Speed up benchmarks that take a long time to run

diff --git a/benchmarks/mm/gen.scala b/benchmarks/mm/gen.scala
index 38d9e6badb9ab478234febc6796dd004d49feb9c..982daa86d7375995b30c5686877a98e32ecd09a9 100644 (file)
--- a/benchmarks/mm/gen.scala
+++ b/benchmarks/mm/gen.scala
@@ -74,7 +74,7 @@ object MMGen {
     ("cp a.out " + Seq("b", m, n, p, m1, n1, p1, "run").reduce(_+"."+_))!
   }
   def main(args: Array[String]): Unit = {
-    test1(4, 5, 6, 36, 35, 36)
+    test1(4, 5, 6, 24, 25, 24)
     //for (i <- 4 to 6; j <- 4 to 6; k <- 4 to 6)
     //  test1(i, j, k, if (i == 5) 35 else 36, if (j == 5) 35 else 36, if (k == 5) 35 else 36)
   }

diff --git a/benchmarks/mm/mm_main.c b/benchmarks/mm/mm_main.c
index 4d08b152350e33fc2a5419375a825cacce2d8acb..133b5a2d73a17434e8aefef7d8e4ebf4ba8d402e 100644 (file)
--- a/benchmarks/mm/mm_main.c
+++ b/benchmarks/mm/mm_main.c
@@ -6,6 +6,8 @@
 #include <stdio.h>
 #include "util.h"
 
+#pragma GCC optimize ("unroll-loops")
+
 void thread_entry(int cid, int nc)
 {
   const int R = 8;

diff --git a/benchmarks/mm/rb.h b/benchmarks/mm/rb.h
index 593b54f134f2b5818c74711708c37da93e56a092..421c9648fb47118a886dadd14b29955f943b21b3 100644 (file)
--- a/benchmarks/mm/rb.h
+++ b/benchmarks/mm/rb.h
@@ -1,7 +1,5 @@
-// See LICENSE for license details.
-
 static const int RBM = 4, RBN = 5, RBK = 6;
-static const int CBM = 36, CBN = 35, CBK = 36;
+static const int CBM = 24, CBN = 25, CBK = 24;
 static inline void kloop(size_t p, t* a0, size_t lda, t* b0, size_t ldb, t* c, size_t ldc)
 {
   t* c_0 = &c[ldc*0];

diff --git a/benchmarks/mt-matmul/matmul.c b/benchmarks/mt-matmul/matmul.c
index 7c23309aab654a7f539a56a0bd6a30f174b2c43b..6d7b97863a5a023ffffa2f04e4152b736a900784 100644 (file)
--- a/benchmarks/mt-matmul/matmul.c
+++ b/benchmarks/mt-matmul/matmul.c
@@ -2,21 +2,22 @@
 
 #include "dataset.h"
 #include "util.h"
+#include <stddef.h>
 
-void __attribute__((noinline)) matmul(const int coreid, const int ncores, const int lda,  const data_t A[], const data_t B[], data_t C[] )
+#pragma GCC optimize ("unroll-loops")
+
+void matmul(const size_t coreid, const size_t ncores, const size_t lda,  const data_t A[], const data_t B[], data_t C[])
 {
-   int i, j, k;
-   int block = lda / ncores;
-   int start = block * coreid;
+  size_t i, j, k;
+  size_t block = lda / ncores;
+  size_t start = block * coreid;
  
-   for ( j = start; j < (start+block); j++ ) 
-   {
-      for ( k = 0; k < lda; k++ )  
-      {
-         for ( i = 0; i < lda; i++ ) 
-         {
-            C[i + j*lda] += A[j*lda + k] * B[k*lda + i];
-         }
-      }
-   }
+  for (i = 0; i < lda; i++) {
+    for (j = start; j < (start+block); j++) {
+      data_t sum = 0;
+      for (k = 0; k < lda; k++)
+        sum += A[j*lda + k] * B[k*lda + i];
+      C[i + j*lda] = sum;
+    }
+  }
 }

diff --git a/benchmarks/mt-matmul/mt-matmul.c b/benchmarks/mt-matmul/mt-matmul.c
index 9cc3f20bbb39d71f511ae8794cb4a2c08cb3c2e8..349e47e0fb07bbf8af9aad8f105de7d34a37baba 100644 (file)
--- a/benchmarks/mt-matmul/mt-matmul.c
+++ b/benchmarks/mt-matmul/mt-matmul.c
@@ -22,6 +22,7 @@
 #include <string.h>
 #include <stdlib.h>
 #include <stdio.h>
+#include <stddef.h>
 
 
 //--------------------------------------------------------------------------
@@ -39,7 +40,7 @@
 //--------------------------------------------------------------------------
 // matmul function
  
- extern void __attribute__((noinline)) matmul(const int coreid, const int ncores, const int lda,  const data_t A[], const data_t B[], data_t C[] );
+extern void matmul(const size_t coreid, const size_t ncores, const size_t lda,  const data_t A[], const data_t B[], data_t C[] );
 
 
 //--------------------------------------------------------------------------

diff --git a/benchmarks/spmv/dataset1.h b/benchmarks/spmv/dataset1.h
index de430e03394b9f985491d8d21b816c65c4823123..4c871d58c33dd62627a748ee7d2e3ce52feed38e 100644 (file)
--- a/benchmarks/spmv/dataset1.h
+++ b/benchmarks/spmv/dataset1.h
@@ -1,23024 +1,11512 @@
 // See LICENSE for license details.
 
-#define R 1000
-#define C 1000
-#define NNZ 10004
-const double val[10004] = {
-  658,
-  279,
-  587,
-  255,
-  359,
-  844,
-  905,
-  456,
-  897,
-  837,
+#define R 500
+#define C 500
+#define NNZ 4998
+const double val[4998] = {
+  644,
+  344,
+  346,
+  101,
+  553,
+  823,
+  33,
+  274,
+  179,
+  575,
+  529,
+  820,
   652,
-  398,
-  885,
-  21,
-  669,
-  738,
-  365,
-  928,
-  713,
+  401,
+  887,
+  736,
+  660,
+  728,
+  65,
+  230,
+  664,
+  131,
+  819,
+  499,
+  450,
+  11,
+  958,
+  535,
+  468,
+  748,
+  539,
+  494,
+  469,
+  834,
+  733,
+  509,
+  86,
+  824,
   771,
-  536,
-  987,
-  917,
-  823,
-  544,
-  40,
-  80,
-  636,
-  263,
-  929,
-  757,
-  677,
-  151,
-  500,
-  875,
-  720,
-  205,
-  292,
-  859,
-  980,
-  97,
-  608,
-  813,
-  840,
-  397,
-  765,
-  294,
-  718,
-  751,
-  7,
-  482,
+  546,
+  662,
+  184,
+  541,
+  344,
+  329,
+  986,
+  910,
   166,
-  653,
+  784,
+  131,
+  120,
+  75,
+  346,
   172,
-  187,
-  79,
+  710,
+  601,
+  777,
+  51,
+  282,
+  395,
+  375,
+  379,
+  551,
+  843,
+  278,
+  259,
+  304,
+  988,
+  975,
+  125,
+  719,
+  193,
+  18,
+  245,
+  754,
+  585,
   228,
-  857,
-  540,
-  760,
-  509,
-  190,
-  396,
-  765,
-  37,
-  85,
-  866,
-  981,
-  999,
-  793,
-  921,
-  664,
-  208,
-  856,
-  528,
-  782,
-  318,
-  170,
-  521,
-  691,
-  726,
-  996,
-  947,
-  326,
-  825,
-  77,
-  823,
-  752,
-  266,
-  834,
-  196,
-  58,
-  430,
-  764,
-  807,
-  568,
-  665,
-  583,
-  178,
-  250,
-  273,
-  654,
-  487,
-  504,
-  729,
-  338,
-  866,
-  981,
   852,
-  842,
-  785,
-  13,
-  588,
-  44,
-  432,
-  408,
-  374,
-  761,
-  653,
-  752,
-  684,
-  6,
-  357,
-  703,
-  447,
-  966,
-  457,
-  738,
-  646,
-  646,
-  217,
-  522,
-  839,
-  417,
-  506,
-  801,
-  233,
-  929,
-  487,
+  840,
+  888,
+  711,
+  960,
+  674,
+  523,
+  339,
+  737,
+  796,
+  607,
+  394,
+  219,
+  370,
+  854,
   353,
-  660,
-  751,
-  738,
-  512,
-  566,
-  130,
-  61,
-  128,
-  698,
-  467,
-  362,
-  867,
-  639,
-  289,
-  371,
-  427,
-  650,
-  16,
-  878,
-  967,
-  369,
-  517,
-  161,
-  330,
-  294,
-  396,
-  606,
-  638,
-  171,
-  602,
-  531,
-  14,
-  968,
-  15,
-  193,
-  225,
-  863,
-  171,
-  254,
-  714,
-  256,
-  873,
-  353,
-  35,
-  910,
-  849,
-  658,
-  546,
-  389,
-  239,
-  355,
-  540,
-  494,
-  968,
-  319,
-  590,
-  608,
-  445,
-  806,
-  51,
-  117,
-  401,
-  314,
-  280,
-  334,
-  44,
-  17,
-  107,
-  108,
-  650,
-  807,
-  385,
-  748,
-  942,
-  719,
-  110,
-  630,
-  559,
+  195,
+  624,
+  951,
+  755,
+  64,
+  825,
+  145,
+  296,
+  456,
+  585,
+  884,
+  242,
+  484,
+  902,
+  884,
+  224,
+  689,
+  321,
+  578,
+  835,
+  891,
+  347,
+  273,
+  285,
+  415,
+  586,
+  402,
+  890,
+  414,
+  723,
   717,
-  375,
-  963,
-  45,
-  403,
-  476,
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-  732,
-  87,
+  383,
+  530,
+  993,
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+  246,
+  219,
+  61,
+  845,
+  430,
+  636,
+  773,
+  371,
+  63,
+  596,
+  492,
+  976,
+  253,
+  92,
+  744,
+  465,
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+  967,
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+  30,
+  789,
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-  201,
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-  564,
-  830,
-  122,
-  929,
-  68,
-  11,
-  354,
-  395,
-  213,
-  766,
-  40,
+  306,
+  805,
+  233,
+  97,
+  348,
+  616,
+  309,
+  99,
+  341,
+  862,
+  6,
+  524,
   995,
-  577,
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-  56,
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-  612,
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-  157,
-  538,
-  682,
-  190,
-  571,
-  847,
-  275,
-  190,
+  786,
+  696,
+  81,
+  517,
+  428,
+  663,
+  895,
+  469,
+  619,
+  620,
+  941,
+  351,
+  285,
+  229,
+  808,
+  18,
+  986,
   824,
-  985,
-  29,
-  426,
-  173,
-  898,
-  297,
-  156,
-  936,
-  1,
-  455,
-  812,
-  173,
-  131,
-  376,
-  947,
-  596,
-  783,
-  800,
-  361,
-  798,
-  598,
+  764,
+  481,
+  519,
+  524,
+  815,
+  910,
+  878,
+  436,
+  810,
+  597,
+  418,
+  64,
+  354,
+  17,
+  72,
+  465,
+  387,
+  445,
+  89,
+  721,
+  75,
+  921,
+  948,
+  725,
+  236,
   710,
-  86,
-  149,
-  457,
-  129,
-  437,
-  352,
-  933,
-  320,
-  709,
-  167,
-  793,
-  46,
-  49,
-  305,
-  704,
-  577,
-  855,
+  456,
+  993,
+  451,
   336,
-  978,
-  206,
-  662,
-  230,
-  93,
-  898,
-  368,
-  422,
-  689,
-  351,
-  87,
-  465,
-  576,
-  33,
-  884,
-  675,
-  548,
-  116,
-  730,
-  385,
-  483,
-  340,
-  809,
-  938,
-  342,
-  576,
-  887,
-  479,
-  455,
-  820,
-  521,
-  320,
-  488,
-  506,
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-  901,
-  505,
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-  5,
-  133,
-  705,
-  561,
-  285,
-  95,
-  918,
-  410,
-  578,
-  347,
-  375,
-  735,
-  624,
-  491,
-  494,
-  931,
-  655,
-  819,
-  883,
-  328,
-  527,
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-  580,
-  584,
-  837,
-  700,
-  681,
-  249,
-  643,
-  958,
-  363,
-  316,
-  397,
-  638,
-  261,
-  459,
-  960,
-  636,
-  458,
-  84,
-  797,
-  696,
-  782,
-  831,
-  419,
-  393,
-  649,
-  312,
-  811,
-  703,
+  223,
+  766,
+  86,
+  927,
   70,
-  688,
-  285,
-  39,
-  617,
-  935,
-  495,
-  392,
-  143,
-  734,
-  166,
-  406,
-  464,
-  732,
-  709,
-  379,
-  143,
-  527,
-  514,
-  709,
-  130,
-  965,
-  632,
-  448,
-  836,
-  62,
-  567,
-  600,
-  520,
-  519,
-  16,
-  394,
-  705,
-  438,
-  548,
-  696,
-  140,
+  402,
+  435,
+  314,
+  666,
+  420,
+  755,
+  145,
+  676,
+  122,
   573,
-  509,
-  968,
-  935,
-  165,
-  868,
-  577,
-  451,
-  865,
-  304,
-  777,
-  828,
-  147,
-  704,
-  821,
-  641,
-  783,
-  376,
-  757,
-  391,
-  170,
-  592,
-  235,
-  920,
-  846,
-  683,
-  249,
+  213,
+  309,
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-  253,
-  386,
-  244,
-  889,
-  607,
-  768,
-  88,
-  836,
-  259,
-  945,
-  33,
-  352,
-  70,
-  83,
-  996,
-  791,
-  18,
-  599,
-  488,
-  43,
-  582,
-  993,
-  692,
-  841,
-  558,
-  530,
-  350,
-  187,
-  295,
-  215,
-  869,
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-  385,
-  722,
-  724,
-  282,
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-  788,
-  836,
-  378,
-  825,
-  93,
-  539,
+  383,
+  430,
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+  192,
+  567,
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+  212,
+  81,
+  431,
+  467,
+  323,
+  62,
+  55,
+  30,
+  973,
+  532,
+  773,
+  960,
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-  505,
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+  327,
