/****************************************************************

 *

 * The author of this software is David M. Gay.

 *

 * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.

 *

 * Permission to use, copy, modify, and distribute this software for any

 * purpose without fee is hereby granted, provided that this entire notice

 * is included in all copies of any software which is or includes a copy

 * or modification of this software and in all copies of the supporting

 * documentation for such software.

 *

 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY

 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

 *

 ***************************************************************/

/* Please send bug reports to David M. Gay (dmg at acm dot org,

 * with " at " changed at "@" and " dot " changed to ".").  */

/* On a machine with IEEE extended-precision registers, it is

 * necessary to specify double-precision (53-bit) rounding precision

 * before invoking strtod or dtoa.  If the machine uses (the equivalent

 * of) Intel 80x87 arithmetic, the call

 *  _control87(PC_53, MCW_PC);

 * does this with many compilers.  Whether this or another call is

 * appropriate depends on the compiler; for this to work, it may be

 * necessary to #include "float.h" or another system-dependent header

 * file.

 */

/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.

 * (Note that IEEE arithmetic is disabled by gcc's -ffast-math flag.)

 *

 * This strtod returns a nearest machine number to the input decimal

 * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are

 * broken by the IEEE round-even rule.  Otherwise ties are broken by

 * biased rounding (add half and chop).

 *

 * Inspired loosely by William D. Clinger's paper "How to Read Floating

 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].

 *

 * Modifications:

 *

 *  1. We only require IEEE, IBM, or VAX double-precision

 *    arithmetic (not IEEE double-extended).

 *  2. We get by with floating-point arithmetic in a case that

 *    Clinger missed -- when we're computing d * 10^n

 *    for a small integer d and the integer n is not too

 *    much larger than 22 (the maximum integer k for which

 *    we can represent 10^k exactly), we may be able to

 *    compute (d*10^k) * 10^(e-k) with just one roundoff.

 *  3. Rather than a bit-at-a-time adjustment of the binary

 *    result in the hard case, we use floating-point

 *    arithmetic to determine the adjustment to within

 *    one bit; only in really hard cases do we need to

 *    compute a second residual.

 *  4. Because of 3., we don't need a large table of powers of 10

 *    for ten-to-e (just some small tables, e.g. of 10^k

 *    for 0 <= k <= 22).

 */

/*

 * #define IEEE_8087 for IEEE-arithmetic machines where the least

 *  significant byte has the lowest address.

 * #define IEEE_MC68k for IEEE-arithmetic machines where the most

 *  significant byte has the lowest address.

 * #define Long int on machines with 32-bit ints and 64-bit longs.

 * #define IBM for IBM mainframe-style floating-point arithmetic.

 * #define VAX for VAX-style floating-point arithmetic (D_floating).

 * #define No_leftright to omit left-right logic in fast floating-point

 *  computation of dtoa.  This will cause dtoa modes 4 and 5 to be

 *  treated the same as modes 2 and 3 for some inputs.

 * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

 *  and strtod and dtoa should round accordingly.  Unless Trust_FLT_ROUNDS

 *  is also #defined, fegetround() will be queried for the rounding mode.

 *  Note that both FLT_ROUNDS and fegetround() are specified by the C99

 *  standard (and are specified to be consistent, with fesetround()

 *  affecting the value of FLT_ROUNDS), but that some (Linux) systems

 *  do not work correctly in this regard, so using fegetround() is more

 *  portable than using FLT_ROUNDS directly.

 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3

 *  and Honor_FLT_ROUNDS is not #defined.

 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines

 *  that use extended-precision instructions to compute rounded

 *  products and quotients) with IBM.

 * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic

 *  that rounds toward +Infinity.

 * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased

 *  rounding when the underlying floating-point arithmetic uses

 *  unbiased rounding.  This prevent using ordinary floating-point

 *  arithmetic when the result could be computed with one rounding error.

 * #define Inaccurate_Divide for IEEE-format with correctly rounded

 *  products but inaccurate quotients, e.g., for Intel i860.

 * #define NO_LONG_LONG on machines that do not have a "long long"

 *  integer type (of >= 64 bits).  On such machines, you can

 *  #define Just_16 to store 16 bits per 32-bit Long when doing

 *  high-precision integer arithmetic.  Whether this speeds things

 *  up or slows things down depends on the machine and the number

 *  being converted.  If long long is available and the name is

 *  something other than "long long", #define Llong to be the name,

 *  and if "unsigned Llong" does not work as an unsigned version of

 *  Llong, #define #ULLong to be the corresponding unsigned type.

 * #define Bad_float_h if your system lacks a float.h or if it does not

 *  define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,

 *  FLT_RADIX, FLT_ROUNDS, and DBL_MAX.

 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)

 *  if memory is available and otherwise does something you deem

 *  appropriate.  If MALLOC is undefined, malloc will be invoked

 *  directly -- and assumed always to succeed.  Similarly, if you

 *  want something other than the system's free() to be called to

 *  recycle memory acquired from MALLOC, #define FREE to be the

 *  name of the alternate routine.  (FREE or free is only called in

 *  pathological cases, e.g., in a dtoa call after a dtoa return in

 *  mode 3 with thousands of digits requested.)

 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making

 *  memory allocations from a private pool of memory when possible.

 *  When used, the private pool is PRIVATE_MEM bytes long:  2304 bytes,

 *  unless #defined to be a different length.  This default length

 *  suffices to get rid of MALLOC calls except for unusual cases,

 *  such as decimal-to-binary conversion of a very long string of

 *  digits.  The longest string dtoa can return is about 751 bytes

 *  long.  For conversions by strtod of strings of 800 digits and

 *  all dtoa conversions in single-threaded executions with 8-byte

 *  pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte

 *  pointers, PRIVATE_MEM >= 7112 appears adequate.

 * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK

 *  #defined automatically on IEEE systems.  On such systems,

 *  when INFNAN_CHECK is #defined, strtod checks

 *  for Infinity and NaN (case insensitively).  On some systems

 *  (e.g., some HP systems), it may be necessary to #define NAN_WORD0

 *  appropriately -- to the most significant word of a quiet NaN.

 *  (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)

 *  When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,

 *  strtod also accepts (case insensitively) strings of the form

 *  NaN(x), where x is a string of hexadecimal digits and spaces;

 *  if there is only one string of hexadecimal digits, it is taken

 *  for the 52 fraction bits of the resulting NaN; if there are two

 *  or more strings of hex digits, the first is for the high 20 bits,

 *  the second and subsequent for the low 32 bits, with intervening

 *  white space ignored; but if this results in none of the 52

 *  fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0

 *  and NAN_WORD1 are used instead.

 * #define MULTIPLE_THREADS if the system offers preemptively scheduled

 *  multiple threads.  In this case, you must provide (or suitably

 *  #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed

 *  by FREE_DTOA_LOCK(n) for n = 0 or 1.  (The second lock, accessed

 *  in pow5mult, ensures lazy evaluation of only one copy of high

 *  powers of 5; omitting this lock would introduce a small

 *  probability of wasting memory, but would otherwise be harmless.)

 *  You must also invoke freedtoa(s) to free the value s returned by

 *  dtoa.  You may do so whether or not MULTIPLE_THREADS is #defined.

 *  When MULTIPLE_THREADS is #defined, this source file provides

 *    void set_max_dtoa_threads(unsigned int n);

 *  and expects

 *    unsigned int dtoa_get_threadno(void);

 *  to be available (possibly provided by

 *    #define dtoa_get_threadno omp_get_thread_num

 *  if OpenMP is in use or by

 *    #define dtoa_get_threadno pthread_self

 *  if Pthreads is in use), to return the current thread number.

 *  If set_max_dtoa_threads(n) was called and the current thread

 *  number is k with k < n, then calls on ACQUIRE_DTOA_LOCK(...) and

 *  FREE_DTOA_LOCK(...) are avoided; instead each thread with thread

 *  number < n has a separate copy of relevant data structures.

 *  After set_max_dtoa_threads(n), a call set_max_dtoa_threads(m)

 *  with m <= n has has no effect, but a call with m > n is honored.

 *  Such a call invokes REALLOC (assumed to be "realloc" if REALLOC

 *  is not #defined) to extend the size of the relevant array.

 * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that

 *  avoids underflows on inputs whose result does not underflow.

 *  If you #define NO_IEEE_Scale on a machine that uses IEEE-format

 *  floating-point numbers and flushes underflows to zero rather

 *  than implementing gradual underflow, then you must also #define

 *  Sudden_Underflow.

 * #define USE_LOCALE to use the current locale's decimal_point value.

 * #define SET_INEXACT if IEEE arithmetic is being used and extra

 *  computation should be done to set the inexact flag when the

 *  result is inexact and avoid setting inexact when the result

 *  is exact.  In this case, dtoa.c must be compiled in

 *  an environment, perhaps provided by #include "dtoa.c" in a

 *  suitable wrapper, that defines two functions,

 *    int get_inexact(void);

 *    void clear_inexact(void);

 *  such that get_inexact() returns a nonzero value if the

 *  inexact bit is already set, and clear_inexact() sets the

 *  inexact bit to 0.  When SET_INEXACT is #defined, strtod

 *  also does extra computations to set the underflow and overflow

 *  flags when appropriate (i.e., when the result is tiny and

 *  inexact or when it is a numeric value rounded to +-infinity).

