe Prime Generation with a Combined Sieve". */

void tmcg_mpz_sprime_test
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize,
	 int (*test)(mpz_ptr, mpz_ptr),
	 const unsigned long int mr_iterations,
	 const size_t primes_size)
{
	unsigned long int R_q[SIEVE_SIZE], R_p[SIEVE_SIZE];
	mpz_t tmp, y, pm1, qm1, a;
	
	mpz_init(tmp), mpz_init(y), mpz_init(pm1), mpz_init(qm1);
	mpz_init_set_ui(a, 2L);
	
	/* Step 1. [CS00]: choose randomly an odd number $q$ of appropriate size */
	do
		tmcg_mpz_srandomb(q, qsize);
	while (mpz_sizeinbase(q, 2L) < qsize);
	if (mpz_even_p(q))
		mpz_add_ui(q, q, 1L);
	
	/* Compute $p = 2q + 1$. */
	mpz_mul_2exp(pm1, q, 1L), mpz_add_ui(p, pm1, 1L);
	mpz_sub_ui(qm1, q, 1L);
	
	/* Initalize the sieves for testing divisability by small primes. */
	for (size_t i = 0; i < SIEVE_SIZE; i++)
	{
		mpz_set_ui(tmp, primes[i]);
		/* R_q[i] = q mod primes[i] */
		mpz_mod(y, q, tmp);
		R_q[i] = mpz_get_ui(y);
		/* R_p[i] = (2q+1) mod primes[i] */
		mpz_mod(y, p, tmp);
		R_p[i] = mpz_get_ui(y);
	}
	
	while (1)
	{
		/* Increase $q$ by 2 (incremental prime number generator). */
		mpz_add_ui(q, q, 2L), mpz_add_ui(qm1, qm1, 2L);
		
		/* Increase $p$ by 4 (actually compute $p = 2q + 1$). */
		mpz_add_ui(p, p, 4L), mpz_add_ui(pm1, pm1, 4L);
		
		/* Use the sieve optimization procedure of Note 4.51(ii) [HAC]. */
		bool fail = false;
		for (size_t i = 0; i < SIEVE_SIZE; i++)
		{
			/* Update the sieves. */
			R_q[i] += 2, R_q[i] %= primes[i], R_p[i] += 4, R_p[i] %= primes[i];
			/* Check whether R_q[i] or R_p[i] is zero. We cannot break this
			   loop, because we have to update the sieves completely for the
			   next round. */
			if ((R_q[i] == 0) || (R_p[i] == 0))
				fail = true;
		}
		if (fail)
			continue;
		
		/* Additional tests? */
		if (!test(p, q))
			continue;
		
		/* Step 2. [CS00]: M.J. Wiener's "Combined Sieve"
		   Check whether $q$ or $p$ are divisable by any primes up to $B$. */
		for (size_t i = 0; i < primes_size; i++)
		{
			if (mpz_congruent_ui_p(q, primes_m1d2[i], primes[i]) ||
				mpz_congruent_ui_p(p, primes_m1d2[i], primes[i]))
			{
				fail = true;
				break;
			}
			if (i >= SIEVE_SIZE)
			{
				if (mpz_congruent_ui_p(q, 0L, primes[i]) ||
					mpz_congruent_ui_p(p, 0L, primes[i]))
				{
					fail = true;
					break;
				}
			}
		}
		if (fail)
			continue;
			
		/* Step 3. [CS00]: Test whether 2 is not a Miller-Rabin witness to the
		   compositeness of $q$. */
		if (tmcg_mpz_mr_witness_fast(q, a, y, qm1, tmp))
			continue;
		
		/* Step 4. [CS00]: Test whether $2^q \equiv \pm 1 \pmod{p}$. */
		mpz_powm(y, a, q, p);
		if ((mpz_cmp_ui(y, 1L) != 0) && (mpz_cmp(y, pm1) != 0))
			continue;
		
		/* Step 5. [CS00]: Apply the Miller-Rabin test to $q$ a defined number
		   of times (maximum error probability $4^{-mr_iterations}$) using
		   randomly selected bases. */
		if (mpz_probab_prime_p(q, mr_iterations - 1))
			break;
	}
	mpz_clear(tmp), mpz_clear(y), mpz_clear(pm1), mpz_clear(qm1), mpz_clear(a);
}