+  77,
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   866,
-  927,
+  66,
+  228,
+  981,
+  9,
+  932,
+  270,
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-  760,
-  541,
   118,
+  231,
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+  937,
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+  956,
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+  936,
+  57,
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+  68,
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+  432,
+  23,
+  636,
+  149,
+  78,
+  885,
+  648,
+  741,
+  168,
   551,
-  574,
-  85,
-  736,
-  999,
-  917,
-  478,
-  35,
-  629,
+  627,
+  619,
+  287,
+  199,
+  533,
+  71,
+  297,
+  920,
+  667,
+  958,
   963,
-  898,
-  826,
-  113,
-  298,
-  606,
-  568,
-  152,
-  926,
-  277,
-  984,
-  549,
-  279,
-  839,
-  348,
-  672,
+  532,
+  1,
+  256,
+  378,
+  820,
+  287,
   278,
-  94,
-  455,
-  590,
-  843,
-  85,
-  222,
-  901,
-  621,
-  30,
-  880,
-  914,
-  27,
-  974,
+  785,
+  382,
+  321,
+  602,
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-  713,
-  306,
-  259,
-  1,
-  253,
-  316,
-  357,
-  155,
-  55,
-  520,
-  687,
-  350,
-  644,
-  974,
-  945,
-  277,
-  654,
-  850,
-  412,
-  847,
-  384,
-  820,
-  512,
-  979,
-  21,
-  823,
-  299,
-  93,
-  793,
-  204,
-  925,
-  130,
-  103,
-  314,
-  105,
-  564,
-  762,
-  524,
-  478,
-  178,
-  807,
-  56,
-  916,
-  711,
-  511,
-  111,
-  865,
-  110,
-  195,
-  982,
-  171,
-  631,
-  960,
-  640,
-  584,
-  600,
-  770,
-  669,
-  649,
-  51,
-  212,
-  828,
-  973,
   448,
+  205,
+  434,
+  153,
+  212,
+  149,
+  970,
+  66,
+  850,
+  553,
+  739,
+  319,
+  616,
+  16,
   101,
-  856,
-  801,
-  679,
-  694,
-  242,
-  334,
-  620,
-  160,
-  667,
-  891,
-  791,
-  659,
-  107,
-  865,
-  126,
-  882,
-  675,
-  726,
-  234,
-  346,
-  875,
-  88,
-  115,
-  592,
-  729,
-  299,
-  177,
-  210,
-  456,
-  766,
-  928,
-  837,
-  417,
-  856,
-  631,
-  142,
-  640,
+  600,
+  845,
+  226,
   848,
-  805,
-  989,
-  509,
-  106,
-  440,
-  276,
-  581,
-  117,
-  187,
-  565,
-  620,
-  433,
-  475,
-  873,
-  626,
-  342,
-  455,
-  373,
-  767,
-  855,
-  866,
-  942,
-  108,
-  117,
-  799,
-  85,
-  936,
-  665,
+  921,
+  625,
+  239,
+  414,
+  822,
+  217,
+  527,
+  12,
+  458,
+  835,
+  420,
+  584,
+  335,
+  98,
+  347,
   975,
-  750,
-  35,
-  769,
-  889,
-  610,
-  210,
-  220,
-  359,
-  981,
-  728,
-  649,
-  0,
-  826,
-  950,
-  120,
-  648,
-  58,
-  383,
-  436,
-  737,
-  11,
-  714,
-  424,
-  251,
-  301,
-  204,
-  287,
-  183,
-  472,
-  265,
-  120,
-  780,
-  369,
-  695,
-  758,
-  740,
-  107,
-  831,
-  93,
-  535,
-  306,
-  777,
-  976,
-  562,
-  59,
-  956,
-  304,
-  83,
-  576,
-  399,
-  999,
-  899,
-  824,
-  350,
-  635,
-  896,
-  802,
-  332,
-  421,
-  878,
-  433,
-  193,
-  353,
-  802,
-  683,
-  456,
-  88,
-  211,
-  132,
   432,
-  354,
-  421,
-  616,
-  53,
-  231,
-  915,
-  510,
-  106,
+  966,
+  138,
+  454,
+  523,
+  660,
+  171,
+  75,
+  50,
+  734,
+  110,
+  584,
+  368,
+  406
+};
+const int idx[4998] = {
+  34,
+  56,
+  132,
+  163,
+  256,
+  260,
+  418,
+  431,
+  466,
+  494,
+  497,
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+  64,
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+  165,
+  225,
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+  339,
+  469,
+  478,
+  494,
+  497,
+  9,
   28,
-  32,
-  600,
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+  282,
+  365,
+  451,
+  453,
   461,
-  131,
-  594,
-  678,
-  744,
-  674,
-  620,
-  290,
-  535,
-  534,
-  543,
-  62,
-  971,
-  905,
-  180,
-  10,
-  234,
-  166,
-  272,
-  73,
-  128,
-  437,
-  613,
-  291,
-  638,
-  610,
-  225,
-  630,
-  309,
-  112,
-  868,
-  557,
-  439,
-  355,
-  555,
-  579,
-  443,
-  843,
-  20,
-  464,
-  987,
-  284,
-  302,
-  450,
+  49,
+  74,
+  81,
+  241,
+  349,
   355,
-  83,
-  407,
-  711,
-  752,
-  187,
-  249,
-  807,
-  883,
-  924,
-  858,
-  110,
-  409,
-  189,
-  998,
-  439,
-  120,
-  321,
-  875,
-  140,
-  640,
-  285,
-  561,
-  873,
+  448,
+  473,
+  51,
+  59,
+  122,
+  258,
+  283,
+  381,
+  18,
+  50,
+  193,
+  227,
+  257,
+  356,
+  467,
+  1,
+  32,
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+  210,
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+  298,
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+  442,
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+  163,
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+  279,
+  326,
+  387,
+  408,
+  472,
+  60,
+  94,
+  143,
+  246,
+  262,
+  297,
+  309,
+  324,
+  327,
+  351,
+  361,
   371,
-  73,
-  4,
-  169,
-  771,
+  380,
+  455,
+  463,
+  25,
+  80,
+  126,
+  128,
+  173,
+  217,
+  220,
+  233,
+  242,
+  293,
+  348,
   413,
   447,
-  985,
-  206,
-  635,
-  943,
-  960,
-  240,
-  554,
-  209,
-  576,
-  254,
+  125,
   163,
-  977,
-  846,
-  610,
-  596,
-  920,
-  524,
-  608,
-  402,
-  249,
-  624,
-  180,
-  875,
-  240,
-  670,
-  421,
-  1,
-  911,
-  505,
-  474,
-  979,
-  623,
-  678,
-  952,
-  909,
-  751,
-  241,
-  269,
-  968,
-  396,
-  641,
-  516,
-  965,
-  406,
-  54,
-  853,
+  179,
+  217,
+  342,
   346,
-  650,
-  787,
-  400,
-  175,
-  929,
-  662,
-  870,
-  170,
-  468,
-  173,
-  620,
-  318,
-  170,
-  995,
-  525,
-  138,
-  520,
-  151,
-  851,
-  30,
-  596,
-  605,
-  802,
-  449,
-  174,
-  518,
-  633,
-  293,
-  652,
-  779,
-  606,
-  444,
-  472,
-  359,
-  204,
-  308,
-  104,
-  274,
-  707,
-  638,
-  193,
-  577,
-  125,
-  28,
-  537,
-  987,
-  521,
-  80,
-  56,
-  111,
-  589,
-  81,
-  794,
-  377,
-  36,
-  680,
-  476,
-  227,
-  778,
-  138,
+  352,
+  389,
+  434,
+  493,
+  18,
+  26,
+  182,
+  220,
+  226,
+  263,
+  332,
+  340,
+  403,
+  1,
   24,
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-  160,
-  590,
-  855,
-  396,
-  289,
-  142,
-  785,
-  551,
-  696,
-  514,
-  268,
-  536,
-  547,
-  207,
-  943,
-  166,
-  0,
-  959,
-  114,
-  322,
-  906,
-  322,
-  892,
-  960,
+  27,
+  71,
+  127,
+  140,
+  263,
+  374,
+  380,
+  424,
+  426,
+  231,
+  237,
+  243,
+  319,
+  353,
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+  35,
+  91,
+  233,
+  271,
+  272,
+  292,
+  381,
+  83,
+  117,
+  121,
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   152,
-  219,
-  944,
-  540,
-  874,
-  965,
-  269,
-  858,
-  681,
-  764,
-  673,
-  30,
-  954,
-  88,
-  521,
-  729,
   159,
-  275,
-  56,
-  125,
-  755,
-  556,
-  505,
-  72,
-  919,
-  180,
-  714,
-  476,
-  557,
-  286,
-  639,
-  983,
-  152,
-  572,
-  584,
-  774,
-  510,
-  716,
-  601,
-  148,
-  732,
-  601,
-  940,
-  969,
-  20,
-  190,
-  364,
-  622,
-  685,
-  61,
-  344,
-  196,
-  7,
-  990,
-  899,
-  252,
-  754,
-  435,
-  284,
+  412,
+  484,
+  489,
+  63,
+  164,
+  170,
+  311,
+  32,
+  68,
+  82,
+  91,
+  115,
+  120,
   201,
-  722,
-  552,
-  343,
-  657,
-  969,
-  888,
-  215,
-  691,
-  409,
-  26,
-  814,
-  955,
-  756,
-  555,
-  490,
-  721,
-  618,
-  204,
-  30,
-  599,
-  134,
-  692,
-  978,
-  825,
-  270,
-  841,
-  504,
-  774,
-  525,
-  384,
-  45,
-  973,
-  630,
-  292,
-  407,
-  67,
-  655,
-  51,
-  321,
-  712,
-  920,
-  987,
-  848,
-  722,
-  54,
-  844,
-  881,
-  2,
-  745,
-  543,
-  18,
-  346,
-  886,
-  284,
-  553,
-  327,
-  745,
-  802,
-  253,
-  852,
-  636,
+  236,
+  252,
+  275,
   390,
-  455,
-  868,
-  740,
-  663,
-  964,
-  729,
-  838,
-  160,
-  466,
-  658,
-  934,
-  788,
-  92,
-  286,
-  175,
-  248,
-  540,
-  880,
-  948,
-  738,
-  221,
-  979,
-  785,
-  992,
-  482,
-  300,
-  55,
-  307,
-  541,
-  695,
-  226,
-  659,
-  648,
-  922,
-  441,
-  203,
-  794,
-  22,
-  970,
-  164,
+  437,
+  20,
   46,
-  259,
-  951,
-  704,
-  886,
-  299,
-  673,
-  173,
-  240,
-  807,
-  719,
-  658,
-  194,
-  357,
-  971,
-  821,
-  711,
-  707,
-  225,
-  482,
-  734,
+  72,
+  77,
+  80,
+  108,
+  118,
+  150,
+  249,
+  282,
+  384,
+  458,
+  486,
+  28,
+  70,
   77,
-  917,
-  665,
-  867,
-  755,
-  544,
-  326,
-  524,
-  598,
   78,
-  244,
-  906,
-  617,
-  928,
-  395,
-  658,
-  732,
-  601,
-  421,
-  359,
-  459,
-  727,
-  409,
-  806,
+  100,
+  261,
+  311,
+  318,
+  394,
+  465,
+  469,
+  489,
+  21,
+  159,
+  250,
+  386,
+  478,
+  57,
+  70,
+  180,
+  217,
+  276,
   285,
-  943,
-  207,
-  630,
-  752,
-  85,
-  819,
-  81,
-  714,
-  599,
-  44,
-  892,
-  139,
-  813,
-  684,
-  175,
-  718,
-  720,
-  697,
-  401,
-  310,
-  84,
-  666,
-  259,
-  357,
-  939,
-  246,
-  527,
-  856,
-  455,
-  533,
-  717,
-  790,
-  923,
-  962,
-  105,
-  447,
-  598,
-  8,
-  941,
-  409,
-  510,
-  130,
-  823,
-  606,
-  773,
-  511,
-  574,
+  291,
+  303,
+  312,
+  318,
+  370,
+  371,
+  426,
+  477,
+  86,
+  122,
+  128,
+  292,
+  309,
+  314,
+  335,
+  421,
+  422,
+  427,
+  452,
+  480,
+  488,
+  45,
+  97,
   98,
-  731,
-  402,
-  862,
-  752,
-  623,
-  991,
-  46,
+  106,
+  302,
+  364,
+  437,
+  7,
+  96,
+  100,
+  130,
+  174,
   307,
-  347,
-  826,
-  698,
-  658,
-  35,
-  642,
-  770,
-  293,
-  385,
-  50,
-  470,
-  908,
-  177,
-  919,
-  460,
-  783,
-  812,
-  885,
-  144,
-  408,
-  659,
-  741,
-  639,
-  741,
-  234,
-  361,
-  975,
-  361,
-  934,
-  345,
-  46,
-  370,
-  804,
-  357,
-  22,
-  797,
-  24,
-  698,
-  274,
-  669,
-  711,
-  610,
+  89,
+  317,
+  354,
+  390,
+  406,
+  498,
+  61,
+  64,
+  130,
+  268,
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+  349,
+  480,
+  9,
+  47,
   104,
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-  121,
-  724,
-  99,
-  296,
-  870,
-  786,
-  907,
-  517,
-  300,
-  369,
-  115,
-  987,
-  98,
-  420,
-  792,
-  167,
-  589,
-  81,
-  929,
-  901,
+  169,
+  170,
+  315,
+  399,
+  437,
   444,
-  109,
-  382,
-  693,
-  593,
-  875,
-  545,
-  683,
-  487,
-  631,
-  35,
-  664,
-  35,
-  465,
-  381,
-  502,
-  512,
-  213,
-  325,
-  921,
-  435,
-  368,
+  469,
+  117,
+  183,
+  192,
+  225,
   265,
-  897,
-  888,
-  773,
-  659,
-  636,
-  822,
-  940,
-  704,
-  937,
-  990,
-  380,
-  22,
-  806,
+  371,
+  43,
+  81,
+  123,
+  224,
+  257,
+  285,
+  321,
+  329,
+  338,
+  436,
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+  475,
+  11,
+  23,
+  141,
+  163,
+  268,
+  398,
+  408,
+  416,
+  430,
+  8,
+  84,
+  318,
+  389,
   443,
-  272,
+  488,
+  8,
+  53,
+  149,
+  172,
   226,
-  75,
-  390,
-  701,
-  604,
-  103,
-  834,
-  836,
-  128,
-  776,
-  390,
-  490,
-  761,
-  481,
-  372,
-  204,
-  99,
-  91,
-  22,
-  808,
-  253,
-  230,
-  576,
-  111,
-  530,
-  569,
-  205,
-  79,
-  723,
-  69,
-  129,
-  157,
-  690,
-  663,
-  960,
-  928,
-  549,
-  861,
-  858,
-  688,
-  269,
-  88,
-  740,