 * #define NO_ERRNO if strtod should not assign errno = ERANGE when

 *  the result overflows to +-Infinity or underflows to 0.

 *  When errno should be assigned, under seemingly rare conditions

 *  it may be necessary to define Set_errno(x) suitably, e.g., in

 *  a local errno.h, such as

 *    #include <errno.h>

 *    #define Set_errno(x) _set_errno(x)

 * #define NO_HEX_FP to omit recognition of hexadecimal floating-point

 *  values by strtod.

 * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)

 *  to disable logic for "fast" testing of very long input strings

 *  to strtod.  This testing proceeds by initially truncating the

 *  input string, then if necessary comparing the whole string with

 *  a decimal expansion to decide close cases. This logic is only

 *  used for input more than STRTOD_DIGLIM digits long (default 40).

 */

#ifndef Long

#define Long int

#endif

#ifndef ULong

typedef unsigned Long ULong;

#endif

#include <assert.h>

#ifdef DEBUG

#include "stdio.h"

#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}

#define Debug(x) x

int dtoa_stats[7]; /* strtod_{64,96,bigcomp},dtoa_{exact,64,96,bigcomp} */

#else

#define Debug(x) /*nothing*/

#endif

#include "stdlib.h"

#include "string.h"

#ifdef USE_LOCALE

#include "locale.h"

#endif

#ifdef Honor_FLT_ROUNDS

#ifndef Trust_FLT_ROUNDS

#include <fenv.h>

#endif

#endif

#ifdef __cplusplus

extern "C" {

#endif

#ifdef MALLOC

extern void *MALLOC(size_t);

#else

#define MALLOC malloc

#endif

#ifdef REALLOC

extern void *REALLOC(void*,size_t);

#else

#define REALLOC realloc

#endif

#ifndef FREE

#define FREE free

#endif

#ifdef __cplusplus

  }

#endif

#ifndef Omit_Private_Memory

#ifndef PRIVATE_MEM

#define PRIVATE_MEM 2304

#endif

#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))

static thread_local double private_mem[PRIVATE_mem], *pmem_next = private_mem;

#endif

#undef IEEE_Arith

#undef Avoid_Underflow

#ifdef IEEE_MC68k

#define IEEE_Arith

#endif

#ifdef IEEE_8087

#define IEEE_Arith

#endif

#ifdef IEEE_Arith

#ifndef NO_INFNAN_CHECK

#undef INFNAN_CHECK

#define INFNAN_CHECK

#endif

#else

#undef INFNAN_CHECK

#define NO_STRTOD_BIGCOMP

#endif

#include "errno.h"

#ifdef NO_ERRNO /*{*/

#undef Set_errno

#define Set_errno(x)

#else

#ifndef Set_errno

#define Set_errno(x) errno = x

#endif

#endif /*}*/

#ifdef Bad_float_h

#ifdef IEEE_Arith

#define DBL_DIG 15

#define DBL_MAX_10_EXP 308

#define DBL_MAX_EXP 1024

#define FLT_RADIX 2

#endif /*IEEE_Arith*/

#ifdef IBM

#define DBL_DIG 16

#define DBL_MAX_10_EXP 75

#define DBL_MAX_EXP 63

#define FLT_RADIX 16

#define DBL_MAX 7.2370055773322621e+75

#endif

#ifdef VAX

#define DBL_DIG 16

#define DBL_MAX_10_EXP 38

#define DBL_MAX_EXP 127

#define FLT_RADIX 2

#define DBL_MAX 1.7014118346046923e+38

#endif

#ifndef LONG_MAX

#define LONG_MAX 2147483647

#endif

#else /* ifndef Bad_float_h */

#include "float.h"

#endif /* Bad_float_h */

#ifndef __MATH_H__

#include "math.h"

#endif

#ifdef __cplusplus

extern "C" {

#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1

Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.

#endif

#undef USE_BF96

#ifdef NO_LONG_LONG /*{{*/

#undef ULLong

#ifdef Just_16

#undef Pack_32

/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.

 * This makes some inner loops simpler and sometimes saves work

 * during multiplications, but it often seems to make things slightly

 * slower.  Hence the default is now to store 32 bits per Long.

 */

#endif

#else /*}{ long long available */

#ifndef Llong

#define Llong long long

#endif

#ifndef ULLong

#define ULLong unsigned Llong

#endif

#ifndef NO_BF96 /*{*/

#define USE_BF96

#ifdef SET_INEXACT

#define dtoa_divmax 27

#else

int dtoa_divmax = 2;  /* Permit experimenting: on some systems, 64-bit integer */

      /* division is slow enough that we may sometimes want to */

      /* avoid using it.   We assume (but do not check) that   */

      /* dtoa_divmax <= 27.*/

#endif

typedef struct BF96 {   /* Normalized 96-bit software floating point numbers */

  unsigned int b0,b1,b2;  /* b0 = most significant, binary point just to its left */

  int e;      /* number represented = b * 2^e, with .5 <= b < 1 */

  } BF96;