// A naive generator for safe primes

void tmcg_mpz_sprime_test_naive
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize,
	 int (*test)(mpz_ptr, mpz_ptr),
	 const unsigned long int mr_iterations,
	 const size_t primes_size)
{
	/* Choose randomly an odd number $q$ of appropriate size. */
	do
		tmcg_mpz_srandomb(q, qsize);
	while (mpz_sizeinbase(q, 2L) < qsize);
	if (mpz_even_p(q))
		mpz_add_ui(q, q, 1L);
	
	while (1)
	{
		/* Increase $q$ by 2 (incremental prime number generator). */
		mpz_add_ui(q, q, 2L);
		/* Compute $p = 2q + 1$. */
		mpz_mul_2exp(p, q, 1L);
		mpz_add_ui(p, p, 1L);
		
		/* Additional tests? */
		if (!test(p, q))
			continue;
		
		/* Check whether $q$ or $p$ are divisable by any primes up to $B$. */
		bool fail = false;
		for (size_t i = 0; i < primes_size; i++)
		{
			if (mpz_congruent_ui_p(q, primes_m1d2[i], primes[i]) ||
				mpz_congruent_ui_p(p, primes_m1d2[i], primes[i]) ||
				mpz_congruent_ui_p(q, 0L, primes[i]) ||
				mpz_congruent_ui_p(p, 0L, primes[i]))
			{
				fail = true;
				break;
			}
		}
		if (fail)
			continue;
		
		if (!mpz_probab_prime_p(p, 1))
			continue;
		
		if (!mpz_probab_prime_p(q, mr_iterations))
			continue;
		
		if (mpz_probab_prime_p(p, mr_iterations - 1))
			break;
	}
}

// A non-incremental generator for safe primes (slow for $\log_2 p \ge 1024$)

void tmcg_mpz_sprime_test_noninc
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize,
	 int (*test)(mpz_ptr, mpz_ptr),
	 const unsigned long int mr_iterations,
	 const size_t primes_size)
{
	while (1)
	{
		/* Choose randomly an odd number $q$ of appropriate size. */
		do
			tmcg_mpz_srandomb(q, qsize);
		while (mpz_sizeinbase(q, 2L) < qsize);
		if (mpz_even_p(q))
			mpz_add_ui(q, q, 1L);
 
		/* Compute $p = 2q + 1$. */
		mpz_mul_2exp(p, q, 1L);
		mpz_add_ui(p, p, 1L);
		
		/* Additional tests? */
		if (!test(p, q))
			continue;
		
		/* Check whether $q$ or $p$ are divisable by any primes up to $B$. */
		bool fail = false;
		for (size_t i = 0; i < primes_size; i++)
		{
			if (mpz_congruent_ui_p(q, primes_m1d2[i], primes[i]) ||
				mpz_congruent_ui_p(p, primes_m1d2[i], primes[i]) ||
				mpz_congruent_ui_p(q, 0L, primes[i]) ||
				mpz_congruent_ui_p(p, 0L, primes[i]))
			{
				fail = true;
				break;
			}
		}
		if (fail)
			continue;
		
		// Check that $p$ and $q$ are probable prime.
		if (!mpz_probab_prime_p(p, 1))
			continue;
		if (!mpz_probab_prime_p(q, mr_iterations))
			continue;
		if (mpz_probab_prime_p(p, mr_iterations - 1))
			break;
	}
}

void tmcg_mpz_sprime
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	tmcg_mpz_sprime_test(p, q, qsize, notest, mr_iterations, PRIMES);
}

void tmcg_mpz_smprime
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	tmcg_mpz_sprime_test(p, q, qsize, notest, mr_iterations, MPRIMES);
}

void tmcg_mpz_sprime_naive
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	tmcg_mpz_sprime_test_naive(p, q, qsize, notest, mr_iterations, PRIMES);
}

void tmcg_mpz_sprime_noninc
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	tmcg_mpz_sprime_test_noninc(p, q, qsize, notest, mr_iterations, PRIMES);
}

void tmcg_mpz_sprime2g
	(mpz_ptr p, mpz_ptr q,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	/* The additional test is required, if we want 2 as generator of
	   $\mathbb{QR}_p$. If $p$ is congruent 7 modulo 8, then 2 is a
	   quadratic residue and hence it will generate the cyclic subgroup
	   of prime order $q = (p-1)/2$. [RS00] */
	tmcg_mpz_sprime_test(p, q, qsize, test7mod8, mr_iterations, PRIMES);
}

void tmcg_mpz_sprime3mod4
	(mpz_ptr p,
	 const unsigned long int psize,
	 const unsigned long int mr_iterations)
{
	mpz_t q;