-  156,
-  907,
-  39,
-  916,
-  907,
-  334,
-  924,
-  489,
-  523,
-  243,
-  832,
-  196,
-  238,
-  353,
-  1,
-  7,
-  314,
-  127,
-  188,
-  96,
-  15,
-  805,
-  54,
+  308,
+  362,
+  466,
   9,
-  827,
-  404,
-  908,
-  152,
-  993,
-  739,
-  18,
-  830,
-  225,
-  119,
-  544,
-  559,
-  312,
-  438,
-  641,
-  301,
-  560,
-  392,
-  365,
-  576,
-  955,
-  898,
-  503,
+  12,
+  32,
+  114,
+  134,
+  226,
+  240,
+  393,
+  138,
+  153,
+  202,
+  216,
+  227,
+  322,
+  358,
+  369,
+  396,
+  427,
+  455,
+  490,
+  22,
+  85,
   118,
-  601,
-  848,
-  464,
-  83,
-  817,
-  190,
-  930,
-  333,
-  675,
-  660,
-  97,
-  975,
-  412,
-  292,
+  181,
+  237,
+  321,
+  338,
+  348,
+  480,
+  0,
+  5,
+  9,
+  12,
+  119,
+  163,
+  226,
+  231,
+  246,
+  259,
+  383,
   419,
+  451,
+  144,
+  146,
+  174,
+  225,
+  309,
+  366,
+  368,
+  395,
   456,
-  795,
-  937,
-  793,
-  775,
-  168,
-  22,
+  117,
+  157,
+  169,
+  178,
+  221,
+  229,
+  244,
+  255,
   285,
-  446,
-  516,
-  479,
-  419,
-  80,
-  724,
-  440,
-  812,
-  799,
-  215,
-  257,
-  254,
-  998,
-  103,
-  914,
-  559,
-  536,
-  588,
-  833,
-  464,
-  188,
-  548,
-  869,
-  359,
-  478,
-  711,
-  413,
-  236,
-  826,
-  534,
-  811,
-  997,
-  919,
-  179,
-  790,
-  869,
-  958,
-  428,
-  792,
-  503,
-  118,
-  329,
-  350,
-  240,
-  390,
-  989,
+  296,
+  328,
+  358,
+  375,
+  429,
+  454,
+  468,
+  473,
+  13,
+  18,
+  84,
+  202,
+  211,
+  370,
+  425,
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-  4,
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-  225,
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-  992,
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-  967,
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-  628,
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-  599,
-  664,
-  46,
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-  396,
-  56,
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-  739,
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-  898,
-  417,
-  948,
-  956,
-  230,
-  884,
-  748,
-  74,
-  938,
-  224,
-  920,
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-  475,
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-  118,
-  398,
+  304,
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+  6,
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+  239,
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   439,
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   461,
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-  877,
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   234,
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+  105,
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   92,
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-  590,
+  131,
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+  450,
   458,
-  232,
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-  187,
-  18,
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-  704,
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-  67,
-  109,
-  88,
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+  115,
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+  90,
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+  45,
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   255,
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   277,
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   381,
-  409,
-  932,
-  31,
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-  55,
-  648,
-  5,
-  12,
-  465,
-  96,
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-  169,
-  325,
-  428,
-  572,
-  47,
-  78,
-  258,
-  525,
-  276,
-  502,
-  972,
-  488,
-  763,
-  798,
-  973,
-  186,
-  490,
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-  205,
-  154,
+  443,
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+  173,
   245,
-  784,
-  493,
-  76,
-  975,
-  459,
-  598,
-  227,
-  161,
-  752,
-  243,
-  858,
-  931,
-  996,
-  543,
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-  240,
-  49,
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-  374,
-  914,
-  52,
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-  329,
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-  925,
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-  748,
-  236,
-  8,
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-  61,
-  77,
-  295,
-  117,
-  323,
-  732,
+  347,
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+  404,
+  449,
+  462,
   493,
-  811,
-  67,
-  694,
-  158,
-  589,
-  247,
-  115,
-  184,
-  682,
-  927,
-  918,
-  353,
+  33,
+  38,
+  51,
+  56,
+  87,
+  132,
+  256,
+  261,
+  270,
+  295,
+  411,
+  439,
+  2,
+  23,
+  82,
+  149,
+  179,
+  196,
   217,
-  904,
-  834,
-  107,
-  728,
-  683,
-  908,
-  596,
-  721,
-  44,
-  412,
-  780,
-  882,
-  682,
-  497,
-  832,
-  559,
-  126,
-  303,
-  100,
-  214,
-  829,
+  240,
+  260,
+  328,
+  332,
+  350,
+  416,
+  422,
+  425,
+  438,
+  494,
+  30,
+  61,
+  97,
+  209,
+  211,
+  283,
+  288,
   344,
-  654,
-  679,
-  336,
-  148,
-  213,
-  982,
-  859,
-  558,
-  855,
-  999,
-  698,
-  38,
-  490,
-  340,
-  846,
-  852,
-  26,
-  942,
-  575,
+  429,
+  441,
+  25,
+  55,
+  92,
+  120,
+  214,
+  264,
+  289,
+  396,
+  409,
+  432,
+  4,
+  27,
+  39,
+  66,
+  140,
+  177,
+  212,
+  246,
+  332,
+  356,
+  382,
+  480,
+  0,
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+  48,
+  154,
+  170,
+  214,
+  219,
+  261,
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+  476,
+  495,
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   383,
-  1,
-  198,
-  836,
-  570,
-  893,
-  950,
-  7,
-  527,
-  628,
-  753,
-  660,
-  180,
-  354,
-  819,
-  775,
-  271,
-  187,
-  374,
-  532,
-  374,
-  900
-};
-const int idx[10004] = {
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-  218,
-  316,
-  502,
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+  405,
   119,
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   167,
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-  252,
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-  621,
-  741,
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-  507,
-  623,
-  666,
-  669,
-  677,
-  707,
-  823,
-  919,
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   187,
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-  881,
-  948,
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-  165,
-  226,
-  446,
-  538,
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-  866,
-  975,
-  979,
-  18,
-  54,
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-  742,
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   194,
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-  927,
-  954,
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-  966,
-  42,
-  45,
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-  141,
-  239,
-  338,
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-  896,
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-  60,
+  299,
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   92,
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   234,
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   296,
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-  834,
-  192,
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-  724,
-  764,
-  928,
-  929,
-  976,
-  17,
+  307,
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   283,
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-  849,
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-  604,
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-  71,
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-  205,
-  234,
+  286,
+  408,
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   456,
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-  579,
-  682,
-  733,
-  767,
-  947,
-  66,
+  43,
+  47,
+  102,
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+  146,
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+  207,
+  264,
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+  365,
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+  497,
+  183,
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+  214,
+  366,
+  382,
   86,
-  157,
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+  197,
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+  305,
+  416,
+  463,
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+  223,
+  240,
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+  339,
+  393,
+  451,
+  1,
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+  99,
+  200,
+  271,
+  298,
+  420,
+  491,
+  21,
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+  158,
+  182,
+  188,
+  328,
+  338,
+  484,
   290,
-  422,
-  441,
-  473,
-  560,
-  607,
-  640,
-  682,
-  888,
-  37,
-  296,
-  439,
-  629,
-  642,
-  733,
-  824,
-  917,
-  969,
+  380,
+  405,
+  413,
+  480,
+  48,
+  73,
+  139,
+  157,
+  298,
+  358,
+  435,
   4,
-  25,
-  580,
-  622,
-  636,
-  666,
-  672,
-  732,
-  802,
-  921,
-  943,
-  130,
-  194,
-  245,
+  29,
+  65,
+  169,
+  339,
+  364,
+  473,
+  486,
+  33,
+  47,
+  160,
+  212,
+  223,
   273,
-  323,
-  344,
-  603,
-  740,
-  795,
-  974,
-  189,
-  422,
-  445,
-  446,
-  831,
-  905,
-  912,
-  36,
-  60,
-  218,
-  428,
-  455,
-  627,
-  743,
-  796,
-  801,
-  903,
-  136,
-  152,
-  166,
-  352,
+  304,
+  354,
   364,
+  444,
+  481,
+  1,
+  22,
+  83,
+  160,
+  275,
+  296,
+  324,
+  332,
+  357,
   369,
-  382,
-  466,
-  521,
-  577,
-  665,
-  746,
-  910,
-  294,
-  345,
-  445,
-  645,
-  686,
-  718,
-  757,
-  762,
-  796,
-  817,
-  832,
-  836,
-  997,
+  380,
+  467,
+  28,
+  198,
+  256,
+  272,
+  319,
+  357,
+  480,
+  122,
+  185,
+  202,
+  252,
+  277,
+  329,
+  403,
+  408,
+  445,
+  492,
+  80,
+  138,
+  221,
+  239,
+  371,
+  406,
+  413,
+  481,
+  495,
+  63,
   127,
-  258,
-  259,
-  449,
-  541,
-  643,
-  665,
-  756,
-  817,
-  854,
-  870,
-  89,
-  134,
-  188,
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-  732,
-  131,
-  206,
+  162,
+  184,
+  267,
   305,
-  669,
-  809,
-  877,
-  986,
-  439,
-  520,
-  567,
-  588,
-  617,
-  712,
-  891,
-  998,
-  274,
-  358,
-  425,
-  495,
-  715,
-  872,
-  918,
-  923,
-  951,
-  980,
-  983,
-  119,
-  123,
-  316,
-  324,
-  349,
-  644,
-  705,
-  718,
-  769,
-  781,
-  795,
-  884,
-  110,
-  133,
-  140,
-  152,
-  157,
-  495,
-  569,
-  608,
-  629,
-  803,
-  827,
-  909,
-  942,
-  9,
-  230,
-  268,
+  309,
+  371,
+  486,
+  49,
+  66,
+  88,
+  107,
+  195,
+  225,
+  272,
+  300,
+  368,
+  469,
+  473,
+  484,
+  20,
+  84,
+  95,
   423,
-  626,
-  707,
-  724,
-  748,
-  828,