 static BF96 pten[667] = {

  { 0xeef453d6, 0x923bd65a, 0x113faa29, -1136 },

  { 0x9558b466, 0x1b6565f8, 0x4ac7ca59, -1132 },

  { 0xbaaee17f, 0xa23ebf76, 0x5d79bcf0, -1129 },

  { 0xe95a99df, 0x8ace6f53, 0xf4d82c2c, -1126 },

  { 0x91d8a02b, 0xb6c10594, 0x79071b9b, -1122 },

  { 0xb64ec836, 0xa47146f9, 0x9748e282, -1119 },

  { 0xe3e27a44, 0x4d8d98b7, 0xfd1b1b23, -1116 },

  { 0x8e6d8c6a, 0xb0787f72, 0xfe30f0f5, -1112 },

  { 0xb208ef85, 0x5c969f4f, 0xbdbd2d33, -1109 },

  { 0xde8b2b66, 0xb3bc4723, 0xad2c7880, -1106 },

  { 0x8b16fb20, 0x3055ac76, 0x4c3bcb50, -1102 },

  { 0xaddcb9e8, 0x3c6b1793, 0xdf4abe24, -1099 },

  { 0xd953e862, 0x4b85dd78, 0xd71d6dad, -1096 },

  { 0x87d4713d, 0x6f33aa6b, 0x8672648c, -1092 },

  { 0xa9c98d8c, 0xcb009506, 0x680efdaf, -1089 },

  { 0xd43bf0ef, 0xfdc0ba48, 0x0212bd1b, -1086 },

  { 0x84a57695, 0xfe98746d, 0x014bb630, -1082 },

  { 0xa5ced43b, 0x7e3e9188, 0x419ea3bd, -1079 },

  { 0xcf42894a, 0x5dce35ea, 0x52064cac, -1076 },

  { 0x818995ce, 0x7aa0e1b2, 0x7343efeb, -1072 },

  { 0xa1ebfb42, 0x19491a1f, 0x1014ebe6, -1069 },

  { 0xca66fa12, 0x9f9b60a6, 0xd41a26e0, -1066 },

  { 0xfd00b897, 0x478238d0, 0x8920b098, -1063 },

  { 0x9e20735e, 0x8cb16382, 0x55b46e5f, -1059 },

  { 0xc5a89036, 0x2fddbc62, 0xeb2189f7, -1056 },

  { 0xf712b443, 0xbbd52b7b, 0xa5e9ec75, -1053 },

  { 0x9a6bb0aa, 0x55653b2d, 0x47b233c9, -1049 },

  { 0xc1069cd4, 0xeabe89f8, 0x999ec0bb, -1046 },

  { 0xf148440a, 0x256e2c76, 0xc00670ea, -1043 },

  { 0x96cd2a86, 0x5764dbca, 0x38040692, -1039 },

  { 0xbc807527, 0xed3e12bc, 0xc6050837, -1036 },

  { 0xeba09271, 0xe88d976b, 0xf7864a44, -1033 },

  { 0x93445b87, 0x31587ea3, 0x7ab3ee6a, -1029 },

  { 0xb8157268, 0xfdae9e4c, 0x5960ea05, -1026 },

  { 0xe61acf03, 0x3d1a45df, 0x6fb92487, -1023 },

  { 0x8fd0c162, 0x06306bab, 0xa5d3b6d4, -1019 },

  { 0xb3c4f1ba, 0x87bc8696, 0x8f48a489, -1016 },

  { 0xe0b62e29, 0x29aba83c, 0x331acdab, -1013 },

  { 0x8c71dcd9, 0xba0b4925, 0x9ff0c08b, -1009 },

  { 0xaf8e5410, 0x288e1b6f, 0x07ecf0ae, -1006 },

  { 0xdb71e914, 0x32b1a24a, 0xc9e82cd9, -1003 },

  { 0x892731ac, 0x9faf056e, 0xbe311c08,  -999 },

  { 0xab70fe17, 0xc79ac6ca, 0x6dbd630a,  -996 },

  { 0xd64d3d9d, 0xb981787d, 0x092cbbcc,  -993 },

  { 0x85f04682, 0x93f0eb4e, 0x25bbf560,  -989 },

  { 0xa76c5823, 0x38ed2621, 0xaf2af2b8,  -986 },

  { 0xd1476e2c, 0x07286faa, 0x1af5af66,  -983 },

  { 0x82cca4db, 0x847945ca, 0x50d98d9f,  -979 },

  { 0xa37fce12, 0x6597973c, 0xe50ff107,  -976 },

  { 0xcc5fc196, 0xfefd7d0c, 0x1e53ed49,  -973 },

  { 0xff77b1fc, 0xbebcdc4f, 0x25e8e89c,  -970 },

  { 0x9faacf3d, 0xf73609b1, 0x77b19161,  -966 },

  { 0xc795830d, 0x75038c1d, 0xd59df5b9,  -963 },

  { 0xf97ae3d0, 0xd2446f25, 0x4b057328,  -960 },

  { 0x9becce62, 0x836ac577, 0x4ee367f9,  -956 },

  { 0xc2e801fb, 0x244576d5, 0x229c41f7,  -953 },

  { 0xf3a20279, 0xed56d48a, 0x6b435275,  -950 },

  { 0x9845418c, 0x345644d6, 0x830a1389,  -946 },

  { 0xbe5691ef, 0x416bd60c, 0x23cc986b,  -943 },

  { 0xedec366b, 0x11c6cb8f, 0x2cbfbe86,  -940 },

  { 0x94b3a202, 0xeb1c3f39, 0x7bf7d714,  -936 },

  { 0xb9e08a83, 0xa5e34f07, 0xdaf5ccd9,  -933 },

  { 0xe858ad24, 0x8f5c22c9, 0xd1b3400f,  -930 },

  { 0x91376c36, 0xd99995be, 0x23100809,  -926 },

  { 0xb5854744, 0x8ffffb2d, 0xabd40a0c,  -923 },

  { 0xe2e69915, 0xb3fff9f9, 0x16c90c8f,  -920 },

  { 0x8dd01fad, 0x907ffc3b, 0xae3da7d9,  -916 },

  { 0xb1442798, 0xf49ffb4a, 0x99cd11cf,  -913 },

  { 0xdd95317f, 0x31c7fa1d, 0x40405643,  -910 },

  { 0x8a7d3eef, 0x7f1cfc52, 0x482835ea,  -906 },

  { 0xad1c8eab, 0x5ee43b66, 0xda324365,  -903 },

  { 0xd863b256, 0x369d4a40, 0x90bed43e,  -900 },

  { 0x873e4f75, 0xe2224e68, 0x5a7744a6,  -896 },

  { 0xa90de353, 0x5aaae202, 0x711515d0,  -893 },

  { 0xd3515c28, 0x31559a83, 0x0d5a5b44,  -890 },

  { 0x8412d999, 0x1ed58091, 0xe858790a,  -886 },

  { 0xa5178fff, 0x668ae0b6, 0x626e974d,  -883 },

  { 0xce5d73ff, 0x402d98e3, 0xfb0a3d21,  -880 },

  { 0x80fa687f, 0x881c7f8e, 0x7ce66634,  -876 },

  { 0xa139029f, 0x6a239f72, 0x1c1fffc1,  -873 },

  { 0xc9874347, 0x44ac874e, 0xa327ffb2,  -870 },

  { 0xfbe91419, 0x15d7a922, 0x4bf1ff9f,  -867 },

  { 0x9d71ac8f, 0xada6c9b5, 0x6f773fc3,  -863 },

  { 0xc4ce17b3, 0x99107c22, 0xcb550fb4,  -860 },

  { 0xf6019da0, 0x7f549b2b, 0x7e2a53a1,  -857 },

  { 0x99c10284, 0x4f94e0fb, 0x2eda7444,  -853 },

  { 0xc0314325, 0x637a1939, 0xfa911155,  -850 },

  { 0xf03d93ee, 0xbc589f88, 0x793555ab,  -847 },

  { 0x96267c75, 0x35b763b5, 0x4bc1558b,  -843 },

  { 0xbbb01b92, 0x83253ca2, 0x9eb1aaed,  -840 },

  { 0xea9c2277, 0x23ee8bcb, 0x465e15a9,  -837 },

  { 0x92a1958a, 0x7675175f, 0x0bfacd89,  -833 },

  { 0xb749faed, 0x14125d36, 0xcef980ec,  -830 },

  { 0xe51c79a8, 0x5916f484, 0x82b7e127,  -827 },

  { 0x8f31cc09, 0x37ae58d2, 0xd1b2ecb8,  -823 },

  { 0xb2fe3f0b, 0x8599ef07, 0x861fa7e6,  -820 },

  { 0xdfbdcece, 0x67006ac9, 0x67a791e0,  -817 },

  { 0x8bd6a141, 0x006042bd, 0xe0c8bb2c,  -813 },

  { 0xaecc4991, 0x4078536d, 0x58fae9f7,  -810 },

  { 0xda7f5bf5, 0x90966848, 0xaf39a475,  -807 },

  { 0x888f9979, 0x7a5e012d, 0x6d8406c9,  -803 },

  { 0xaab37fd7, 0xd8f58178, 0xc8e5087b,  -800 },

  { 0xd5605fcd, 0xcf32e1d6, 0xfb1e4a9a,  -797 },

  { 0x855c3be0, 0xa17fcd26, 0x5cf2eea0,  -793 },

  { 0xa6b34ad8, 0xc9dfc06f, 0xf42faa48,  -790 },

  { 0xd0601d8e, 0xfc57b08b, 0xf13b94da,  -787 },

  { 0x823c1279, 0x5db6ce57, 0x76c53d08,  -783 },

  { 0xa2cb1717, 0xb52481ed, 0x54768c4b,  -780 },

  { 0xcb7ddcdd, 0xa26da268, 0xa9942f5d,  -777 },

  { 0xfe5d5415, 0x0b090b02, 0xd3f93b35,  -774 },

  { 0x9efa548d, 0x26e5a6e1, 0xc47bc501,  -770 },

  { 0xc6b8e9b0, 0x709f109a, 0x359ab641,  -767 },