	/* This test is required, if we want to construct a Blum integer $n$,
	   i.e. a number where both factors are primes congruent 3 modulo 4. */
	mpz_init(q);
	tmcg_mpz_sprime_test(p, q, psize - 1L, test3mod4, mr_iterations, PRIMES);
	mpz_clear(q);
}

void tmcg_mpz_lprime
	(mpz_ptr p, mpz_ptr q, mpz_ptr k, 
	 const unsigned long int psize,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	mpz_t foo;
	if (qsize >= psize)
		throw std::invalid_argument("tmcg_mpz_lprime: qsize >= psize");
	
	/* Choose randomly a prime number $q$ of appropriate size.
	   Primes of this type are only for public usage, because
	   we use weak random numbers here! */
	do
		tmcg_mpz_wrandomb(q, qsize);
	while ((mpz_sizeinbase(q, 2L) < qsize) ||
		!mpz_probab_prime_p(q, mr_iterations));
	
	mpz_init(foo);
	do
	{
		/* Choose randomly an even number $k$ and compute $p:= qk + 1$. */
		do
			tmcg_mpz_wrandomb(k, psize - qsize);
		while (mpz_sizeinbase(k, 2L) < (psize - qsize));
		if (mpz_odd_p(k))
			mpz_add_ui(k, k, 1L);
		mpz_mul(p, q, k);
		mpz_add_ui(p, p, 1L);
		/* Check wether $k$ and $q$ are coprime, i.e. $gcd(k, q) = 1$. */
		mpz_gcd(foo, k, q);
	}
	while (mpz_cmp_ui(foo, 1L) || (mpz_sizeinbase(p, 2L) < psize) || 
		!mpz_probab_prime_p(p, mr_iterations));
	mpz_clear(foo);
}

void tmcg_mpz_lprime_prefix
	(mpz_ptr p, mpz_ptr q, mpz_ptr k, 
	 const unsigned long int psize,
	 const unsigned long int qsize, 
	 const unsigned long int mr_iterations)
{
	mpz_t foo;
	if (qsize >= psize)
		throw std::invalid_argument("tmcg_mpz_lprime_prefix: qsize >= psize");
	
	mpz_init(foo);
	do
	{
		/* Choose randomly a prime number $q$ of appropriate size.
		   Primes of this type are only for public usage, because
		   we use weak random numbers here! */
		do
			tmcg_mpz_wrandomb(q, qsize);
		while ((mpz_sizeinbase(q, 2L) < qsize) || 
			!mpz_probab_prime_p(q, mr_iterations));
		/* Enhance given $k$ by multiples of TMCG_MPZ_IO_BASE. */
		while (mpz_sizeinbase(k, 2L) < (psize - qsize))
			mpz_mul_ui(k, k, TMCG_MPZ_IO_BASE);
		if (mpz_odd_p(k))
			mpz_add_ui(k, k, 1L);
		mpz_mul(p, q, k);
		mpz_add_ui(p, p, 1L);
		/* Check wether $k$ and $q$ are coprime, i.e. $gcd(k, q) = 1$. */
		mpz_gcd(foo, k, q);
	}
	while (mpz_cmp_ui(foo, 1L) || (mpz_sizeinbase(p, 2L) < psize) || 
		!mpz_probab_prime_p(p, mr_iterations));
	mpz_clear(foo);
}

void tmcg_mpz_oprime
	(mpz_ptr p,
	const unsigned long int psize,
	const unsigned long int mr_iterations)
{
	/* Choose randomly an odd number $p$ of appropriate size. */
	do
		tmcg_mpz_srandomb(p, psize);
	while (mpz_sizeinbase(p, 2L) < psize);
	if (mpz_even_p(p))
		mpz_add_ui(p, p, 1L);
	
	/* Add two as long as $p$ is not probable prime. */
	while (!mpz_probab_prime_p(p, mr_iterations))
		mpz_add_ui(p, p, 2L);
}

void tmcg_mpz_oprime_noninc
	(mpz_ptr p,
	const unsigned long int psize,
	const unsigned long int mr_iterations)
{
	do
	{
		/* Choose randomly an odd number $p$ of appropriate size. */
		do
			tmcg_mpz_srandomb(p, psize);
		while (mpz_sizeinbase(p, 2L) < psize);
		if (mpz_even_p(p))
			mpz_add_ui(p, p, 1L);
		/* Check whether this number is probably prime. */
	}
	while (!mpz_probab_prime_p(p, mr_iterations));
}