-  996,
-  274,
-  308,
-  436,
-  722,
-  879,
-  213,
-  259,
-  324,
-  329,
-  377,
-  534,
-  588,
-  827,
-  896,
-  149,
-  261,
-  591,
-  597,
-  785,
-  813,
-  883,
-  920,
-  996,
-  10,
-  64,
+  60,
+  63,
+  141,
+  148,
+  150,
+  169,
+  200,
+  390,
+  414,
+  493,
+  218,
   237,
-  417,
-  535,
-  686,
-  709,
-  717,
-  744,
+  271,
+  374,
+  407,
+  425,
+  439,
+  444,
   41,
-  67,
-  260,
+  50,
+  187,
+  199,
+  262,
+  353,
+  86,
+  97,
+  115,
+  155,
+  197,
+  273,
+  286,
+  291,
+  307,
+  315,
+  332,
   370,
-  405,
-  407,
-  520,
-  632,
-  893,
-  955,
-  127,
-  250,
-  336,
-  354,
-  388,
-  474,
-  591,
-  703,
-  805,
-  811,
-  833,
-  871,
-  881,
-  991,
-  994,
-  17,
-  91,
-  113,
+  438,
+  476,
+  487,
+  498,
+  60,
+  66,
+  85,
+  108,
+  117,
   122,
-  300,
-  301,
-  463,
-  716,
-  741,
-  776,
-  784,
-  906,
-  994,
+  139,
+  169,
+  173,
+  234,
+  269,
+  343,
+  346,
+  433,
+  438,
+  451,
+  469,
+  480,
+  482,
+  16,
   33,
-  57,
+  42,
+  86,
+  95,
+  172,
+  200,
+  216,
+  295,
+  303,
+  362,
+  408,
+  409,
+  428,
+  460,
+  476,
+  497,
+  67,
+  83,
+  142,
+  156,
+  192,
+  306,
+  389,
+  421,
+  444,
+  59,
+  72,
+  228,
+  229,
+  295,
+  348,
+  351,
+  391,
+  392,
+  452,
+  462,
+  58,
+  91,
+  364,
+  366,
+  380,
+  433,
+  446,
+  488,
+  28,
+  45,
+  70,
+  96,
+  109,
+  197,
+  204,
   206,
-  448,
-  520,
-  612,
-  769,
-  834,
-  282,
-  393,
-  441,
-  461,
-  503,
-  796,
+  207,
+  230,
+  313,
+  396,
+  407,
+  121,
+  149,
+  205,
+  216,
+  258,
+  283,
+  355,
+  375,
+  7,
+  28,
+  116,
+  169,
+  182,
+  216,
+  219,
+  229,
+  235,
+  276,
+  325,
+  447,
+  42,
+  80,
+  88,
+  147,
+  174,
+  203,
+  223,
+  242,
+  324,
+  382,
+  432,
+  445,
+  33,
+  108,
+  237,
+  314,
+  409,
+  421,
+  443,
+  49,
+  87,
+  189,
+  210,
+  237,
+  242,
+  391,
+  444,
+  38,
+  65,
+  96,
+  163,
+  224,
+  225,
+  241,
+  269,
+  274,
+  298,
+  328,
+  348,
+  35,
+  45,
   72,
-  206,
-  304,
+  75,
+  109,
+  115,
+  145,
+  171,
+  191,
+  262,
+  319,
+  328,
+  435,
+  26,
+  48,
+  81,
+  118,
+  164,
+  192,
+  351,
   381,
-  565,
-  723,
-  114,
-  121,
+  400,
+  13,
+  101,
+  102,
+  109,
+  220,
+  308,
+  311,
+  403,
+  451,
+  72,
+  104,
   130,
-  259,
-  346,
-  386,
-  432,
-  538,
-  575,
-  595,
-  855,
-  945
-};
-const double x[1000] = {
-  602,
-  730,
-  528,
-  886,
-  890,
-  755,
-  124,
-  435,
-  24,
-  245,
-  112,
-  144,
-  171,
-  746,
-  547,
-  172,
-  905,
-  97,
-  70,
-  133,
-  117,
-  951,
-  783,
-  271,
-  174,
-  263,
-  769,
-  889,
-  920,
-  698,
-  644,
   138,
-  34,
-  866,
-  831,
-  249,
-  611,
-  672,
-  502,
-  450,
-  225,
-  557,
-  793,
-  244,
-  336,
-  942,
-  604,
-  135,
-  507,
-  328,
-  36,
+  180,
+  196,
   299,
-  769,
-  323,
-  957,
-  171,
-  455,
-  627,
-  701,
-  624,
-  383,
-  354,
-  675,
-  971,
-  562,
-  945,
-  354,
-  90,
-  495,
-  269,
-  684,
-  468,
-  832,
-  38,
+  327,
+  353,
+  467,
+  17,
+  30,
+  39,
+  62,
+  88,
+  142,
   189,
-  103,
-  509,
-  754,
-  85,
-  70,
-  727,
-  897,
-  441,
-  745,
-  443,
-  561,
-  23,
-  796,
-  104,
-  178,
+  234,
+  246,
+  351,
+  404,
+  409,
+  3,
+  111,
+  133,
+  171,
+  266,
+  292,
+  337,
   388,
-  178,
-  663,
-  652,
-  533,
-  738,
-  423,
-  500,
-  390,
-  567,
-  834,
-  806,
-  97,
-  517,
-  352,
-  636,
-  158,
-  839,
-  822,
-  68,
-  707,
-  838,
-  778,
-  15,
-  201,
-  364,
-  397,
-  166,
-  372,
-  39,
-  525,
-  360,
-  596,
-  664,
-  606,
-  182,
-  684,
-  147,
-  941,
-  695,
-  815,
-  721,
+  425,
+  427,
+  121,
+  211,
+  293,
+  313,
+  317,
+  437,
+  6,
+  17,
+  46,
+  54,
+  122,
+  130,
+  266,
+  297,
+  395,
+  439,
+  56,
+  64,
+  146,
+  165,
+  168,
+  272,
+  293,
+  355,
+  425,
+  486,
+  1,
+  22,
+  45,
+  265,
+  290,
+  323,
+  459,
+  473,
+  482,
+  5,
+  67,
+  90,
+  106,
+  270,
+  315,
+  4,
+  9,
+  20,
+  110,
+  119,
+  143,
+  188,
+  207,
+  266,
+  276,
+  296,
+  428,
+  445,
+  462,
+  44,
+  48,
+  151,
+  259,
+  260,
+  285,
+  315,
+  321,
+  366,
+  405,
+  420,
+  496,
+  36,
+  38,
+  45,
+  51,
+  176,
+  241,
+  332,
+  341,
+  355,
+  357,
+  385,
+  409,
+  85,
+  233,
+  250,
   377,
+  495,
+  42,
   215,
-  386,
-  265,
-  598,
-  890,
-  241,
-  302,
-  423,
-  623,
-  610,
-  26,
-  311,
-  887,
+  250,
+  329,
+  341,
+  355,
+  451,
+  493,
   496,
-  968,
-  549,
-  581,
-  421,
-  638,
-  154,
-  471,
-  768,
-  953,
-  7,
-  906,
-  894,
-  155,
-  687,
-  813,
-  376,
-  463,
-  815,
+  36,
+  145,
+  159,
+  212,
+  297,
+  370,
+  426,
+  447,
+  464,
+  14,
+  34,
+  35,
+  74,
+  75,
+  123,
+  128,
+  138,
+  147,
+  160,
+  225,
+  315,
+  343,
+  351,
+  354,
+  371,
+  426,
   436,
-  817,
-  5,
+  27,
+  173,
+  249,
+  327,
+  337,
+  364,
+  441,
+  454,
+  489,
+  117,
+  128,
+  137,
+  200,
+  217,
+  238,
+  314,
+  353,
+  403,
+  462,
+  11,
+  101,
+  156,
+  195,
+  259,
+  299,
+  331,
+  400,
+  34,
+  64,
+  102,
+  208,
+  255,
+  301,
+  324,
+  333,
   366,
   412,
-  435,
-  825,
-  437,
-  614,
-  437,
-  14,
-  492,
-  117,
-  610,
-  0,
-  837,
-  665,
-  464,
-  847,
-  513,
-  606,
-  532,
-  503,
-  566,
-  270,
-  559,
-  509,
-  634,
-  339,
-  535,
-  708,
-  663,
-  1,
-  837,
-  508,
-  499,
-  216,
-  758,
-  36,
+  23,
+  28,
+  38,
+  95,
+  101,
+  133,
+  198,
+  318,
+  354,
+  385,
+  447,
+  35,
+  71,
+  139,
+  196,
+  240,
+  363,
+  371,
+  427,
+  35,
+  132,
+  162,
+  206,
+  238,
+  366,
+  382,
+  426,
+  445,
+  455,
+  478,
+  21,
+  120,
+  186,
+  209,
+  239,
+  265,
+  313,
+  476,
+  497,
+  26,
+  74,
+  90,
+  111,
+  146,
+  351,
+  10,
+  144,
+  192,
+  241,
+  264,
+  314,
+  331,
+  337,
+  405,
+  431,
+  465,
+  466,
+  493,
+  10,
+  56,
+  93,
+  137,
+  145,
+  160,
+  191,
+  199,
+  248,
+  324,
+  355,
+  362,
+  414,
+  472,
+  483,
+  16,
+  30,
+  34,
+  37,
+  80,
+  92,
+  97,
+  103,
+  179,
+  183,
+  206,
+  336,
+  338,
+  402,
+  25,
+  38,
+  66,
+  119,
+  196,
+  222,
+  238,
+  371,
+  389,
+  390,
+  417,
+  425,
+  450,
+  491,
+  493,
+  20,
+  51,
+  181,
+  196,
   242,
-  351,
-  432,
-  439,
-  562,
-  307,
-  643,
-  498,
-  659,
+  435,
+  479,
+  55,
+  71,
+  295,
+  382,
+  476,
+  9,
+  66,
+  76,
+  184,
+  186,
+  197,
+  295,
+  313,
+  320,
+  395,
+  413,
+  429,
+  6,
   16,
+  23,
+  51,
+  133,
+  137,
+  168,
+  186,
+  200,
+  213,
+  274,
+  276,
+  301,
+  340,
+  395,
+  463,
+  33,
+  174,
+  304,
+  483,
+  171,
+  253,
   265,
-  653,
-  105,
-  527,
-  595,
-  448,
-  832,
-  381,
-  714,
-  533,
-  178,
-  644,
-  455,
-  667,
-  7,
-  378,
-  639,
-  19,
-  50,
-  415,
-  591,
-  827,
-  956,
-  69,
-  712,
-  767,
-  368,
-  552,
-  230,
   288,
+  296,
+  316,
+  365,
+  372,
+  443,
+  76,
+  136,
+  182,
+  210,
+  221,
+  233,
+  263,
+  329,
+  339,
+  398,
+  428,
+  450,
+  454,
+  3,
+  55,
+  140,
   146,
-  676,
-  651,
-  333,
-  284,
-  782,
-  283,
-  774,
-  791,
-  451,
-  795,
-  991,
-  618,
-  620,
-  547,
-  769,
-  226,
-  563,
-  117,
-  524,
-  287,
-  615,
-  322,
-  41,
-  582,
-  156,
-  664,
-  261,
-  368,
-  702,
-  25,
-  439,
-  382,
-  123,
-  682,
-  970,
-  511,
-  928,
-  870,
-  453,
-  865,
-  724,
-  255,
-  504,
-  567,
-  105,
-  465,
-  146,
-  349,
-  616,
-  419,
-  389,
-  629,
-  964,
-  482,
-  483,
-  252,
-  183,
-  300,
-  578,
-  255,
-  825,
-  702,
-  650,
-  468,
-  808,
-  939,
-  360,
-  830,
-  281,
-  969,
-  139,
-  488,
-  603,
-  449,
-  731,
-  941,
-  172,
-  643,
-  569,
-  90,
-  966,
-  468,
-  818,
+  203,
+  206,
+  207,
   249,
-  649,
-  661,
-  661,
-  955,
-  52,
-  17,
-  364,
-  472,
-  854,
-  154,
-  543,
-  110,
-  327,
-  905,
-  715,
-  940,
-  612,
-  248,
-  634,
-  690,
-  326,
-  622,
-  52,
-  935,
-  244,
-  406,
-  604,
-  351,
-  303,
-  268,
-  717,
-  247,
-  475,
-  718,
-  835,
-  885,
-  534,
-  842,
-  942,
-  929,
-  713,
-  786,
-  72,
-  122,
-  443,
-  64,
-  512,
+  276,
+  430,
+  466,
+  483,
+  190,
+  222,
+  224,
+  232,
+  360,
+  421,
+  458,
+  473,
+  498,
+  117,
+  120,
+  123,
+  168,
+  181,
+  197,
+  227,
+  234,
+  315,
+  372,
+  425,
+  459,
+  484,
   38,
+  71,
+  90,
   189,
-  552,
-  935,
-  778,
-  832,
-  569,
-  144,
-  810,
-  634,
-  399,
-  261,
-  918,
-  728,
-  648,
   340,
-  730,
-  358,
-  496,
-  928,
-  344,
-  929,
-  572,
-  876,
-  667,
-  933,
-  584,
-  122,
-  739,
-  978,
-  37,
-  250,
-  192,
-  113,
-  763,
-  214,
-  852,
-  365,
-  638,
-  570,
-  82,
-  861,
-  448,
-  649,
-  813,
-  950,
-  843,
-  154,
-  527,
-  12,
-  953,
-  153,
-  311,
-  177,
-  490,
-  754,
-  973,
-  511,
-  777,
-  649,
-  605,
-  311,
-  539,
-  133,
-  245,
-  940,
-  717,
-  851,
-  189,
-  905,
-  410,
-  214,
-  170,
-  983,
-  998,
-  404,
-  599,
-  843,
-  41,
-  955,
-  505,
-  916,
-  947,
-  851,
-  397,
-  194,
-  288,
-  781,
-  897,
-  546,
-  305,
+  342,
+  370,
+  391,
+  395,
+  418,
+  86,
+  174,
+  201,
+  355,
+  360,
+  401,
+  478,
+  59,
+  163,
+  249,
+  350,
+  408,
+  409,
+  81,
+  83,
   113,
-  356,
-  454,
-  679,
-  774,
-  314,
-  897,
-  452,
-  169,
+  143,
+  279,
+  289,
+  470,
+  473,
+  17,
+  38,
+  43,
+  47,
+  106,
+  198,
+  257,
+  350,
+  373,
+  389,
+  457,
+  462,
+  494,
+  10,
+  22,
+  69,
+  108,
+  172,
+  273,
+  348,
+  370,
+  373,
   391,
-  344,
-  880,
-  840,
-  327,
-  404,
+  419,
+  495,
+  497,
+  0,
+  73,
+  102,
+  104,
+  143,
+  157,
+  180,
+  190,
+  241,
+  247,
+  330,
+  374,
+  378,
+  433,
+  474,
+  34,
+  38,
+  52,
+  73,
+  140,
+  184,
+  247,
+  259,
+  268,
+  353,
+  406,
+  468,
+  23,
   29,
+  96,
+  114,
+  143,
+  198,
+  283,
+  295,
+  416,
+  476,
+  51,
+  285,
+  394,
+  7,
+  28,
+  62,
+  85,
+  244,
+  301,
+  376,
+  387,
+  460,
+  481,
+  61,
+  76,
+  117,
+  131,
+  140,
+  175,
+  219,
+  254,
+  259,
+  275,
   353,
-  688,
-  196,
-  135,
-  860,
-  878,
-  288,
-  523,
-  335,
-  1,
-  680,
-  923,
+  392,
+  394,
+  395,
+  441,
+  499,
+  8,
+  12,
+  126,
+  190,
+  292,
+  360,
+  460,
+  98,
+  247,
+  262,
+  271,
+  290,
+  301,
+  353,
+  408,
+  450,
   480,
-  108,
-  10,
-  188,
-  165,
-  500,
-  331,
-  668,
-  279,
-  939,
-  797,
-  203,
-  925,
-  768,
-  310,
-  453,
-  213,
-  909,
-  769,
+  43,
+  124,
+  171,
+  316,
+  413,
+  12,
+  43,
+  115,
+  147,
+  227,
+  240,
+  255,
+  300,
+  335,
+  378,
+  380,
+  397,
+  6,
+  15,
+  23,
+  64,
+  78,
+  132,
+  227,
+  321,
+  385,
+  413,
+  461,
+  2,
+  53,
+  74,
+  86,
+  115,
   136,
-  93,
-  501,
-  926,
-  249,
-  888,
-  591,
-  628,
-  317,
-  668,
-  364,
-  375,
-  951,
-  432,
-  217,
-  765,
-  469,
-  458,
-  25,
+  154,