  { 0xf867241c, 0x8cc6d4c0, 0xc30163d2,  -764 },

  { 0x9b407691, 0xd7fc44f8, 0x79e0de63,  -760 },

  { 0xc2109436, 0x4dfb5636, 0x985915fc,  -757 },

  { 0xf294b943, 0xe17a2bc4, 0x3e6f5b7b,  -754 },

  { 0x979cf3ca, 0x6cec5b5a, 0xa705992c,  -750 },

  { 0xbd8430bd, 0x08277231, 0x50c6ff78,  -747 },

  { 0xece53cec, 0x4a314ebd, 0xa4f8bf56,  -744 },

  { 0x940f4613, 0xae5ed136, 0x871b7795,  -740 },

  { 0xb9131798, 0x99f68584, 0x28e2557b,  -737 },

  { 0xe757dd7e, 0xc07426e5, 0x331aeada,  -734 },

  { 0x9096ea6f, 0x3848984f, 0x3ff0d2c8,  -730 },

  { 0xb4bca50b, 0x065abe63, 0x0fed077a,  -727 },

  { 0xe1ebce4d, 0xc7f16dfb, 0xd3e84959,  -724 },

  { 0x8d3360f0, 0x9cf6e4bd, 0x64712dd7,  -720 },

  { 0xb080392c, 0xc4349dec, 0xbd8d794d,  -717 },

  { 0xdca04777, 0xf541c567, 0xecf0d7a0,  -714 },

  { 0x89e42caa, 0xf9491b60, 0xf41686c4,  -710 },

  { 0xac5d37d5, 0xb79b6239, 0x311c2875,  -707 },

  { 0xd77485cb, 0x25823ac7, 0x7d633293,  -704 },

  { 0x86a8d39e, 0xf77164bc, 0xae5dff9c,  -700 },

  { 0xa8530886, 0xb54dbdeb, 0xd9f57f83,  -697 },

  { 0xd267caa8, 0x62a12d66, 0xd072df63,  -694 },

  { 0x8380dea9, 0x3da4bc60, 0x4247cb9e,  -690 },

  { 0xa4611653, 0x8d0deb78, 0x52d9be85,  -687 },

  { 0xcd795be8, 0x70516656, 0x67902e27,  -684 },

  { 0x806bd971, 0x4632dff6, 0x00ba1cd8,  -680 },

  { 0xa086cfcd, 0x97bf97f3, 0x80e8a40e,  -677 },

  { 0xc8a883c0, 0xfdaf7df0, 0x6122cd12,  -674 },

  { 0xfad2a4b1, 0x3d1b5d6c, 0x796b8057,  -671 },

  { 0x9cc3a6ee, 0xc6311a63, 0xcbe33036,  -667 },

  { 0xc3f490aa, 0x77bd60fc, 0xbedbfc44,  -664 },

  { 0xf4f1b4d5, 0x15acb93b, 0xee92fb55,  -661 },

  { 0x99171105, 0x2d8bf3c5, 0x751bdd15,  -657 },

  { 0xbf5cd546, 0x78eef0b6, 0xd262d45a,  -654 },

  { 0xef340a98, 0x172aace4, 0x86fb8971,  -651 },

  { 0x9580869f, 0x0e7aac0e, 0xd45d35e6,  -647 },

  { 0xbae0a846, 0xd2195712, 0x89748360,  -644 },

  { 0xe998d258, 0x869facd7, 0x2bd1a438,  -641 },

  { 0x91ff8377, 0x5423cc06, 0x7b6306a3,  -637 },

  { 0xb67f6455, 0x292cbf08, 0x1a3bc84c,  -634 },

  { 0xe41f3d6a, 0x7377eeca, 0x20caba5f,  -631 },

  { 0x8e938662, 0x882af53e, 0x547eb47b,  -627 },

  { 0xb23867fb, 0x2a35b28d, 0xe99e619a,  -624 },

  { 0xdec681f9, 0xf4c31f31, 0x6405fa00,  -621 },

  { 0x8b3c113c, 0x38f9f37e, 0xde83bc40,  -617 },

  { 0xae0b158b, 0x4738705e, 0x9624ab50,  -614 },

  { 0xd98ddaee, 0x19068c76, 0x3badd624,  -611 },

  { 0x87f8a8d4, 0xcfa417c9, 0xe54ca5d7,  -607 },

  { 0xa9f6d30a, 0x038d1dbc, 0x5e9fcf4c,  -604 },

  { 0xd47487cc, 0x8470652b, 0x7647c320,  -601 },

  { 0x84c8d4df, 0xd2c63f3b, 0x29ecd9f4,  -597 },

  { 0xa5fb0a17, 0xc777cf09, 0xf4681071,  -594 },

  { 0xcf79cc9d, 0xb955c2cc, 0x7182148d,  -591 },

  { 0x81ac1fe2, 0x93d599bf, 0xc6f14cd8,  -587 },

  { 0xa21727db, 0x38cb002f, 0xb8ada00e,  -584 },

  { 0xca9cf1d2, 0x06fdc03b, 0xa6d90811,  -581 },

  { 0xfd442e46, 0x88bd304a, 0x908f4a16,  -578 },

  { 0x9e4a9cec, 0x15763e2e, 0x9a598e4e,  -574 },

  { 0xc5dd4427, 0x1ad3cdba, 0x40eff1e1,  -571 },

  { 0xf7549530, 0xe188c128, 0xd12bee59,  -568 },

  { 0x9a94dd3e, 0x8cf578b9, 0x82bb74f8,  -564 },

  { 0xc13a148e, 0x3032d6e7, 0xe36a5236,  -561 },

  { 0xf18899b1, 0xbc3f8ca1, 0xdc44e6c3,  -558 },

  { 0x96f5600f, 0x15a7b7e5, 0x29ab103a,  -554 },

  { 0xbcb2b812, 0xdb11a5de, 0x7415d448,  -551 },

  { 0xebdf6617, 0x91d60f56, 0x111b495b,  -548 },

  { 0x936b9fce, 0xbb25c995, 0xcab10dd9,  -544 },

  { 0xb84687c2, 0x69ef3bfb, 0x3d5d514f,  -541 },

  { 0xe65829b3, 0x046b0afa, 0x0cb4a5a3,  -538 },

  { 0x8ff71a0f, 0xe2c2e6dc, 0x47f0e785,  -534 },

  { 0xb3f4e093, 0xdb73a093, 0x59ed2167,  -531 },

  { 0xe0f218b8, 0xd25088b8, 0x306869c1,  -528 },

  { 0x8c974f73, 0x83725573, 0x1e414218,  -524 },

  { 0xafbd2350, 0x644eeacf, 0xe5d1929e,  -521 },

  { 0xdbac6c24, 0x7d62a583, 0xdf45f746,  -518 },

  { 0x894bc396, 0xce5da772, 0x6b8bba8c,  -514 },

  { 0xab9eb47c, 0x81f5114f, 0x066ea92f,  -511 },

  { 0xd686619b, 0xa27255a2, 0xc80a537b,  -508 },

  { 0x8613fd01, 0x45877585, 0xbd06742c,  -504 },

  { 0xa798fc41, 0x96e952e7, 0x2c481138,  -501 },

  { 0xd17f3b51, 0xfca3a7a0, 0xf75a1586,  -498 },

  { 0x82ef8513, 0x3de648c4, 0x9a984d73,  -494 },

  { 0xa3ab6658, 0x0d5fdaf5, 0xc13e60d0,  -491 },

  { 0xcc963fee, 0x10b7d1b3, 0x318df905,  -488 },

  { 0xffbbcfe9, 0x94e5c61f, 0xfdf17746,  -485 },

  { 0x9fd561f1, 0xfd0f9bd3, 0xfeb6ea8b,  -481 },

  { 0xc7caba6e, 0x7c5382c8, 0xfe64a52e,  -478 },

  { 0xf9bd690a, 0x1b68637b, 0x3dfdce7a,  -475 },

  { 0x9c1661a6, 0x51213e2d, 0x06bea10c,  -471 },

  { 0xc31bfa0f, 0xe5698db8, 0x486e494f,  -468 },

  { 0xf3e2f893, 0xdec3f126, 0x5a89dba3,  -465 },

  { 0x986ddb5c, 0x6b3a76b7, 0xf8962946,  -461 },

  { 0xbe895233, 0x86091465, 0xf6bbb397,  -458 },

  { 0xee2ba6c0, 0x678b597f, 0x746aa07d,  -455 },

  { 0x94db4838, 0x40b717ef, 0xa8c2a44e,  -451 },

  { 0xba121a46, 0x50e4ddeb, 0x92f34d62,  -448 },

  { 0xe896a0d7, 0xe51e1566, 0x77b020ba,  -445 },

  { 0x915e2486, 0xef32cd60, 0x0ace1474,  -441 },

  { 0xb5b5ada8, 0xaaff80b8, 0x0d819992,  -438 },

  { 0xe3231912, 0xd5bf60e6, 0x10e1fff6,  -435 },

  { 0x8df5efab, 0xc5979c8f, 0xca8d3ffa,  -431 },

  { 0xb1736b96, 0xb6fd83b3, 0xbd308ff8,  -428 },

  { 0xddd0467c, 0x64bce4a0, 0xac7cb3f6,  -425 },

  { 0x8aa22c0d, 0xbef60ee4, 0x6bcdf07a,  -421 },

  { 0xad4ab711, 0x2eb3929d, 0x86c16c98,  -418 },

  { 0xd89d64d5, 0x7a607744, 0xe871c7bf,  -415 },

  { 0x87625f05, 0x6c7c4a8b, 0x11471cd7,  -411 },

  { 0xa93af6c6, 0xc79b5d2d, 0xd598e40d,  -408 },

  { 0xd389b478, 0x79823479, 0x4aff1d10,  -405 },

  { 0x843610cb, 0x4bf160cb, 0xcedf722a,  -401 },

  { 0xa54394fe, 0x1eedb8fe, 0xc2974eb4,  -398 },

  { 0xce947a3d, 0xa6a9273e, 0x733d2262,  -395 },

  { 0x811ccc66, 0x8829b887, 0x0806357d,  -391 },

  { 0xa163ff80, 0x2a3426a8, 0xca07c2dc,  -388 },

  { 0xc9bcff60, 0x34c13052, 0xfc89b393,  -385 },

  { 0xfc2c3f38, 0x41f17c67, 0xbbac2078,  -382 },

  { 0x9d9ba783, 0x2936edc0, 0xd54b944b,  -378 },

  { 0xc5029163, 0xf384a931, 0x0a9e795e,  -375 },

  { 0xf64335bc, 0xf065d37d, 0x4d4617b5,  -372 },

  { 0x99ea0196, 0x163fa42e, 0x504bced1,  -368 },

  { 0xc06481fb, 0x9bcf8d39, 0xe45ec286,  -365 },

  { 0xf07da27a, 0x82c37088, 0x5d767327,  -362 },

  { 0x964e858c, 0x91ba2655, 0x3a6a07f8,  -358 },

  { 0xbbe226ef, 0xb628afea, 0x890489f7,  -355 },

  { 0xeadab0ab, 0xa3b2dbe5, 0x2b45ac74,  -352 },

  { 0x92c8ae6b, 0x464fc96f, 0x3b0b8bc9,  -348 },

  { 0xb77ada06, 0x17e3bbcb, 0x09ce6ebb,  -345 },

  { 0xe5599087, 0x9ddcaabd, 0xcc420a6a,  -342 },

  { 0x8f57fa54, 0xc2a9eab6, 0x9fa94682,  -338 },

  { 0xb32df8e9, 0xf3546564, 0x47939822,  -335 },

  { 0xdff97724, 0x70297ebd, 0x59787e2b,  -332 },

  { 0x8bfbea76, 0xc619ef36, 0x57eb4edb,  -328 },

  { 0xaefae514, 0x77a06b03, 0xede62292,  -325 },

  { 0xdab99e59, 0x958885c4, 0xe95fab36,  -322 },

  { 0x88b402f7, 0xfd75539b, 0x11dbcb02,  -318 },

  { 0xaae103b5, 0xfcd2a881, 0xd652bdc2,  -315 },

  { 0xd59944a3, 0x7c0752a2, 0x4be76d33,  -312 },

  { 0x857fcae6, 0x2d8493a5, 0x6f70a440,  -308 },

  { 0xa6dfbd9f, 0xb8e5b88e, 0xcb4ccd50,  -305 },

  { 0xd097ad07, 0xa71f26b2, 0x7e2000a4,  -302 },

  { 0x825ecc24, 0xc873782f, 0x8ed40066,  -298 },

  { 0xa2f67f2d, 0xfa90563b, 0x72890080,  -295 },

  { 0xcbb41ef9, 0x79346bca, 0x4f2b40a0,  -292 },

  { 0xfea126b7, 0xd78186bc, 0xe2f610c8,  -289 },

  { 0x9f24b832, 0xe6b0f436, 0x0dd9ca7d,  -285 },

  { 0xc6ede63f, 0xa05d3143, 0x91503d1c,  -282 },

  { 0xf8a95fcf, 0x88747d94, 0x75a44c63,  -279 },

  { 0x9b69dbe1, 0xb548ce7c, 0xc986afbe,  -275 },

  { 0xc24452da, 0x229b021b, 0xfbe85bad,  -272 },

  { 0xf2d56790, 0xab41c2a2, 0xfae27299,  -269 },

  { 0x97c560ba, 0x6b0919a5, 0xdccd879f,  -265 },

  { 0xbdb6b8e9, 0x05cb600f, 0x5400e987,  -262 },

  { 0xed246723, 0x473e3813, 0x290123e9,  -259 },

  { 0x9436c076, 0x0c86e30b, 0xf9a0b672,  -255 },

  { 0xb9447093, 0x8fa89bce, 0xf808e40e,  -252 },

  { 0xe7958cb8, 0x7392c2c2, 0xb60b1d12,  -249 },

  { 0x90bd77f3, 0x483bb9b9, 0xb1c6f22b,  -245 },

  { 0xb4ecd5f0, 0x1a4aa828, 0x1e38aeb6,  -242 },

  { 0xe2280b6c, 0x20dd5232, 0x25c6da63,  -239 },

  { 0x8d590723, 0x948a535f, 0x579c487e,  -235 },

  { 0xb0af48ec, 0x79ace837, 0x2d835a9d,  -232 },

  { 0xdcdb1b27, 0x98182244, 0xf8e43145,  -229 },

  { 0x8a08f0f8, 0xbf0f156b, 0x1b8e9ecb,  -225 },

  { 0xac8b2d36, 0xeed2dac5, 0xe272467e,  -222 },

  { 0xd7adf884, 0xaa879177, 0x5b0ed81d,  -219 },

  { 0x86ccbb52, 0xea94baea, 0x98e94712,  -215 },

  { 0xa87fea27, 0xa539e9a5, 0x3f2398d7,  -212 },

  { 0xd29fe4b1, 0x8e88640e, 0x8eec7f0d,  -209 },

  { 0x83a3eeee, 0xf9153e89, 0x1953cf68,  -205 },

  { 0xa48ceaaa, 0xb75a8e2b, 0x5fa8c342,  -202 },

  { 0xcdb02555, 0x653131b6, 0x3792f412,  -199 },

  { 0x808e1755, 0x5f3ebf11, 0xe2bbd88b,  -195 },

  { 0xa0b19d2a, 0xb70e6ed6, 0x5b6aceae,  -192 },

  { 0xc8de0475, 0x64d20a8b, 0xf245825a,  -189 },

  { 0xfb158592, 0xbe068d2e, 0xeed6e2f0,  -186 },

  { 0x9ced737b, 0xb6c4183d, 0x55464dd6,  -182 },

  { 0xc428d05a, 0xa4751e4c, 0xaa97e14c,  -179 },

  { 0xf5330471, 0x4d9265df, 0xd53dd99f,  -176 },

  { 0x993fe2c6, 0xd07b7fab, 0xe546a803,  -172 },

  { 0xbf8fdb78, 0x849a5f96, 0xde985204,  -169 },

  { 0xef73d256, 0xa5c0f77c, 0x963e6685,  -166 },

  { 0x95a86376, 0x27989aad, 0xdde70013,  -162 },

  { 0xbb127c53, 0xb17ec159, 0x5560c018,  -159 },

  { 0xe9d71b68, 0x9dde71af, 0xaab8f01e,  -156 },

  { 0x92267121, 0x62ab070d, 0xcab39613,  -152 },

  { 0xb6b00d69, 0xbb55c8d1, 0x3d607b97,  -149 },

  { 0xe45c10c4, 0x2a2b3b05, 0x8cb89a7d,  -146 },

  { 0x8eb98a7a, 0x9a5b04e3, 0x77f3608e,  -142 },

  { 0xb267ed19, 0x40f1c61c, 0x55f038b2,  -139 },

  { 0xdf01e85f, 0x912e37a3, 0x6b6c46de,  -136 },

  { 0x8b61313b, 0xbabce2c6, 0x2323ac4b,  -132 },

  { 0xae397d8a, 0xa96c1b77, 0xabec975e,  -129 },

  { 0xd9c7dced, 0x53c72255, 0x96e7bd35,  -126 },

  { 0x881cea14, 0x545c7575, 0x7e50d641,  -122 },

  { 0xaa242499, 0x697392d2, 0xdde50bd1,  -119 },

  { 0xd4ad2dbf, 0xc3d07787, 0x955e4ec6,  -116 },

  { 0x84ec3c97, 0xda624ab4, 0xbd5af13b,  -112 },

  { 0xa6274bbd, 0xd0fadd61, 0xecb1ad8a,  -109 },

  { 0xcfb11ead, 0x453994ba, 0x67de18ed,  -106 },

  { 0x81ceb32c, 0x4b43fcf4, 0x80eacf94,  -102 },

  { 0xa2425ff7, 0x5e14fc31, 0xa1258379,   -99 },

  { 0xcad2f7f5, 0x359a3b3e, 0x096ee458,   -96 },

  { 0xfd87b5f2, 0x8300ca0d, 0x8bca9d6e,   -93 },

  { 0x9e74d1b7, 0x91e07e48, 0x775ea264,   -89 },

  { 0xc6120625, 0x76589dda, 0x95364afe,   -86 },

  { 0xf79687ae, 0xd3eec551, 0x3a83ddbd,   -83 },

  { 0x9abe14cd, 0x44753b52, 0xc4926a96,   -79 },

  { 0xc16d9a00, 0x95928a27, 0x75b7053c,   -76 },

  { 0xf1c90080, 0xbaf72cb1, 0x5324c68b,   -73 },

  { 0x971da050, 0x74da7bee, 0xd3f6fc16,   -69 },

  { 0xbce50864, 0x92111aea, 0x88f4bb1c,   -66 },

  { 0xec1e4a7d, 0xb69561a5, 0x2b31e9e3,   -63 },

  { 0x9392ee8e, 0x921d5d07, 0x3aff322e,   -59 },

  { 0xb877aa32, 0x36a4b449, 0x09befeb9,   -56 },

  { 0xe69594be, 0xc44de15b, 0x4c2ebe68,   -53 },

  { 0x901d7cf7, 0x3ab0acd9, 0x0f9d3701,   -49 },

  { 0xb424dc35, 0x095cd80f, 0x538484c1,   -46 },

  { 0xe12e1342, 0x4bb40e13, 0x2865a5f2,   -43 },

  { 0x8cbccc09, 0x6f5088cb, 0xf93f87b7,   -39 },

  { 0xafebff0b, 0xcb24aafe, 0xf78f69a5,   -36 },

  { 0xdbe6fece, 0xbdedd5be, 0xb573440e,   -33 },

  { 0x89705f41, 0x36b4a597, 0x31680a88,   -29 },

  { 0xabcc7711, 0x8461cefc, 0xfdc20d2b,   -26 },

  { 0xd6bf94d5, 0xe57a42bc, 0x3d329076,   -23 },

  { 0x8637bd05, 0xaf6c69b5, 0xa63f9a49,   -19 },

  { 0xa7c5ac47, 0x1b478423, 0x0fcf80dc,   -16 },