+  261,
+  370,
+  383,
+  466,
+  22,
+  122,
+  163,
+  198,
+  200,
+  240,
+  263,
+  294,
+  363,
+  408,
+  499,
+  27,
+  53,
+  71,
+  102,
+  133,
+  236,
+  261,
+  368,
+  434,
+  472,
+  34,
+  79,
+  163,
+  176,
+  222,
+  273,
   330,
-  279,
-  734,
-  995,
-  187,
-  150,
-  739,
-  179,
-  551,
-  844,
-  920,
-  871,
-  906,
-  397,
-  540,
-  376,
-  123,
-  233,
-  19,
+  352,
+  400,
+  10,
+  61,
+  95,
+  144,
+  172,
+  204,
   227,
-  109,
+  301,
+  312,
+  331,
+  103,
+  259,
+  272,
+  295,
+  332,
+  139,
+  175,
+  191,
+  230,
+  289,
+  295,
+  298,
+  352,
+  370,
+  383,
+  401,
+  421,
+  79,
+  117,
+  135,
+  153,
+  180,
+  203,
+  283,
+  365,
+  420,
+  92,
+  104,
+  113,
+  124,
+  138,
   158,
-  20,
-  11,
-  899,
-  462,
-  655,
-  837,
-  756,
-  930,
-  580,
-  304,
-  655,
-  419,
-  695,
-  319,
-  496,
-  856,
-  575,
-  700,
-  223,
-  793,
-  462,
-  666,
-  274,
-  967,
-  650,
-  287,
-  521,
-  69,
-  898,
-  684,
-  759,
-  31,
-  373,
-  515,
-  56,
-  966,
-  971,
-  836,
-  950,
-  94,
-  647,
-  948,
-  766,
-  988,
-  556,
-  458,
-  415,
-  46,
-  741,
-  519,
-  186,
-  393,
-  409,
-  658,
-  349,
-  833,
-  339,
-  61,
+  288,
+  318,
+  381,
+  484,
+  13,
+  16,
+  72,
+  96,
+  135,
+  138,
+  259,
+  297,
+  352,
+  469,
+  4,
+  27,
+  219,
+  225,
   250,
-  49,
-  63,
-  503,
-  21,
-  951,
-  809,
+  255,
+  290,
+  329,
+  430,
+  448,
+  96,
+  119,
+  169,
+  177,
+  181,
+  207,
+  236,
+  267,
+  286,
+  342,
+  370,
+  373,
+  411,
+  414,
+  422,
+  463,
+  478,
+  52,
+  60,
+  112,
+  220,
+  254,
+  257,
+  331,
+  382,
   391,
-  242,
-  739,
-  823,
-  9,
-  548,
-  876,
-  431,
-  920,
-  451,
-  967,
-  291,
-  529,
-  37,
-  133,
-  656,
-  240,
-  981,
-  223,
+  488,
+  93,
+  171,
+  179,
+  227,
+  356,
+  376,
+  381,
+  424,
+  426,
+  36,
+  126,
+  200,
+  280,
+  383,
+  402,
+  407,
+  472,
+  489,
+  497,
+  53,
+  62,
+  88,
+  101,
+  130,
   167,
-  458,
-  624,
-  473,
-  570,
-  942,
-  260,
-  808,
-  16,
-  792,
-  699,
-  537,
-  84,
-  906,
-  429,
-  728,
-  320,
-  785,
-  301,
-  9,
-  679,
-  882,
-  98,
-  431,
-  223,
-  920,
-  173,
-  895,
-  605,
-  68,
-  698,
-  696,
-  987,
-  855,
+  188,
   191,
-  657,
-  533,
+  285,
+  320,
+  339,
+  384,
+  436,
   478,
-  321,
-  846,
-  921,
-  490,
-  278,
-  145,
-  500,
-  274,
-  974,
-  505,
-  33,
-  936,
-  691,
-  922,
-  140,
-  846,
-  951,
-  745,
-  893,
-  803,
-  316,
-  689,
-  960,
-  509,
-  518,
-  911,
-  121,
+  485,
+  11,
   12,
-  477,
-  702,
-  94,
-  521,
-  751,
-  840,
-  492,
-  666,
-  922,
-  714,
-  43,
-  683,
-  871,
-  531,
-  774,
-  137,
-  914,
-  745,
-  722,
+  143,
+  154,
+  227,
+  230,
+  300,
+  307,
+  326,
+  483,
+  28,
+  70,
+  110,
+  358,
+  468,
+  55,
+  104,
+  111,
+  122,
+  179,
+  204,
+  206,
+  236,
+  292,
+  403,
+  410,
+  426,
+  465,
+  10,
+  204,
+  291,
+  390,
+  394,
+  497,
+  25,
+  47,
+  152,
+  190,
+  328,
+  329,
+  339,
+  365,
+  367,
+  378,
+  34,
+  36,
+  67,
+  136,
+  216,
+  259,
+  358,
+  408,
+  419,
+  450,
+  462,
+  499,
+  42,
+  48,
+  187,
+  192,
+  286,
+  291,
+  297,
+  368,
+  396,
+  422,
+  423,
+  90,
+  121,
+  202,
+  254,
+  278,
+  335,
+  336,
+  430,
+  453,
+  475,
+  490,
+  35,
+  71,
+  76,
+  129,
+  136,
+  210,
+  218,
+  396,
+  411,
+  428,
+  460,
+  38,
+  79,
+  98,
+  158,
+  217,
+  237,
+  401,
+  484,
+  35,
+  88,
+  103,
+  212,
+  433,
+  2,
+  197,
+  206,
+  215,
+  244,
+  338,
+  21,
+  24,
+  57,
+  111,
+  116,
+  213,
+  251,
+  274,
+  328,
+  432,
+  483,
+  489,
+  4,
   78,
-  398,
-  384,
-  536,
-  365,
+  89,
+  107,
+  132,
+  176,
+  204,
+  207,
+  246,
+  282,
+  294,
+  420,
+  473,
+  34,
+  49,
+  89,
+  93,
+  116,
+  140,
+  162,
+  267,
+  327,
+  356,
+  357,
+  369,
+  13,
+  37,
+  59,
+  79,
+  183,
+  292,
+  295,
+  321,
+  473,
+  1,
+  141,
+  197,
+  309,
+  324,
+  356,
+  461,
+  497,
+  31,
+  77,
+  138,
+  149,
+  200,
+  227,
   245,
-  807,
-  925,
-  201,
-  917,
-  368,
-  214,
   246,
-  143,
-  388,
-  937,
-  483,
-  480,
-  793,
-  415,
-  835,
-  554,
-  514,
-  838,
-  655,
-  837,
-  481,
-  483,
-  777,
+  261,
+  318,
+  350,
+  450,
+  452,
+  14,
+  43,
+  50,
+  118,
+  255,
+  348,
+  444,
+  489,
+  22,
+  53,
+  78,
+  121,
+  225,
+  274,
+  300,
+  317,
+  324,
+  343,
+  374,
+  390,
+  404,
+  462,
+  473,
+  490,
+  42,
+  149,
+  191,
+  341,
+  362,
+  381,
+  463,
+  55,
+  70,
+  77,
+  79,
+  93,
+  126,
+  142,
+  166,
+  192,
+  202,
+  222,
+  440,
+  457,
+  489,
+  496,
+  128,
+  134,
+  177,
+  292,
+  295,
+  305,
+  325,
+  361,
+  362,
   447,
-  963,
-  596,
-  248,
-  819,
-  696,
-  540,
-  163,
+  0,
+  5,
+  188,
+  264,
+  270,
+  310,
   333,
-  589,
-  863,
-  603,
-  835,
-  952,
-  253,
-  329,
-  552,
+  344,
+  5,
+  19,
+  126,
   207,
-  684,
-  593,
-  618,
-  742,
-  53,
-  90,
-  27,
-  955,
-  217,
-  955,
-  20,
-  520,
-  221,
-  316,
-  45,
-  948,
-  552,
-  110,
-  594,
-  774,
-  517,
-  880,
-  32,
-  575,
-  852,
-  463,
-  685,
+  270,
+  274,
+  345,
+  498,
+  15,
+  55,
+  56,
+  64,
+  96,
+  122,
+  143,
+  195,
+  215,
+  295,
+  313,
+  320,
+  444,
+  449,
+  476,
+  483,
+  88,
+  158,
+  256,
+  311,
+  356,
+  395,
+  407,
+  14,
+  18,
+  22,
+  68,
+  71,
+  108,
+  168,
+  170,
+  172,
+  206,
+  207,
+  340,
+  395,
+  397,
+  435,
+  19,
+  77,
+  153,
+  166,
+  415,
+  22,
+  83,
+  173,
+  247,
+  289,
+  324,
+  417,
+  430,
   10,
+  152,
+  160,
+  170,
+  203,
+  284,
+  287,
+  395,
+  497,
+  37,
+  68,
+  96,
+  135,
+  201,
+  305,
+  457,
+  465,
+  86,
+  90,
+  175,
+  183,
+  198,
+  214,
+  233,
+  280,
+  60,
+  113,
+  141,
+  150,
+  494,
+  17,
+  54,
+  65,
+  72,
+  93,
+  137,
+  145,
+  150,
+  238,
+  264,
+  333,
+  356,
+  373,
+  440,
+  446,
+  37,
+  43,
+  143,
+  156,
+  169,
+  236,
+  257,
+  351,
+  365,
+  369,
+  374,
+  381,
+  395,
+  456,
+  19,
   58,
-  945,
-  572,
-  875,
-  633,
-  942,
-  880,
+  138,
+  194,
+  285,
   426,
-  283,
-  491,
-  848,
+  446,
+  450,
   491,
-  280,
+  492,
+  201,
+  312,
+  385,
   412,
-  1,
-  819,
+  484,
+  56,
+  76,
+  103,
+  210,
+  213,
+  214,
+  359,
+  384,
+  159,
+  191,
+  195,
+  251,
+  295,
+  356,
+  378,
+  399,
+  416,
+  418,
+  441,
+  3,
+  19,
+  63,
+  125,
+  198,
+  214,
+  254,
+  291,
+  297,
+  326,
+  331,
+  342,
+  371,
+  465,
+  466,
+  141,
+  162,
+  181,
+  253,
+  281,
+  413,
+  417,
+  444,
+  474,
+  31,
+  134,
+  212,
+  281,
+  343,
+  354,
+  428,
+  493,
+  27,
+  135,
+  147,
+  169,
+  186,
   199,
-  190,
-  577,
+  223,
+  225,
+  230,
+  251,
+  462,
+  170,
+  201,
+  215,
+  235,
+  278,
+  376,
+  394,
+  71,
+  162,
+  173,
+  241,
+  263,
+  309,
+  37,
+  54,
+  99,
+  118,
+  172,
+  188,
+  234,
+  256,
+  450,
+  38,
+  55,
+  98,
+  101,
+  110,
+  151,
+  182,
+  304,
+  306,
+  376,
+  378,
+  400,
+  409
+};
+const double x[500] = {
+  353,
+  528,
+  855,
+  623,
+  693,
+  26,
+  928,
+  283,
+  710,
+  154,
+  423,
+  193,
+  627,
+  362,
+  271,
+  632,
+  502,
+  254,
+  655,
+  589,
+  809,
+  858,
+  427,
+  70,
+  305,
+  618,
+  419,
+  16,
+  840,
+  389,
+  773,
+  270,
+  546,
+  455,
+  278,
+  647,
+  926,
+  882,
+  158,
+  785,
+  620,
+  56,
+  154,
+  592,
+  293,
+  496,
+  810,
+  429,
+  509,
+  562,
+  26,
+  981,
+  21,
+  849,
+  374,
+  495,
+  549,
+  124,
+  687,
+  137,
+  719,
+  232,
+  690,
+  616,
+  824,
+  46,
+  712,
+  650,
+  223,
+  868,
+  576,
+  707,
+  999,
+  883,
+  551,
+  159,
+  306,
+  101,
+  618,
+  194,
+  787,
   488,
-  936,
-  678,
-  79,
-  317,
-  408,
-  689,
-  353,
-  889,
-  294,
-  561,
-  501,
-  411,
-  554,
-  321,
-  193,
-  748,
-  309,
-  110,
-  454,
-  33,
-  28,
-  193,
-  166,
-  804,
-  710,
-  581,
-  70,
-  726,
-  805,
-  673,
-  751,
-  147,
-  793,
   395,
-  151,
-  129,
-  143,
-  610,
-  700,
-  590,
-  577,
-  814,
-  104,
-  990,
-  56,
-  254,
-  816,
-  278,
-  108,
-  765,
-  31,
+  970,
+  29,
+  260,
+  223,
+  605,
+  682,
+  293,
   208,
-  804,
+  5,
+  947,
+  244,
+  126,
+  692,
+  95,
+  888,
+  776,
+  502,
+  375,
+  237,
+  176,
   730,
+  837,
+  407,
+  757,
+  772,
+  365,
+  21,
+  250,
+  938,
+  804,
+  940,
+  859,
+  945,
+  173,
+  215,
+  72,
+  331,
+  339,
+  880,
+  874,
+  375,
+  920,
+  254,
+  675,
+  614,
+  19,
+  570,
+  850,
+  93,
+  200,
   960,
+  276,
+  332,
+  218,
+  895,
+  270,
+  922,
+  220,
+  44,
+  566,
+  330,
+  645,
+  834,
+  129,
+  926,
+  265,
+  78,
+  975,
+  822,
+  300,
+  394,
+  731,
+  917,
+  89,
+  136,
+  894,
+  441,
+  681,
+  144,
+  867,
+  157,
+  759,
+  432,
+  830,
+  252,
+  929,
+  784,
+  702,
+  572,
+  753,
+  887,
+  697,
+  437,
+  409,
+  29,
+  999,
+  445,
+  532,
+  189,
+  326,
+  729,
+  73,
+  478,
+  428,
+  713,
+  627,
+  240,
+  540,
+  25,
+  932,
+  406,
+  639,
+  472,
+  544,
+  763,
+  4,
+  695,
+  69,
+  37,
+  802,
+  351,
+  865,
+  169,
+  17,
+  439,
+  844,
+  65,
+  857,
+  193,
+  404,
+  337,
+  307,
+  208,
+  591,
+  658,
+  515,
+  761,
+  162,
+  528,
+  15,
+  34,
+  416,
+  831,
+  937,
+  67,
+  495,
+  765,
+  288,
+  408,
+  517,
+  35,
+  813,
+  112,
+  632,
+  61,
+  465,
+  357,
+  626,
+  284,
+  276,
+  632,
   323,
-  152,
-  202,
-  449,
-  238,
-  907,
+  661,
+  840,
+  864,
+  880,
+  928,
+  268,
+  703,
+  170,
+  30,
+  628,
+  850,
+  450,
+  807,
+  758,
+  810,
+  128,
+  992,
+  760,
+  603,
+  34,
+  910,
+  884,
+  937,
+  737,
+  521,
+  61,
+  394,
+  0,
+  504,
+  868,
+  85,
+  294,
+  997,
+  251,
   532,
-  618,
-  377,
-  295,
-  625,
-  252,
-  383,
-  345,
-  46,
-  934,
-  908,
-  851,
-  304,
-  235,
-  623,
-  808,
-  363,
-  80,
-  373,
-  858,
-  839,
-  385,
-  426,
-  727,
-  615,
-  675,
-  860,
-  602,
-  623,
-  780,
-  246,
-  22,
-  681,
-  623,
-  293,
-  421,
-  908,
-  419,
-  811,
-  631,
-  155,
-  139,
-  861,
-  262,
-  789,
-  344,
-  507,
-  14,
-  445,
-  995,
-  316,
-  74,
+  499,
+  596,
+  594,
+  744,
+  606,
+  709,
+  928,
+  506,
+  397,
+  988,
+  689,
+  161,
+  654,
+  729,
+  238,
+  869,
+  298,
+  817,
+  571,
+  887,
+  2,
+  137,
+  593,
+  651,
+  529,
+  34,
+  452,
+  667,
   32,
-  239,
-  932,
-  586,
-  167,
-  578,
-  555,
-  8,
-  720,
-  804,
-  18,
-  185,
-  637,
-  185,
-  21,
+  189,
+  734,
   121,
-  993,
-  457,
-  0,
-  911,
-  330,
-  214,
-  343,
-  600,
-  720,
-  645,
-  542,
+  473,
+  675,
+  594,
+  264,
+  492,
+  402,
+  437,
+  640,
+  141,
+  528,
+  351,
+  740,
+  326,
+  613,
+  640,
+  50,
+  104,
+  433,
+  613,
+  470,
+  125,
+  671,
+  81,
+  155,
+  209,
+  69,
+  856,
+  999,
+  143,
+  601,
   991,
-  704,
-  261,
+  458,
+  120,
+  169,
+  839,