  { 0xd1b71758, 0xe219652b, 0xd3c36113,   -13 },

  { 0x83126e97, 0x8d4fdf3b, 0x645a1cac,    -9 },

  { 0xa3d70a3d, 0x70a3d70a, 0x3d70a3d7,    -6 },

  { 0xcccccccc, 0xcccccccc, 0xcccccccc,    -3 },

  { 0x80000000, 0x00000000, 0x00000000,    1 },

  { 0xa0000000, 0x00000000, 0x00000000,    4 },

  { 0xc8000000, 0x00000000, 0x00000000,    7 },

  { 0xfa000000, 0x00000000, 0x00000000,   10 },

  { 0x9c400000, 0x00000000, 0x00000000,   14 },

  { 0xc3500000, 0x00000000, 0x00000000,   17 },

  { 0xf4240000, 0x00000000, 0x00000000,   20 },

  { 0x98968000, 0x00000000, 0x00000000,   24 },

  { 0xbebc2000, 0x00000000, 0x00000000,   27 },

  { 0xee6b2800, 0x00000000, 0x00000000,   30 },

  { 0x9502f900, 0x00000000, 0x00000000,   34 },

  { 0xba43b740, 0x00000000, 0x00000000,   37 },

  { 0xe8d4a510, 0x00000000, 0x00000000,   40 },

  { 0x9184e72a, 0x00000000, 0x00000000,   44 },

  { 0xb5e620f4, 0x80000000, 0x00000000,   47 },

  { 0xe35fa931, 0xa0000000, 0x00000000,   50 },

  { 0x8e1bc9bf, 0x04000000, 0x00000000,   54 },

  { 0xb1a2bc2e, 0xc5000000, 0x00000000,   57 },

  { 0xde0b6b3a, 0x76400000, 0x00000000,   60 },

  { 0x8ac72304, 0x89e80000, 0x00000000,   64 },

  { 0xad78ebc5, 0xac620000, 0x00000000,   67 },

  { 0xd8d726b7, 0x177a8000, 0x00000000,   70 },

  { 0x87867832, 0x6eac9000, 0x00000000,   74 },

  { 0xa968163f, 0x0a57b400, 0x00000000,   77 },

  { 0xd3c21bce, 0xcceda100, 0x00000000,   80 },

  { 0x84595161, 0x401484a0, 0x00000000,   84 },

  { 0xa56fa5b9, 0x9019a5c8, 0x00000000,   87 },

  { 0xcecb8f27, 0xf4200f3a, 0x00000000,   90 },

  { 0x813f3978, 0xf8940984, 0x40000000,   94 },

  { 0xa18f07d7, 0x36b90be5, 0x50000000,   97 },

  { 0xc9f2c9cd, 0x04674ede, 0xa4000000,  100 },

  { 0xfc6f7c40, 0x45812296, 0x4d000000,  103 },

  { 0x9dc5ada8, 0x2b70b59d, 0xf0200000,  107 },

  { 0xc5371912, 0x364ce305, 0x6c280000,  110 },

  { 0xf684df56, 0xc3e01bc6, 0xc7320000,  113 },

  { 0x9a130b96, 0x3a6c115c, 0x3c7f4000,  117 },

  { 0xc097ce7b, 0xc90715b3, 0x4b9f1000,  120 },

  { 0xf0bdc21a, 0xbb48db20, 0x1e86d400,  123 },

  { 0x96769950, 0xb50d88f4, 0x13144480,  127 },

  { 0xbc143fa4, 0xe250eb31, 0x17d955a0,  130 },

  { 0xeb194f8e, 0x1ae525fd, 0x5dcfab08,  133 },

  { 0x92efd1b8, 0xd0cf37be, 0x5aa1cae5,  137 },

  { 0xb7abc627, 0x050305ad, 0xf14a3d9e,  140 },

  { 0xe596b7b0, 0xc643c719, 0x6d9ccd05,  143 },

  { 0x8f7e32ce, 0x7bea5c6f, 0xe4820023,  147 },

  { 0xb35dbf82, 0x1ae4f38b, 0xdda2802c,  150 },

  { 0xe0352f62, 0xa19e306e, 0xd50b2037,  153 },

  { 0x8c213d9d, 0xa502de45, 0x4526f422,  157 },

  { 0xaf298d05, 0x0e4395d6, 0x9670b12b,  160 },

  { 0xdaf3f046, 0x51d47b4c, 0x3c0cdd76,  163 },

  { 0x88d8762b, 0xf324cd0f, 0xa5880a69,  167 },

  { 0xab0e93b6, 0xefee0053, 0x8eea0d04,  170 },

  { 0xd5d238a4, 0xabe98068, 0x72a49045,  173 },

  { 0x85a36366, 0xeb71f041, 0x47a6da2b,  177 },

  { 0xa70c3c40, 0xa64e6c51, 0x999090b6,  180 },

  { 0xd0cf4b50, 0xcfe20765, 0xfff4b4e3,  183 },

  { 0x82818f12, 0x81ed449f, 0xbff8f10e,  187 },

  { 0xa321f2d7, 0x226895c7, 0xaff72d52,  190 },

  { 0xcbea6f8c, 0xeb02bb39, 0x9bf4f8a6,  193 },

  { 0xfee50b70, 0x25c36a08, 0x02f236d0,  196 },

  { 0x9f4f2726, 0x179a2245, 0x01d76242,  200 },

  { 0xc722f0ef, 0x9d80aad6, 0x424d3ad2,  203 },

  { 0xf8ebad2b, 0x84e0d58b, 0xd2e08987,  206 },

  { 0x9b934c3b, 0x330c8577, 0x63cc55f4,  210 },

  { 0xc2781f49, 0xffcfa6d5, 0x3cbf6b71,  213 },

  { 0xf316271c, 0x7fc3908a, 0x8bef464e,  216 },

  { 0x97edd871, 0xcfda3a56, 0x97758bf0,  220 },

  { 0xbde94e8e, 0x43d0c8ec, 0x3d52eeed,  223 },

  { 0xed63a231, 0xd4c4fb27, 0x4ca7aaa8,  226 },

  { 0x945e455f, 0x24fb1cf8, 0x8fe8caa9,  230 },

  { 0xb975d6b6, 0xee39e436, 0xb3e2fd53,  233 },

  { 0xe7d34c64, 0xa9c85d44, 0x60dbbca8,  236 },

  { 0x90e40fbe, 0xea1d3a4a, 0xbc8955e9,  240 },

  { 0xb51d13ae, 0xa4a488dd, 0x6babab63,  243 },

  { 0xe264589a, 0x4dcdab14, 0xc696963c,  246 },

  { 0x8d7eb760, 0x70a08aec, 0xfc1e1de5,  250 },

  { 0xb0de6538, 0x8cc8ada8, 0x3b25a55f,  253 },

  { 0xdd15fe86, 0xaffad912, 0x49ef0eb7,  256 },

  { 0x8a2dbf14, 0x2dfcc7ab, 0x6e356932,  260 },

  { 0xacb92ed9, 0x397bf996, 0x49c2c37f,  263 },

  { 0xd7e77a8f, 0x87daf7fb, 0xdc33745e,  266 },

  { 0x86f0ac99, 0xb4e8dafd, 0x69a028bb,  270 },

  { 0xa8acd7c0, 0x222311bc, 0xc40832ea,  273 },

  { 0xd2d80db0, 0x2aabd62b, 0xf50a3fa4,  276 },

  { 0x83c7088e, 0x1aab65db, 0x792667c6,  280 },

  { 0xa4b8cab1, 0xa1563f52, 0x577001b8,  283 },

  { 0xcde6fd5e, 0x09abcf26, 0xed4c0226,  286 },

  { 0x80b05e5a, 0xc60b6178, 0x544f8158,  290 },

  { 0xa0dc75f1, 0x778e39d6, 0x696361ae,  293 },

  { 0xc913936d, 0xd571c84c, 0x03bc3a19,  296 },

  { 0xfb587849, 0x4ace3a5f, 0x04ab48a0,  299 },

  { 0x9d174b2d, 0xcec0e47b, 0x62eb0d64,  303 },

  { 0xc45d1df9, 0x42711d9a, 0x3ba5d0bd,  306 },

  { 0xf5746577, 0x930d6500, 0xca8f44ec,  309 },

  { 0x9968bf6a, 0xbbe85f20, 0x7e998b13,  313 },

  { 0xbfc2ef45, 0x6ae276e8, 0x9e3fedd8,  316 },

  { 0xefb3ab16, 0xc59b14a2, 0xc5cfe94e,  319 },

  { 0x95d04aee, 0x3b80ece5, 0xbba1f1d1,  323 },

  { 0xbb445da9, 0xca61281f, 0x2a8a6e45,  326 },

  { 0xea157514, 0x3cf97226, 0xf52d09d7,  329 },

  { 0x924d692c, 0xa61be758, 0x593c2626,  333 },

  { 0xb6e0c377, 0xcfa2e12e, 0x6f8b2fb0,  336 },

  { 0xe498f455, 0xc38b997a, 0x0b6dfb9c,  339 },

  { 0x8edf98b5, 0x9a373fec, 0x4724bd41,  343 },

  { 0xb2977ee3, 0x00c50fe7, 0x58edec91,  346 },

  { 0xdf3d5e9b, 0xc0f653e1, 0x2f2967b6,  349 },

  { 0x8b865b21, 0x5899f46c, 0xbd79e0d2,  353 },

  { 0xae67f1e9, 0xaec07187, 0xecd85906,  356 },

  { 0xda01ee64, 0x1a708de9, 0xe80e6f48,  359 },

  { 0x884134fe, 0x908658b2, 0x3109058d,  363 },

  { 0xaa51823e, 0x34a7eede, 0xbd4b46f0,  366 },

  { 0xd4e5e2cd, 0xc1d1ea96, 0x6c9e18ac,  369 },

  { 0x850fadc0, 0x9923329e, 0x03e2cf6b,  373 },

  { 0xa6539930, 0xbf6bff45, 0x84db8346,  376 },

  { 0xcfe87f7c, 0xef46ff16, 0xe6126418,  379 },

  { 0x81f14fae, 0x158c5f6e, 0x4fcb7e8f,  383 },

  { 0xa26da399, 0x9aef7749, 0xe3be5e33,  386 },

  { 0xcb090c80, 0x01ab551c, 0x5cadf5bf,  389 },

  { 0xfdcb4fa0, 0x02162a63, 0x73d9732f,  392 },

  { 0x9e9f11c4, 0x014dda7e, 0x2867e7fd,  396 },

  { 0xc646d635, 0x01a1511d, 0xb281e1fd,  399 },

  { 0xf7d88bc2, 0x4209a565, 0x1f225a7c,  402 },

  { 0x9ae75759, 0x6946075f, 0x3375788d,  406 },

  { 0xc1a12d2f, 0xc3978937, 0x0052d6b1,  409 },

  { 0xf209787b, 0xb47d6b84, 0xc0678c5d,  412 },

  { 0x9745eb4d, 0x50ce6332, 0xf840b7ba,  416 },

  { 0xbd176620, 0xa501fbff, 0xb650e5a9,  419 },

  { 0xec5d3fa8, 0xce427aff, 0xa3e51f13,  422 },

  { 0x93ba47c9, 0x80e98cdf, 0xc66f336c,  426 },

  { 0xb8a8d9bb, 0xe123f017, 0xb80b0047,  429 },

  { 0xe6d3102a, 0xd96cec1d, 0xa60dc059,  432 },

  { 0x9043ea1a, 0xc7e41392, 0x87c89837,  436 },

  { 0xb454e4a1, 0x79dd1877, 0x29babe45,  439 },

  { 0xe16a1dc9, 0xd8545e94, 0xf4296dd6,  442 },

  { 0x8ce2529e, 0x2734bb1d, 0x1899e4a6,  446 },

  { 0xb01ae745, 0xb101e9e4, 0x5ec05dcf,  449 },

  { 0xdc21a117, 0x1d42645d, 0x76707543,  452 },

  { 0x899504ae, 0x72497eba, 0x6a06494a,  456 },

  { 0xabfa45da, 0x0edbde69, 0x0487db9d,  459 },

  { 0xd6f8d750, 0x9292d603, 0x45a9d284,  462 },

  { 0x865b8692, 0x5b9bc5c2, 0x0b8a2392,  466 },

  { 0xa7f26836, 0xf282b732, 0x8e6cac77,  469 },

  { 0xd1ef0244, 0xaf2364ff, 0x3207d795,  472 },

  { 0x8335616a, 0xed761f1f, 0x7f44e6bd,  476 },

  { 0xa402b9c5, 0xa8d3a6e7, 0x5f16206c,  479 },

  { 0xcd036837, 0x130890a1, 0x36dba887,  482 },

  { 0x80222122, 0x6be55a64, 0xc2494954,  486 },

  { 0xa02aa96b, 0x06deb0fd, 0xf2db9baa,  489 },

  { 0xc83553c5, 0xc8965d3d, 0x6f928294,  492 },

  { 0xfa42a8b7, 0x3abbf48c, 0xcb772339,  495 },

  { 0x9c69a972, 0x84b578d7, 0xff2a7604,  499 },

  { 0xc38413cf, 0x25e2d70d, 0xfef51385,  502 },

  { 0xf46518c2, 0xef5b8cd1, 0x7eb25866,  505 },

  { 0x98bf2f79, 0xd5993802, 0xef2f773f,  509 },

  { 0xbeeefb58, 0x4aff8603, 0xaafb550f,  512 },

  { 0xeeaaba2e, 0x5dbf6784, 0x95ba2a53,  515 },

  { 0x952ab45c, 0xfa97a0b2, 0xdd945a74,  519 },

  { 0xba756174, 0x393d88df, 0x94f97111,  522 },

  { 0xe912b9d1, 0x478ceb17, 0x7a37cd56,  525 },

  { 0x91abb422, 0xccb812ee, 0xac62e055,  529 },

  { 0xb616a12b, 0x7fe617aa, 0x577b986b,  532 },

  { 0xe39c4976, 0x5fdf9d94, 0xed5a7e85,  535 },

  { 0x8e41ade9, 0xfbebc27d, 0x14588f13,  539 },

  { 0xb1d21964, 0x7ae6b31c, 0x596eb2d8,  542 },

  { 0xde469fbd, 0x99a05fe3, 0x6fca5f8e,  545 },

  { 0x8aec23d6, 0x80043bee, 0x25de7bb9,  549 },

  { 0xada72ccc, 0x20054ae9, 0xaf561aa7,  552 },

  { 0xd910f7ff, 0x28069da4, 0x1b2ba151,  555 },

  { 0x87aa9aff, 0x79042286, 0x90fb44d2,  559 },

  { 0xa99541bf, 0x57452b28, 0x353a1607,  562 },

  { 0xd3fa922f, 0x2d1675f2, 0x42889b89,  565 },

  { 0x847c9b5d, 0x7c2e09b7, 0x69956135,  569 },

  { 0xa59bc234, 0xdb398c25, 0x43fab983,  572 },

  { 0xcf02b2c2, 0x1207ef2e, 0x94f967e4,  575 },

  { 0x8161afb9, 0x4b44f57d, 0x1d1be0ee,  579 },

  { 0xa1ba1ba7, 0x9e1632dc, 0x6462d92a,  582 },

  { 0xca28a291, 0x859bbf93, 0x7d7b8f75,  585 },

  { 0xfcb2cb35, 0xe702af78, 0x5cda7352,  588 },

  { 0x9defbf01, 0xb061adab, 0x3a088813,  592 },

  { 0xc56baec2, 0x1c7a1916, 0x088aaa18,  595 },

  { 0xf6c69a72, 0xa3989f5b, 0x8aad549e,  598 },

  { 0x9a3c2087, 0xa63f6399, 0x36ac54e2,  602 },

  { 0xc0cb28a9, 0x8fcf3c7f, 0x84576a1b,  605 },

  { 0xf0fdf2d3, 0xf3c30b9f, 0x656d44a2,  608 },

  { 0x969eb7c4, 0x7859e743, 0x9f644ae5,  612 },

  { 0xbc4665b5, 0x96706114, 0x873d5d9f,  615 },

  { 0xeb57ff22, 0xfc0c7959, 0xa90cb506,  618 },

  { 0x9316ff75, 0xdd87cbd8, 0x09a7f124,  622 },

  { 0xb7dcbf53, 0x54e9bece, 0x0c11ed6d,  625 },

  { 0xe5d3ef28, 0x2a242e81, 0x8f1668c8,  628 },

  { 0x8fa47579, 0x1a569d10, 0xf96e017d,  632 },

  { 0xb38d92d7, 0x60ec4455, 0x37c981dc,  635 },

  { 0xe070f78d, 0x3927556a, 0x85bbe253,  638 },

  { 0x8c469ab8, 0x43b89562, 0x93956d74,  642 },

  { 0xaf584166, 0x54a6babb, 0x387ac8d1,  645 },

  { 0xdb2e51bf, 0xe9d0696a, 0x06997b05,  648 },

  { 0x88fcf317, 0xf22241e2, 0x441fece3,  652 },

  { 0xab3c2fdd, 0xeeaad25a, 0xd527e81c,  655 },

  { 0xd60b3bd5, 0x6a5586f1, 0x8a71e223,  658 },

  { 0x85c70565, 0x62757456, 0xf6872d56,  662 },

  { 0xa738c6be, 0xbb12d16c, 0xb428f8ac,  665 },

  { 0xd106f86e, 0x69d785c7, 0xe13336d7,  668 },

  { 0x82a45b45, 0x0226b39c, 0xecc00246,  672 },

  { 0xa34d7216, 0x42b06084, 0x27f002d7,  675 },

  { 0xcc20ce9b, 0xd35c78a5, 0x31ec038d,  678 },

  { 0xff290242, 0xc83396ce, 0x7e670471,  681 },

  { 0x9f79a169, 0xbd203e41, 0x0f0062c6,  685 },

  { 0xc75809c4, 0x2c684dd1, 0x52c07b78,  688 },

  { 0xf92e0c35, 0x37826145, 0xa7709a56,  691 },

  { 0x9bbcc7a1, 0x42b17ccb, 0x88a66076,  695 },

  { 0xc2abf989, 0x935ddbfe, 0x6acff893,  698 },

  { 0xf356f7eb, 0xf83552fe, 0x0583f6b8,  701 },

  { 0x98165af3, 0x7b2153de, 0xc3727a33,  705 },

  { 0xbe1bf1b0, 0x59e9a8d6, 0x744f18c0,  708 },

  { 0xeda2ee1c, 0x7064130c, 0x1162def0,  711 },

  { 0x9485d4d1, 0xc63e8be7, 0x8addcb56,  715 },

  { 0xb9a74a06, 0x37ce2ee1, 0x6d953e2b,  718 },

  { 0xe8111c87, 0xc5c1ba99, 0xc8fa8db6,  721 },

  { 0x910ab1d4, 0xdb9914a0, 0x1d9c9892,  725 },

  { 0xb54d5e4a, 0x127f59c8, 0x2503beb6,  728 },

  { 0xe2a0b5dc, 0x971f303a, 0x2e44ae64,  731 },

  { 0x8da471a9, 0xde737e24, 0x5ceaecfe,  735 },

  { 0xb10d8e14, 0x56105dad, 0x7425a83e,  738 },

  { 0xdd50f199, 0x6b947518, 0xd12f124e,  741 },

  { 0x8a5296ff, 0xe33cc92f, 0x82bd6b70,  745 },

  { 0xace73cbf, 0xdc0bfb7b, 0x636cc64d,  748 },

  { 0xd8210bef, 0xd30efa5a, 0x3c47f7e0,  751 },