+  667,
+  566,
+  119,
+  713,
+  943,
+  646,
+  559,
+  755,
+  223,
+  436,
+  15,
+  768,
+  580,
+  416,
+  906,
+  118,
+  738,
+  583,
+  112,
+  65,
+  150,
+  933,
+  54,
+  901,
+  102,
+  733,
+  357,
+  505,
+  155,
+  723,
+  210,
+  142,
+  413,
+  768,
+  602,
+  614,
+  268,
+  485,
+  679,
+  330,
+  110,
+  819,
+  11,
+  116,
+  90,
+  615,
+  327,
+  131,
+  351,
+  275,
+  121,
+  77,
+  465,
+  831,
+  617,
+  663,
+  314,
+  519,
+  670,
+  39,
+  705,
+  86,
+  201,
+  619,
+  746,
+  736,
+  813,
+  138,
+  186,
+  693,
+  538,
+  160,
+  244,
+  257,
+  997,
+  751,
+  157,
+  512,
+  253,
+  536,
+  433,
+  87,
+  333,
+  881,
+  784,
+  102,
+  1,
+  809,
+  456,
+  425,
+  783,
+  839,
+  55,
+  78,
+  51,
   481,
-  242,
-  949,
-  909,
-  745,
+  310,
+  416,
+  518,
+  816,
+  605,
+  130,
+  100,
+  999,
+  727,
+  24,
+  761,
+  45,
+  579,
+  103,
+  856,
+  304,
+  691,
+  957,
+  120,
+  250,
+  941,
+  59,
+  411,
+  976,
+  420,
   799,
-  644,
+  227,
+  692,
+  842,
+  677,
+  763,
+  660,
+  292,
+  702,
+  560,
+  27,
+  138,
+  41,
+  75,
+  694,
+  577,
+  101,
+  92,
+  9,
+  959,
+  33,
+  11,
+  248,
+  515,
+  290,
+  742,
   858,
-  132,
-  886,
-  194,
-  886,
-  695,
-  912,
-  980,
-  956,
-  51,
-  885,
-  410,
-  88,
-  578,
-  636,
-  698,
-  636,
-  532,
-  579,
-  389,
-  124,
-  386,
-  54,
-  616,
-  203,
-  838,
-  732,
-  152,
-  775,
-  749,
-  373
+  294,
+  900,
+  107,
+  567,
+  890
 };
-const int ptr[1001] = {
+const int ptr[501] = {
   0,
-  6,
-  18,
-  31,
+  11,
+  22,
+  32,
   40,
-  49,
-  58,
-  67,
-  75,
-  85,
-  98,
-  111,
+  46,
+  53,
+  64,
+  74,
+  89,
+  102,
+  112,
   121,
-  135,
-  139,
-  146,
-  159,
-  169,
-  175,
-  181,
-  191,
-  203,
-  210,
-  217,
-  228,
-  238,
-  245,
-  254,
+  132,
+  140,
+  147,
+  156,
+  160,
+  172,
+  185,
+  197,
+  202,
+  216,
+  229,
+  236,
+  242,
+  248,
+  255,
   265,
-  278,
-  290,
+  271,
+  283,
+  292,
   298,
-  311,
-  323,
-  332,
-  343,
-  353,
-  360,
-  370,
+  306,
+  314,
+  326,
+  335,
+  348,
+  357,
+  374,
   383,
-  396,
-  407,
-  415,
-  427,
-  433,
-  440,
-  449,
-  461,
-  467,
-  474,
-  487,
-  503,
-  510,
-  522,
-  530,
-  542,
-  549,
-  556,
-  570,
-  584,
-  594,
-  605,
-  614,
-  624,
+  392,
+  403,
+  414,
+  425,
+  436,
+  446,
+  462,
+  470,
+  476,
+  488,
+  506,
+  520,
+  528,
+  534,
+  541,
+  550,
+  565,
+  577,
+  591,
+  600,
+  609,
+  615,
   629,
-  637,
-  644,
-  653,
-  663,
+  635,
+  648,
+  661,
   674,
-  685,
-  691,
-  701,
-  712,
-  723,
-  734,
-  746,
-  754,
-  766,
-  779,
-  788,
-  802,
-  809,
-  820,
-  831,
-  846,
-  860,
-  869,
-  874,
-  883,
-  886,
-  900,
-  915,
-  929,
-  937,
-  946,
-  955,
-  969,
-  985,
-  993,
-  1004,
-  1014,
-  1026,
-  1035,
-  1040,
-  1053,
-  1064,
-  1073,
-  1078,
-  1089,
-  1097,
-  1105,
-  1108,
-  1119,
-  1131,
-  1143,
-  1156,
-  1165,
-  1175,
-  1187,
-  1196,
-  1205,
-  1209,
-  1218,
-  1230,
-  1242,
-  1253,
-  1263,
-  1277,
-  1288,
-  1306,
-  1323,
+  682,
+  694,
+  709,
+  717,
+  727,
+  733,
+  743,
+  753,
+  762,
+  776,
+  783,
+  794,
+  806,
+  813,
+  818,
+  827,
+  835,
+  845,
+  857,
+  867,
+  876,
+  885,
+  893,
+  899,
+  905,
+  914,
+  919,
+  932,
+  942,
+  954,
+  963,
+  972,
+  981,
+  994,
+  1001,
+  1007,
+  1016,
+  1023,
+  1031,
+  1039,
+  1049,
+  1057,
+  1069,
+  1082,
+  1099,
+  1107,
+  1117,
+  1129,
+  1136,
+  1148,
+  1161,
+  1171,
+  1183,
+  1189,
+  1204,
+  1217,
+  1229,
+  1238,
+  1251,
+  1258,
+  1265,
+  1266,
+  1281,
+  1291,
+  1301,
+  1310,
+  1319,
+  1324,
   1331,
-  1345,
-  1355,
-  1362,
-  1372,
-  1380,
+  1340,
+  1349,
+  1357,
+  1367,
+  1379,
   1388,
-  1395,
+  1398,
   1412,
-  1424,
-  1428,
-  1436,
-  1443,
-  1457,
-  1473,
-  1488,
+  1418,
+  1423,
+  1426,
+  1431,
+  1444,
+  1453,
+  1466,
+  1475,
+  1482,
   1498,
-  1511,
-  1520,
-  1533,
-  1543,
-  1556,
-  1567,
-  1578,
-  1590,
-  1598,
-  1609,
-  1618,
-  1627,
-  1634,
-  1638,
-  1643,
-  1649,
-  1654,
-  1660,
-  1675,
+  1509,
+  1514,
+  1522,
+  1534,
+  1546,
+  1557,
+  1572,
+  1584,
+  1595,
+  1600,
+  1611,
+  1621,
+  1628,
+  1637,
+  1644,
+  1653,
+  1672,
+  1681,
   1688,
-  1698,
-  1712,
-  1722,
-  1730,
-  1738,
-  1746,
-  1758,
-  1765,
-  1778,
-  1787,
-  1802,
-  1814,
-  1821,
-  1833,
-  1842,
-  1851,
-  1864,
-  1877,
-  1886,
-  1890,
+  1701,
+  1714,
+  1728,
+  1737,
+  1742,
+  1755,
+  1766,
+  1775,
+  1784,
+  1789,
+  1799,
+  1812,
+  1819,
+  1826,
+  1832,
+  1845,
+  1857,
+  1869,
+  1881,
   1898,
-  1904,
-  1916,
-  1931,
-  1942,
-  1953,
-  1966,
-  1975,
-  1988,
-  1999,
-  2008,
-  2021,
-  2027,
-  2036,
-  2049,
-  2058,
-  2069,
-  2078,
-  2086,
-  2099,
-  2109,
-  2115,
-  2123,
-  2133,
-  2142,
-  2155,
-  2166,
-  2175,
-  2185,
-  2191,
-  2202,
-  2215,
-  2220,
-  2234,
-  2248,
-  2260,
-  2271,
-  2277,
-  2285,
-  2297,
-  2310,
-  2318,
-  2328,
-  2337,
-  2352,
-  2358,
-  2370,
-  2378,
-  2391,
-  2397,
-  2407,
-  2413,
+  1908,
+  1918,
+  1930,
+  1941,
+  1949,
+  1957,
+  1964,
+  1972,
+  1981,
+  1993,
+  1998,
+  2004,
+  2014,
+  2025,
+  2034,
+  2048,
+  2060,
+  2067,
+  2073,
+  2087,
+  2092,
+  2101,
+  2111,
+  2120,
+  2129,
+  2134,
+  2141,
+  2149,
+  2160,
+  2172,
+  2179,
+  2189,
+  2198,
+  2210,
+  2218,
+  2230,
+  2237,
+  2249,
+  2259,
+  2270,
+  2278,
+  2287,
+  2293,
+  2309,
+  2324,
+  2334,
+  2341,
+  2359,
+  2368,
+  2376,
+  2383,
+  2392,
+  2402,
+  2408,
+  2417,
   2425,
-  2434,
-  2442,
-  2452,
-  2462,
-  2476,
-  2480,
-  2487,
-  2500,
-  2512,
-  2525,
-  2533,
-  2545,
-  2552,
-  2563,
+  2435,
+  2444,
+  2451,
+  2465,
+  2474,
+  2479,
+  2489,
+  2499,
+  2510,
+  2518,
+  2534,
+  2541,
+  2557,
+  2567,
   2576,
-  2585,
-  2591,
-  2599,
-  2608,
-  2619,
+  2586,
+  2594,
+  2611,
   2629,
-  2643,
-  2658,
-  2664,
-  2675,
-  2682,
-  2696,
-  2705,
-  2715,
-  2718,
-  2736,
+  2638,
+  2649,
+  2665,
+  2679,
+  2687,
+  2695,
+  2702,
+  2711,
+  2727,
+  2739,
   2746,
+  2753,
   2765,
-  2771,
-  2787,
-  2793,
-  2802,
-  2813,
-  2826,
+  2778,
+  2792,
+  2798,
+  2816,
+  2829,
   2837,
-  2849,
-  2863,
-  2870,
-  2885,
-  2895,
-  2904,
-  2914,
+  2844,
+  2851,
+  2860,
+  2872,
+  2886,
+  2898,
+  2911,
+  2919,
   2925,
-  2931,
+  2930,
   2944,
-  2949,
-  2957,
-  2973,
-  2982,
-  2995,
-  3009,
-  3025,
-  3031,
+  2956,
+  2964,
+  2976,
+  2985,
+  2999,
+  3014,
+  3029,
   3046,
-  3061,
-  3069,
-  3082,
-  3089,
-  3100,
-  3106,
-  3116,
-  3119,
-  3123,
-  3130,
-  3136,
-  3144,
-  3153,
-  3162,
-  3180,
-  3185,
-  3200,
-  3205,
-  3215,
-  3225,
+  3054,
+  3065,
+  3071,
+  3085,
+  3094,
+  3102,
+  3115,
+  3125,
+  3135,
+  3149,
+  3158,
+  3170,
+  3183,
+  3195,
+  3199,
+  3208,
+  3218,
+  3228,
   3234,
-  3246,
-  3255,
-  3266,
-  3273,
-  3283,
+  3243,
+  3251,
+  3258,
+  3267,
+  3275,
+  3284,
   3293,
-  3303,
+  3301,
   3312,
   3320,
-  3331,
+  3330,
   3342,
-  3349,
-  3357,
-  3367,
-  3372,
-  3380,
-  3387,
-  3398,
+  3358,
+  3366,
+  3371,
+  3382,
+  3395,
   3405,
-  3417,
-  3425,
-  3432,
-  3443,
-  3449,
-  3456,
-  3461,
-  3471,
-  3480,
+  3415,
+  3429,
+  3438,
+  3447,
+  3460,
+  3467,
+  3476,
   3491,
-  3498,
-  3521,
-  3530,
-  3539,
-  3554,
-  3562,
+  3503,
+  3509,
+  3520,
+  3527,
+  3541,
+  3550,
+  3558,
   3569,
   3579,
-  3585,
-  3597,
-  3604,
+  3591,
+  3595,
+  3605,
   3613,
-  3628,
-  3646,
-  3657,
-  3673,
-  3681,
+  3619,
+  3635,
+  3654,
+  3671,
+  3680,
   3691,
-  3696,
-  3709,
-  3717,
-  3731,
-  3745,
-  3756,
-  3763,
-  3769,
-  3774,
-  3786,
-  3799,
-  3810,
-  3819,
-  3827,
-  3838,
-  3854,
-  3867,
-  3876,
-  3885,
-  3902,
-  3911,
-  3926,
+  3699,
+  3712,
+  3720,
+  3732,
+  3744,
+  3751,
+  3759,
+  3771,
+  3784,
+  3793,
+  3802,
+  3812,
+  3824,
+  3834,
+  3840,
+  3850,
+  3860,
+  3869,
+  3875,
+  3889,
+  3901,
+  3913,
+  3918,
+  3927,
   3936,
-  3948,
-  3959,
-  3970,
-  3983,
+  3954,
+  3963,
+  3973,
+  3981,
   3991,
   4002,
-  4009,
-  4023,
-  4032,
-  4043,
-  4058,
-  4065,
+  4010,
+  4021,
+  4030,
+  4036,
+  4049,
+  4064,
   4078,
-  4087,
-  4099,
-  4106,
-  4114,
-  4120,
-  4132,
+  4093,
+  4100,
+  4105,
+  4117,
+  4133,
+  4137,
   4146,
-  4155,
-  4168,
-  4177,
-  4189,
-  4199,
-  4212,
-  4219,
-  4231,
-  4241,
-  4253,
-  4260,
-  4266,
-  4278,
+  4159,
+  4171,
+  4180,
+  4193,
+  4203,
+  4210,
+  4216,
+  4224,
+  4237,
+  4250,
+  4265,
+  4277,
   4287,
-  4303,
-  4310,
-  4322,
-  4334,
-  4344,
-  4354,
-  4368,
-  4376,
+  4290,
+  4300,
+  4316,
+  4323,
+  4333,
+  4338,
+  4350,
+  4361,
+  4372,
   4383,
-  4399,
-  4408,
-  4416,
-  4431,
-  4444,
+  4393,
+  4402,
+  4412,
+  4417,
+  4429,
+  4438,
+  4448,
   4458,
-  4467,
-  4474,
-  4486,
+  4468,
+  4485,
   4495,
-  4506,
-  4515,
-  4521,
-  4536,
-  4549,
-  4564,
-  4571,
-  4580,
-  4593,
-  4602,
-  4613,
+  4504,
+  4514,
+  4529,
+  4539,
+  4544,
+  4557,
+  4563,
+  4573,
+  4585,
+  4596,
+  4607,
   4618,
-  4627,
-  4635,
-  4644,
-  4659,
-  4664,
-  4675,
-  4684,
-  4690,
-  4702,
-  4713,
-  4723,
+  4626,
+  4631,
+  4637,
+  4649,
+  4662,
+  4674,
+  4683,
+  4691,
+  4704,
+  4712,
+  4728,
   4735,
-  4743,
-  4751,
-  4759,
+  4750,
+  4760,
   4768,
-  4779,
-  4790,
+  4776,
+  4792,
   4799,
-  4811,
-  4818,
-  4823,
-  4830,
-  4838,
-  4850,
-  4861,
-  4870,
-  4878,
-  4890,
-  4897,
-  4908,
-  4916,
-  4930,
-  4939,
-  4950,
-  4959,
-  4971,
-  4977,
+  4814,
+  4819,
+  4827,
+  4836,
+  4844,
+  4852,
+  4857,
+  4872,
+  4886,
+  4896,
+  4901,
+  4909,
+  4920,
+  4935,
+  4944,
+  4952,
+  4963,
+  4970,
+  4976,
   4985,
-  4996,
-  4999,
-  5003,
-  5012,
-  5018,
-  5026,
-  5041,
-  5048,
-  5058,
-  5071,
-  5081,
-  5086,
-  5094,
-  5099,
-  5109,
-  5114,
-  5127,
-  5137,
-  5147,
-  5162,
-  5172,
-  5179,
-  5187,
-  5197,
-  5209,
-  5226,
-  5231,
-  5239,
-  5248,
-  5263,
-  5270,
-  5283,
-  5293,
-  5301,
-  5308,
-  5318,
-  5327,
-  5342,
-  5349,
-  5357,
-  5367,
-  5374,
-  5381,
-  5395,
-  5406,
-  5418,
-  5428,
-  5435,
-  5440,
-  5452,
-  5464,
-  5477,
-  5490,
-  5497,
-  5504,
-  5510,
-  5518,
-  5529,
-  5542,
-  5561,
-  5579,
-  5588,
-  5599,
-  5601,
-  5609,
-  5618,
-  5627,
-  5631,
-  5640,
-  5646,
-  5654,
-  5661,
-  5672,
-  5690,
-  5699,
-  5712,
-  5723,
-  5733,
-  5742,
-  5752,
-  5759,
-  5766,
-  5776,
-  5788,
-  5799,
-  5801,
-  5813,
-  5825,
-  5829,
-  5841,
-  5846,
-  5858,
-  5867,
-  5878,
-  5892,
-  5902,
-  5910,
-  5921,
-  5933,
-  5941,
-  5957,
-  5964,
-  5975,
-  5988,
-  6000,
-  6007,
-  6019,
-  6027,
-  6036,
-  6046,
-  6055,
-  6065,
-  6080,
-  6090,
-  6098,
-  6110,
-  6122,
-  6139,
-  6151,
-  6160,
-  6168,
-  6181,
-  6190,
-  6202,
-  6209,
-  6221,
-  6228,
-  6238,
-  6249,
-  6260,
-  6266,
-  6274,
-  6289,
-  6302,
-  6310,
-  6325,
-  6334,
-  6349,
-  6367,
-  6370,
-  6382,
-  6391,
-  6399,
-  6414,
-  6423,
-  6435,
-  6442,
-  6452,
-  6461,
-  6469,
-  6479,
-  6493,
-  6502,
-  6517,
-  6524,
-  6539,
-  6549,
-  6555,
-  6561,
-  6568,
-  6575,
-  6594,
-  6605,
-  6613,
-  6620,
-  6626,
-  6637,
-  6643,
-  6656,
-  6669,
-  6679,
-  6687,
-  6698,
-  6706,
-  6715,
-  6730,
-  6739,
-  6746,
-  6762,
-  6768,
-  6776,
-  6785,
-  6791,
-  6798,
-  6805,
-  6818,
-  6827,
-  6836,
-  6846,
-  6853,
-  6861,
-  6877,
-  6885,
-  6894,
-  6901,
-  6912,
-  6924,
-  6937,
-  6947,
-  6951,
-  6966,
-  6975,
-  6985,
-  6996,
-  7003,
-  7019,
-  7029,
-  7037,
-  7046,
-  7053,
-  7060,
-  7068,
-  7075,
-  7081,
-  7088,
-  7094,
-  7108,
-  7117,
-  7123,
-  7139,
-  7150,
-  7162,
-  7168,
-  7182,
-  7191,
-  7203,
-  7219,
-  7222,
-  7229,
-  7243,
-  7251,
-  7260,
-  7269,
-  7279,
-  7289,
-  7294,
-  7307,
-  7321,
-  7338,
-  7349,
-  7353,
-  7361,
-  7371,
-  7379,
-  7386,
-  7397,
-  7411,
-  7422,
-  7428,
-  7437,
-  7442,
-  7452,
-  7463,
-  7474,
-  7483,
-  7491,
-  7499,
-  7514,
-  7523,
-  7536,
-  7542,
-  7549,
-  7556,
-  7568,
-  7577,
-  7586,
-  7597,
-  7609,
-  7623,
-  7633,
-  7645,
-  7658,
-  7664,
-  7677,
-  7694,
-  7703,
-  7718,
-  7727,
-  7736,
-  7749,
-  7758,
-  7768,
-  7775,
-  7782,
-  7790,
-  7803,
-  7812,
-  7823,
-  7833,
-  7842,
-  7859,
-  7870,
-  7879,
-  7891,
-  7901,
-  7912,
-  7921,
-  7928,
-  7935,
-  7943,
-  7958,
-  7965,
-  7972,
-  7984,
-  7991,
-  7997,
-  8010,
-  8020,
-  8033,
-  8041,
-  8048,
-  8059,
-  8069,
-  8080,
-  8088,
-  8097,
-  8108,
-  8113,
-  8119,
-  8128,
-  8135,
-  8148,
-  8163,
-  8172,
-  8182,
-  8194,
-  8203,
-  8214,
-  8223,
-  8237,
-  8246,
-  8252,
-  8264,
-  8269,
-  8282,
-  8293,
-  8305,
-  8317,
-  8330,
-  8336,
-  8347,
-  8354,
-  8364,
-  8376,
-  8383,
-  8398,
-  8406,
-  8414,
-  8429,
-  8443,
-  8460,
-  8467,
-  8475,
-  8484,
-  8493,
-  8503,
-  8510,
-  8518,
-  8527,
-  8535,
-  8544,
-  8548,
-  8555,
-  8561,
-  8571,
-  8578,
-  8590,
-  8599,
-  8603,
-  8614,
-  8621,
-  8628,
-  8638,
-  8644,
-  8654,
-  8664,
-  8675,
-  8688,
-  8698,
-  8705,
-  8711,
-  8721,
-  8729,
-  8739,
-  8754,
-  8770,
-  8775,
-  8792,
-  8802,
-  8812,
-  8824,
-  8829,
-  8838,
-  8847,
-  8858,
-  8869,
-  8878,
-  8889,
-  8906,
-  8911,
-  8916,
-  8928,
-  8939,
-  8950,
-  8957,
-  8969,
-  8980,
-  8988,
-  8992,
-  9005,
-  9014,
-  9024,
-  9032,
-  9048,
-  9060,
-  9069,
-  9079,
-  9086,
-  9098,
-  9112,
-  9123,
-  9135,
-  9143,
-  9152,
-  9163,
-  9168,
-  9176,
-  9184,
-  9193,
-  9203,
-  9214,
-  9229,
-  9239,
-  9252,
-  9260,
-  9272,
-  9283,
-  9290,
-  9299,
-  9313,
-  9329,
-  9335,
-  9348,
-  9359,
-  9370,
-  9375,
-  9384,
-  9395,
-  9402,
-  9410,
-  9429,
-  9440,
-  9454,
-  9468,
-  9479,
-  9489,
-  9497,
-  9507,
-  9518,
-  9530,
-  9538,
-  9549,
-  9560,
-  9570,
-  9581,
-  9590,
-  9600,
-  9613,
-  9624,
-  9637,
-  9654,
-  9664,
-  9675,
-  9686,
-  9697,
-  9714,
-  9724,
-  9737,
-  9754,
-  9767,
-  9776,
-  9781,
-  9791,
-  9804,
-  9809,
-  9823,
-  9833,
-  9841,
-  9848,
-  9856,
-  9867,
-  9879,
-  9892,
-  9902,
-  9907,
-  9916,
-  9925,
-  9934,
-  9944,
-  9959,
-  9972,
-  9980,
-  9986,
-  9992,
-  10004
+  4998
 };
-const double verify_data[1000] = {
-  1971101,
-  3601995,
-  3608374,
-  3068439,
-  2756891,
-  1644445,
-  2326970,
-  3571797,
-  2167311,
-  3272467,
-  5257490,
-  2287052,
-  5507394,
-  1707471,
-  1181529,
-  2596954,
-  2999820,
-  1456597,
-  1755714,
-  2783599,
-  2224880,
-  953747,
-  1863442,
-  2375479,
-  3838149,
-  1472958,
-  2613759,
-  1412651,
-  2454897,
-  4139599,
-  1540527,
-  2373885,
-  2371153,
-  2496043,
-  2946006,
-  3041837,
-  2102841,
-  3413598,
-  3937131,
-  3428786,
-  2323528,
-  1657458,
-  3358521,
-  1821261,
-  937257,
-  2638848,
-  3351703,
-  2436591,
-  1387045,
-  3372777,
-  4422352,
-  2696491,
-  2775768,
-  1711500,
-  2463910,
-  1906176,
-  2655972,
-  2176802,
-  4025605,
-  1836921,
-  2902963,
-  1950818,
-  2553243,
-  2012524,
-  2449182,
-  1632320,
-  2628093,
-  1093587,
-  3089207,
-  3020390,
-  1485696,
-  1932818,
-  3334949,
-  1610563,
-  2076427,
-  3114683,
-  1548840,
-  3339439,
-  3335032,
-  1366398,
-  1685659,
-  1668385,
-  2510712,
-  2871270,
-  3270369,
-  4311377,
-  1982006,
-  1326681,
-  1381634,
-  398901,
-  3333661,
-  3352243,
-  2878790,
-  1577319,
-  2415255,
-  1191188,
-  3219765,
-  3467850,
-  1940862,
-  2056258,
-  1786527,
-  2278347,
-  2077897,
-  1457888,
-  3707208,
-  1405999,
-  952210,
-  1600564,
-  2343319,
-  1781556,
-  2474389,
-  522450,
-  3674982,
-  3619187,
-  3211390,
-  3586103,
-  1475431,
-  3546147,
-  3698208,
-  2049193,
-  1979189,
-  1111515,
-  2790498,
-  3439083,
-  4279066,
-  2774436,
-  2077245,
-  4390617,
-  3149593,
-  5326535,
-  3848199,
-  2772446,
-  2682304,
-  2277814,
-  1222790,
-  2067874,
-  1982666,
-  2371257,
-  1270393,
-  3228410,
-  2598823,
-  2428645,
-  904561,
-  2100006,
-  2337148,
-  3164102,
-  3908197,
-  1529402,
-  3084375,
-  1927419,
-  3196639,
-  2303890,
-  4265937,
-  2061281,
-  2212135,
-  2407656,
-  1723976,
-  2903704,
-  3276733,
-  1491735,
-  1684162,
-  1307018,
-  1201185,
-  636997,
-  1186016,
-  1774809,
-  2607471,
-  2619840,
-  3493545,
-  3226129,
-  1737347,
-  2380184,
-  1201957,
-  983240,
-  2529069,
-  2689857,
-  3022018,
-  2223714,
-  3625235,
-  3008732,
-  2417998,
-  4428750,
-  2270952,
-  2186948,
-  4812008,
-  2233927,
-  3334976,
-  1264519,
-  1626345,
-  1123879,
-  3098605,
-  4036407,
-  3104973,
-  2897790,
-  3788865,
-  2422217,
-  3611590,
-  1749696,
-  2447434,
-  2977777,
-  1573650,
-  2620107,
-  2319242,
-  2902283,
-  1882200,
-  1787017,
-  2436605,
-  3467551,
-  2413830,
-  187567,
-  2242075,
-  1754385,
-  1836061,
-  4245412,
-  3751015,
-  2715151,
-  1557751,
-  421948,
-  2963355,
-  2050843,
-  1758567,
-  2680768,
-  4076059,
-  4484640,
-  3293151,
-  1433126,
-  1649435,
-  4409656,
-  2223098,
-  2455979,
-  1874200,
-  2098066,
-  4020158,
-  1312572,
-  2801068,
-  3341899,
-  3785087,
-  1569098,
-  2778159,
-  1992179,
-  2669866,
-  1914494,
-  1619868,
-  2274333,
-  1857912,
-  3099797,
-  809499,
-  1679713,
-  3531350,
-  2599926,
-  1970143,
-  2920228,
-  2883295,
-  1394658,
-  3554897,
-  3534392,
-  1625041,
-  1492274,
-  1451033,
-  2248274,
-  2910569,
-  2341827,
-  2768016,
-  3567361,
-  781606,
-  2434644,
-  1782504,
-  4124675,
-  3646132,
-  2864945,
-  512560,
-  3618571,
-  2223074,
-  4315721,
-  1195043,
-  4737421,
-  1748427,
-  3474050,
-  1798506,
-  4916152,
-  2411793,
-  3382242,
-  5132409,
-  810557,
-  4870878,
-  1368859,
-  2955757,
-  1940419,
-  3146202,
-  880792,
-  3448573,
-  1017493,
-  2481321,
-  3652309,
-  3475252,
-  2845994,
-  3182841,
-  5898263,
-  1771223,
-  3346757,
-  2512678,
-  1778448,
-  3432671,
-  2814247,
-  3403195,
-  812303,
-  2104162,
-  85040,
-  989115,
-  1897384,
-  1248980,
-  2002961,
-  1371732,
-  2373820,
-  5178478,
-  1511192,
-  5127654,
-  1468260,
-  2185303,
-  2436412,
-  2978141,
-  2230665,
-  1707852,
-  2529167,
-  1152196,
-  3239187,
-  2498749,
-  2707774,
-  1502699,
-  1633289,
-  2782744,
-  4089832,
-  1548833,
-  1704769,
-  2712629,
-  992084,
-  1369606,
-  2480517,
-  2846051,
-  3100172,
-  2371224,
-  1173652,
-  1837754,
-  3822172,
-  1417367,
-  1538908,
-  1146694,
-  2528965,
-  2800885,
-  3461160,
-  786155,
-  6573509,
-  3071638,
-  1511640,
-  3652853,
-  1475533,
-  1525596,
-  2695806,
-  1277883,
-  3278333,
-  2226936,
-  2030339,
-  3914645,
-  4318373,
-  2059669,
-  3961569,
-  1772074,
-  3135802,
-  1261862,
-  4771438,
-  1587528,
-  2435428,
-  2869031,
-  2629400,
-  1533986,
-  1866116,
-  1203541,
-  2007311,
-  4295134,
-  3082652,
-  2127515,
-  3110833,
-  2895900,
-  4701588,
-  2727753,
-  2324739,
-  2142817,
-  4359375,
-  2762710,
-  2675084,
-  2776056,
-  2906201,
-  2859945,
-  1471060,
-  3224362,
-  2455374,
-  2030195,
-  909337,
-  2716237,
-  2230075,
-  3070171,
-  4476596,
-  2646370,
-  3421732,
-  2163616,
-  4043766,
-  2111374,
-  2016619,
-  1318843,
-  3586217,
-  3000490,
-  2914687,
-  2728187,
-  3496083,
-  3137438,
-  1555757,
-  2975780,
-  864871,
-  3568793,
-  3273559,
-  4362169,
-  1225951,
-  1858409,
-  1867854,
-  2081582,
-  4028493,
-  1772236,
-  2634979,
-  3563733,
-  1734270,
-  2430471,
-  3597625,
-  1010411,
-  1086456,
-  3717761,
-  3038402,
-  1630224,
-  4565438,
-  3347069,
-  2543316,
-  3034145,
-  1190307,
-  3710367,
-  2894919,
-  4122408,
-  1917891,
-  1308296,
-  1847812,
-  2799933,
-  5544619,
-  990734,
-  2302389,
-  2828494,
-  2767749,
-  2734181,
-  1584801,
-  2096227,
-  2132396,
-  1605917,
-  3953389,
-  489065,
-  3370917,
-  1246610,
-  1859633,
-  3905768,
-  2375583,
-  2352791,
-  3066605,
-  3023804,
-  1714567,
-  1630198,
-  3244096,
-  3311209,
-  2837076,
-  1806523,
-  3111912,
-  924345,
-  891749,
-  1710635,
-  2779972,
-  2288984,
-  2104226,
-  2726511,
-  2994247,
-  4159385,
-  927922,
-  3372483,
-  2093351,
-  3228595,
-  1549615,
-  3203118,
-  1566786,
-  2046013,
-  1122663,
-  902592,
-  2101848,
-  633763,
-  1382735,
-  2235887,
-  1595380,
-  1684910,
-  4534882,
-  1927642,
-  3881319,
-  4091228,
-  3489550,
-  1186206,
-  1089968,
-  1673520,
-  2908231,
-  1060251,
-  4422500,
-  2814892,
-  2014163,
-  3954105,
-  2685902,
-  1427353,
-  1040905,
-  2481509,
-  2984177,
-  5050926,
-  1266027,
-  2158372,
-  2317752,
-  4020554,
-  1226253,
-  3034218,
-  3335936,
-  3282626,
-  1782262,
-  3007006,
-  2399815,
-  4116453,
-  1101525,
-  2175742,
-  1919181,
-  1935647,
-  3021439,
-  2975812,
-  1409385,
-  3435714,
-  2843659,
-  2535310,
-  973352,
-  4051148,
-  3198667,
-  3025227,
-  3821291,
-  2634495,
-  1066026,
-  1015860,
-  2374721,
-  1893315,
-  2896157,
-  5768610,
-  4638503,
-  1096525,
-  2521763,
-  201516,
-  1885950,
-  2456554,
-  2395576,
-  1805310,
-  3539192,
-  706652,
-  3652867,
-  1803915,
-  2740108,
-  4902727,
-  2480670,
-  4763486,
-  2831231,
-  2804267,
-  2958655,
-  1180330,
-  1377988,
-  1967048,
-  3251495,
-  3641699,
-  2327118,
-  518996,
-  3627226,
-  4512513,
-  821503,
-  4513458,
-  1746977,
-  3396668,
-  2072470,
-  3064446,
-  4435618,
-  2734309,
-  2193304,
-  4275484,
-  3468741,
-  2498396,
-  3068739,
-  1699359,
-  2816909,
-  2705770,
-  2392503,
-  1288021,
-  2667346,
-  1722567,
-  2924017,
-  3160472,
-  1098169,
-  3756129,
-  5913618,
-  3768712,
-  2089078,
-  2340072,
-  2483109,
-  4368798,
-  2778403,
-  1706517,
-  2503001,
-  2633764,
-  2488649,
-  3759253,
-  1596753,
-  1671868,
-  1377167,
-  2721074,
-  2026518,
-  3148597,
-  1753515,
-  2407030,
-  3191030,
-  3974792,
-  1798541,
-  4805468,
-  2569249,
-  4324091,
-  3385093,
-  745588,
-  2231981,
-  2000465,
-  2339460,
-  3327609,
-  3719613,
-  4276833,
-  1018769,
-  2495582,
-  2942706,
-  2035953,
-  2227503,
-  3631249,
-  2988856,
-  2784977,
-  1822310,
-  4621193,
-  2352625,
-  1249877,
-  1540945,
-  1241921,
-  1994350,
-  5628798,
-  1620488,
-  1897543,
-  952310,
-  1052254,
-  3358187,
-  2994928,
-  2959189,
-  2720309,
-  2875425,
-  2144130,
-  4548462,
-  2048162,
-  1339841,
-  4090958,
-  1862715,
-  1268274,
-  4042390,
-  1581631,
-  2874452,
-  1735445,
-  1588799,
-  1331885,
-  2179684,
-  5179645,
-  1959366,
-  2027198,
-  2755029,
-  2265692,
-  2335785,
-  4348426,
-  1879924,
-  2696539,
-  1106357,
-  2932568,
-  2492358,
-  3120132,
-  3691105,
-  1442767,
-  4534420,
-  2112951,
-  2625910,
-  3375099,
-  1555111,
-  4988419,
-  1174798,
-  1332818,
-  1869705,
-  1696774,
-  1175511,
-  1819161,
-  1548388,
-  1420761,
-  1580164,
-  943541,
-  4405558,
-  2240390,
-  1501984,
-  4062955,
-  3082580,
-  2967491,
-  1152855,
-  3788527,
-  2868984,
-  4078134,
-  3701904,
-  752170,
-  1758523,
-  3256074,
-  2335111,
-  2496969,
-  2165110,
-  2589055,
-  1648006,
-  966763,
-  3719559,
-  4883836,
-  2489406,
-  2900336,
-  1003207,
-  914713,
-  2687415,
-  2957174,
-  991602,
-  3005713,
-  3016805,
-  3646583,
-  2002778,
-  2188117,
-  996416,
-  3940661,
-  3749144,
-  1702093,
-  1779575,
-  2135189,
-  1198463,
-  1665170,
-  1230802,
-  3071243,
-  1250575,
-  1159769,
-  2008716,
-  2577482,
-  1680782,
-  2755046,
-  2798673,
-  2779172,
-  4719731,
-  2451896,
-  2268516,
-  3364116,
-  2139930,
-  4014502,
-  5474835,
-  2379560,
-  3272928,
-  2133308,
-  2638465,
-  3610736,
-  2437161,
-  2469816,
-  1951246,
-  1998282,
-  2022421,
-  2093450,
-  2415039,
-  4011191,
-  2829334,
-  2863331,
-  4093600,
-  2661113,
-  2923200,
-  2198013,
-  2162835,
-  2958211,
-  1829311,
-  750764,
-  1125263,
-  1293794,
-  4883789,
-  1165273,
-  1322292,
-  2045605,
-  1796576,
-  1587215,
-  3595048,
-  2442957,
-  3675117,
-  2022610,
-  2207877,
-  3164247,
-  2539827,
-  2289433,
-  2050621,
-  2033111,
-  2996013,
-  643859,
-  1353849,
-  2284477,
-  1687120,
-  2374034,
-  3975861,
-  3174103,
-  3090405,
-  3004853,
-  1655110,
-  2881453,
-  3229992,
-  3406893,
-  1953384,
-  2162162,
-  3005248,
-  1806960,
-  2262637,
-  2658934,
-  3172203,
-  2346601,
-  2083857,
-  1905139,
-  2243485,
-  1779413,
-  2958736,
-  2324181,
-  1167937,
-  2487352,
-  2195558,
-  2511598,
-  3374057,
-  3239559,
-  3989322,
-  2007874,
-  1142953,
-  1917363,
-  1413284,
-  2254989,
-  2519517,
-  2612721,
-  1979898,
-  1472130,
-  4246577,
-  678823,
-  1032892,
-  1956684,
-  2963972,
-  2501714,
-  3206467,
-  3867577,
-  1866296,
-  1852756,
-  2674353,
-  2068891,
-  2485623,
-  1691978,
-  3224678,
-  2235530,
-  2642436,
-  3528805,
-  3154289,
-  763332,
-  2188687,
-  2175236,
-  3423181,
-  2228774,
-  4926897,
-  4720293,
-  1365097,
-  4384144,
-  1933318,
-  1538742,
-  3060760,
-  891455,
-  2247727,
-  1481978,
-  2009726,
-  3389542,
-  737932,
-  4035426,
-  4661761,
-  1332633,
-  913928,
-  2479290,
-  1992229,
-  2961682,
-  1641167,
-  3217414,
-  3225260,
-  2595246,
-  591918,
-  5566353,
-  2528672,
-  2502651,
-  1241588,
-  2590376,
-  3876970,
-  1793155,
-  1501528,
-  1838442,
-  2522918,
-  2422260,
-  3056321,
-  2273838,
-  2071241,
-  1658722,
-  2562266,
-  1338349,
-  1376886,
-  2223907,
-  1921712,
-  2211260,
-  1602704,
-  5260200,
-  2189077,
-  3019251,
-  2106858,
-  3976347,
-  2463524,
-  1576729,
-  491605,
-  3168168,
-  4672180,
-  1922298,
-  2396219,
-  2857066,
-  3012596,
-  874988,
-  2600192,
-  2197450,
-  1567978,
-  1636166,
-  4334187,
-  2964752,
-  4434709,
-  2753079,
-  2384760,
-  1534463,
-  2112708,
-  2065799,
-  1431116,
-  3960134,
-  2861238,
-  2406750,
-  2744852,
-  2940188,
-  3343790,
-  2451949,
-  2431427,
-  2343771,
-  4247520,
-  2386347,
-  5806313,
-  2995484,
-  3520605,
-  1723394,
-  2278390,
-  4240678,
-  1794433,
-  3515379,
-  4577968,
-  2412014,
-  1533701,
-  733354,
-  2879952,
-  4102595,
-  1847856,
-  1920316,
-  2281251,
-  1136467,
-  2032967,
-  2387741,
-  2059754,
-  3098458,
-  2813846,
-  2264943,
-  1328950,
-  1544527,
-  1143015,
-  2417418,
-  2816076,
-  4485204,
-  2576250,
-  2144794,
-  1827914,
-  1906691,
-  2348923
+const double verify_data[500] = {
+  1751892,
+  4022164,
+  2995301,
+  1936186,
+  2246564,
+  1202307,
+  2403226,
+  1665245,
+  5460723,
+  2991420,
+  3189946,
+  2005088,
+  2579979,
+  2016203,
+  2065819,
+  1993671,
+  851952,
+  2135521,
+  3528253,
+  2792868,
+  1075529,
+  2502885,
+  3364671,
+  2066539,
+  1126092,
+  850035,
+  802328,
+  2264690,
+  2378605,
+  4461773,
+  1329616,
+  312081,
+  1746678,
+  2141730,
+  2744934,
+  1367783,
+  3595144,
+  2432898,
+  4071407,
+  1302967,
+  1652018,
+  2211899,
+  3912143,
+  2373635,
+  2666922,
+  2038278,
+  4698422,
+  1954640,
+  1563508,
+  2694611,
+  3827590,
+  5206087,
+  1870941,
+  966474,
+  2645084,
+  2531376,
+  3163745,
+  3967912,
+  3292737,
+  2492971,
+  2883924,
+  1528423,
+  3145472,
+  1625261,
+  2200485,
+  3632184,
+  3178738,
+  1893515,
+  3126495,
+  3348716,
+  1528265,
+  3525430,
+  1008772,
+  2181826,
+  1833788,
+  3009546,
+  3850859,
+  1929502,
+  1305357,
+  3389808,
+  2443621,
+  914320,
+  3097972,
+  3175599,
+  1918158,
+  1956635,
+  1197144,
+  3283923,
+  2362512,
+  2914914,
+  1519627,
+  1082679,
+  1779165,
+  1459222,
+  2562841,
+  3792210,
+  3315753,
+  2428061,
+  1900458,
+  2028141,
+  2355412,
+  1292213,
+  1657778,
+  4938329,
+  2347809,
+  1922563,
+  2178935,
+  3429211,
+  1904099,
+  3797974,
+  4230001,
+  4774548,
+  1692473,
+  2457473,
+  2131820,
+  2246792,
+  3107036,
+  2656237,
+  3099219,
+  2499844,
+  2118926,
+  2890550,
+  3012532,
+  4213593,
+  2060214,
+  3903181,
+  2016912,
+  1140389,
+  4680,
+  2876480,
+  1234517,
+  2373109,
+  1792007,
+  2735030,
+  639171,
+  916044,
+  2224239,
+  3146731,
+  739354,
+  2583186,
+  3583728,
+  2421324,
+  3028482,
+  2592653,
+  2321744,
+  122903,
+  1482609,
+  2463478,
+  2661306,
+  1865018,
+  1835144,
+  2248110,
+  1343097,
+  3672393,
+  2587367,
+  1636239,
+  2104489,
+  2804393,
+  3800231,
+  2717304,
+  3257716,
+  3054647,
+  2495991,
+  1415149,
+  3084172,
+  1994685,
+  954071,
+  1957822,
+  1297275,
+  2084477,
+  5911038,
+  2566905,
+  1296529,
+  2975518,
+  4786414,
+  4556733,
+  982088,
+  1150776,
+  1646590,
+  2140085,
+  2241812,
+  1322324,
+  1390654,
+  1994451,
+  3063562,
+  2938663,
+  831619,
+  2398209,
+  3238091,
+  3546592,
+  2816082,
+  2597318,
+  4012074,
+  2281778,
+  2335358,
+  2686566,
+  2327944,
+  1705695,
+  2384479,
+  1179412,
+  1992230,
+  1416632,
+  2817471,
+  1387997,
+  1825629,
+  2633212,
+  2854174,
+  1316538,
+  3318034,
+  2605299,
+  1813554,
+  748564,
+  2719292,
+  733866,
+  3685554,
+  2644942,
+  1581429,
+  2519177,
+  1406937,
+  2571958,
+  1036663,
+  3105668,
+  2899062,
+  822910,
+  3023464,
+  1517572,
+  3695365,
+  1576120,
+  2679724,
+  2340800,
+  2461794,
+  1442615,
+  3277667,
+  1551164,
+  2304202,
+  1765246,
+  4648243,
+  4695139,
+  3015121,
+  784265,
+  4854308,
+  1612748,
+  2023149,
+  2677811,
+  1891837,
+  2386603,
+  1303948,
+  1246705,
+  3997369,
+  1795004,
+  1868899,
+  1915102,
+  2277702,
+  3086432,
+  1091596,
+  1325425,
+  2700950,
+  2713785,
+  2580723,
+  3320788,
+  2169754,
+  2987529,
+  1820551,
+  1096402,
+  2820334,
+  3653130,
+  3944932,
+  2661607,
+  1875359,
+  1985688,
+  4170507,
+  2697623,
+  1240240,
+  1565958,
+  1687827,
+  2909302,
+  4076509,
+  3669438,
+  1654204,
+  990589,
+  1871143,
+  2555426,
+  3194652,
+  806454,
+  4579598,
+  3818316,
+  1862530,
+  1621008,
+  1213914,
+  2387732,
+  2656075,
+  5016017,
+  1483839,
+  2590576,
+  1911599,
+  1808891,
+  1727178,
+  3593503,
+  3426809,
+  1966443,
+  2615395,
+  1977162,
+  2814727,
+  4347284,
+  2571418,
+  4336262,
+  2380488,
+  3176855,
+  2075237,
+  3073444,
+  2268286,
+  2778827,
+  2533675,
+  2075240,
+  1739479,
+  3343874,
+  1213649,
+  3400144,
+  3390958,
+  4350901,
+  807565,
+  1723230,
+  2880274,
+  1846068,
+  1797277,
+  3535845,
+  1817421,
+  763905,
+  2975099,
+  1885669,
+  2520346,
+  2673876,
+  1965064,
+  1840927,
+  1479284,
+  2479045,
+  4854652,
+  3371227,
+  1602463,
+  1064398,
+  4303279,
+  2014749,
+  2088115,
+  4643355,
+  2423573,
+  2486594,
+  2015285,
+  2865268,
+  1567515,
+  3091645,
+  2650208,
+  2257731,
+  1828360,
+  3038495,
+  1456526,
+  4139422,
+  1860654,
+  2119333,
+  3560316,
+  2195765,
+  2965846,
+  1558436,
+  2201930,
+  1368838,
+  2280143,
+  6722772,
+  4966973,
+  3816690,
+  3063525,
+  3303821,
+  942869,
+  3048634,
+  2607825,
+  2846487,
+  3062389,
+  1204358,
+  1587952,
+  1407524,
+  3481628,
+  1683145,
+  670695,
+  2652500,
+  2063266,
+  3256247,
+  2228455,
+  3169118,
+  2068041,
+  3336492,
+  648877,
+  2914647,
+  2398692,
+  2468827,
+  466982,
+  1350452,
+  2494059,
+  3884284,
+  2176018,
+  1971822,
+  1717729,
+  2285788,
+  2457787,
+  2585558,
+  2001380,
+  1574379,
+  1896149,
+  2954717,
+  3571138,
+  4547560,
+  3121350,
+  911837,
+  2191633,
+  2590573,
+  3983511,
+  1138220,
+  1489367,
+  2480956,
+  3092304,
+  2007316,
+  2627569,
+  1961734,
+  1404827,
+  2016109,
+  3155800,
+  2035916,
+  1981052,
+  3740896,
+  3647095,
+  3554375,
+  657851,
+  2060326,
+  3239738,
+  2510830,
+  3003505,
+  1293641,
+  2819722,
+  2461229,
+  4391164,
+  2381527,
+  3609051,
+  2225837,
+  2269809,
+  1794757,
+  5429892,
+  2122459,
+  3549547,
+  2159187,
+  2055078,
+  2863249,
+  2624453,
+  1682530,
+  1966234,
+  4732670,
+  2420234,
+  1126780,
+  4198630,
+  873578,
+  1472698,
+  4399047,
+  2373444,
+  3046576,
+  2946567,
+  1499502,
+  1196441,
+  785704,
+  3074204,
+  3127393,
+  2310407,
+  3555659,
+  729185,
+  2534506,
+  881530,
+  3913703,
+  1712814,
+  3391585,
+  1623517,
+  1629315,
+  1290503,
+  3135796,
+  2543727,
+  3671833,
+  1144358,
+  3571303,
+  1517907,
+  1728666,
+  1346738,
+  1521662,
+  3214189,
+  3185014,
+  3308145,
+  1175588,
+  1908736,
+  2065913,
+  3720352,
+  1718329,
+  1846629,
+  2752115,
+  1254780,
+  1638702,
+  2435264,
+  1935295
 };