  { 0x8714a775, 0xe3e95c78, 0x65acfaec,  755 },

  { 0xa8d9d153, 0x5ce3b396, 0x7f1839a7,  758 },

  { 0xd31045a8, 0x341ca07c, 0x1ede4811,  761 },

  { 0x83ea2b89, 0x2091e44d, 0x934aed0a,  765 },

  { 0xa4e4b66b, 0x68b65d60, 0xf81da84d,  768 },

  { 0xce1de406, 0x42e3f4b9, 0x36251260,  771 },

  { 0x80d2ae83, 0xe9ce78f3, 0xc1d72b7c,  775 },

  { 0xa1075a24, 0xe4421730, 0xb24cf65b,  778 },

  { 0xc94930ae, 0x1d529cfc, 0xdee033f2,  781 },

  { 0xfb9b7cd9, 0xa4a7443c, 0x169840ef,  784 },

  { 0x9d412e08, 0x06e88aa5, 0x8e1f2895,  788 },

  { 0xc491798a, 0x08a2ad4e, 0xf1a6f2ba,  791 },

  { 0xf5b5d7ec, 0x8acb58a2, 0xae10af69,  794 },

  { 0x9991a6f3, 0xd6bf1765, 0xacca6da1,  798 },

  { 0xbff610b0, 0xcc6edd3f, 0x17fd090a,  801 },

  { 0xeff394dc, 0xff8a948e, 0xddfc4b4c,  804 },

  { 0x95f83d0a, 0x1fb69cd9, 0x4abdaf10,  808 },

  { 0xbb764c4c, 0xa7a4440f, 0x9d6d1ad4,  811 },

  { 0xea53df5f, 0xd18d5513, 0x84c86189,  814 },

  { 0x92746b9b, 0xe2f8552c, 0x32fd3cf5,  818 },

  { 0xb7118682, 0xdbb66a77, 0x3fbc8c33,  821 },

  { 0xe4d5e823, 0x92a40515, 0x0fabaf3f,  824 },

  { 0x8f05b116, 0x3ba6832d, 0x29cb4d87,  828 },

  { 0xb2c71d5b, 0xca9023f8, 0x743e20e9,  831 },

  { 0xdf78e4b2, 0xbd342cf6, 0x914da924,  834 },

  { 0x8bab8eef, 0xb6409c1a, 0x1ad089b6,  838 },

  { 0xae9672ab, 0xa3d0c320, 0xa184ac24,  841 },

  { 0xda3c0f56, 0x8cc4f3e8, 0xc9e5d72d,  844 },

  { 0x88658996, 0x17fb1871, 0x7e2fa67c,  848 },

  { 0xaa7eebfb, 0x9df9de8d, 0xddbb901b,  851 },

  { 0xd51ea6fa, 0x85785631, 0x552a7422,  854 },

  { 0x8533285c, 0x936b35de, 0xd53a8895,  858 },

  { 0xa67ff273, 0xb8460356, 0x8a892aba,  861 },

  { 0xd01fef10, 0xa657842c, 0x2d2b7569,  864 },

  { 0x8213f56a, 0x67f6b29b, 0x9c3b2962,  868 },

  { 0xa298f2c5, 0x01f45f42, 0x8349f3ba,  871 },

  { 0xcb3f2f76, 0x42717713, 0x241c70a9,  874 },

  { 0xfe0efb53, 0xd30dd4d7, 0xed238cd3,  877 },

  { 0x9ec95d14, 0x63e8a506, 0xf4363804,  881 },

  { 0xc67bb459, 0x7ce2ce48, 0xb143c605,  884 },

  { 0xf81aa16f, 0xdc1b81da, 0xdd94b786,  887 },

  { 0x9b10a4e5, 0xe9913128, 0xca7cf2b4,  891 },

  { 0xc1d4ce1f, 0x63f57d72, 0xfd1c2f61,  894 },

  { 0xf24a01a7, 0x3cf2dccf, 0xbc633b39,  897 },

  { 0x976e4108, 0x8617ca01, 0xd5be0503,  901 },

  { 0xbd49d14a, 0xa79dbc82, 0x4b2d8644,  904 },

  { 0xec9c459d, 0x51852ba2, 0xddf8e7d6,  907 },

  { 0x93e1ab82, 0x52f33b45, 0xcabb90e5,  911 },

  { 0xb8da1662, 0xe7b00a17, 0x3d6a751f,  914 },

  { 0xe7109bfb, 0xa19c0c9d, 0x0cc51267,  917 },

  { 0x906a617d, 0x450187e2, 0x27fb2b80,  921 },

  { 0xb484f9dc, 0x9641e9da, 0xb1f9f660,  924 },

  { 0xe1a63853, 0xbbd26451, 0x5e7873f8,  927 },

  { 0x8d07e334, 0x55637eb2, 0xdb0b487b,  931 },

  { 0xb049dc01, 0x6abc5e5f, 0x91ce1a9a,  934 },

  { 0xdc5c5301, 0xc56b75f7, 0x7641a140,  937 },

  { 0x89b9b3e1, 0x1b6329ba, 0xa9e904c8,  941 },

  { 0xac2820d9, 0x623bf429, 0x546345fa,  944 },

  { 0xd732290f, 0xbacaf133, 0xa97c1779,  947 },

  { 0x867f59a9, 0xd4bed6c0, 0x49ed8eab,  951 },

  { 0xa81f3014, 0x49ee8c70, 0x5c68f256,  954 },

  { 0xd226fc19, 0x5c6a2f8c, 0x73832eec,  957 },

  { 0x83585d8f, 0xd9c25db7, 0xc831fd53,  961 },

  { 0xa42e74f3, 0xd032f525, 0xba3e7ca8,  964 },

  { 0xcd3a1230, 0xc43fb26f, 0x28ce1bd2,  967 },

  { 0x80444b5e, 0x7aa7cf85, 0x7980d163,  971 },

  { 0xa0555e36, 0x1951c366, 0xd7e105bc,  974 },

  { 0xc86ab5c3, 0x9fa63440, 0x8dd9472b,  977 },

  { 0xfa856334, 0x878fc150, 0xb14f98f6,  980 },

  { 0x9c935e00, 0xd4b9d8d2, 0x6ed1bf9a,  984 },

  { 0xc3b83581, 0x09e84f07, 0x0a862f80,  987 },

  { 0xf4a642e1, 0x4c6262c8, 0xcd27bb61,  990 },

  { 0x98e7e9cc, 0xcfbd7dbd, 0x8038d51c,  994 },

  { 0xbf21e440, 0x03acdd2c, 0xe0470a63,  997 },

  { 0xeeea5d50, 0x04981478, 0x1858ccfc, 1000 },

  { 0x95527a52, 0x02df0ccb, 0x0f37801e, 1004 },

  { 0xbaa718e6, 0x8396cffd, 0xd3056025, 1007 },

  { 0xe950df20, 0x247c83fd, 0x47c6b82e, 1010 },

  { 0x91d28b74, 0x16cdd27e, 0x4cdc331d, 1014 },

  { 0xb6472e51, 0x1c81471d, 0xe0133fe4, 1017 },

  { 0xe3d8f9e5, 0x63a198e5, 0x58180fdd, 1020 },

  { 0x8e679c2f, 0x5e44ff8f, 0x570f09ea, 1024 },

  { 0xb201833b, 0x35d63f73, 0x2cd2cc65, 1027 },

  { 0xde81e40a, 0x034bcf4f, 0xf8077f7e, 1030 },

  { 0x8b112e86, 0x420f6191, 0xfb04afaf, 1034 },

  { 0xadd57a27, 0xd29339f6, 0x79c5db9a, 1037 },

  { 0xd94ad8b1, 0xc7380874, 0x18375281, 1040 },

  { 0x87cec76f, 0x1c830548, 0x8f229391, 1044 },

  { 0xa9c2794a, 0xe3a3c69a, 0xb2eb3875, 1047 },

  { 0xd433179d, 0x9c8cb841, 0x5fa60692, 1050 },

  { 0x849feec2, 0x81d7f328, 0xdbc7c41b, 1054 },

  { 0xa5c7ea73, 0x224deff3, 0x12b9b522, 1057 },

  { 0xcf39e50f, 0xeae16bef, 0xd768226b, 1060 },

  { 0x81842f29, 0xf2cce375, 0xe6a11583, 1064 },

  { 0xa1e53af4, 0x6f801c53, 0x60495ae3, 1067 },

  { 0xca5e89b1, 0x8b602368, 0x385bb19c, 1070 },

  { 0xfcf62c1d, 0xee382c42, 0x46729e03, 1073 },

  { 0x9e19db92, 0xb4e31ba9, 0x6c07a2c2, 1077 }

  };

 static short int Lhint[2098] = {

     /*18,*/19,    19,    19,    19,    20,    20,    20,    21,    21,

     21,    22,    22,    22,    23,    23,    23,    23,    24,    24,

     24,    25,    25,    25,    26,    26,    26,    26,    27,    27,

     27,    28,    28,    28,    29,    29,    29,    29,    30,    30,

     30,    31,    31,    31,    32,    32,    32,    32,    33,    33,

     33,    34,    34,    34,    35,    35,    35,    35,    36,    36,

     36,    37,    37,    37,    38,    38,    38,    38,    39,    39,

     39,    40,    40,    40,    41,    41,    41,    41,    42,    42,

     42,    43,    43,    43,    44,    44,    44,    44,    45,    45,

     45,    46,    46,    46,    47,    47,    47,    47,    48,    48,

     48,    49,    49,    49,    50,    50,    50,    51,    51,    51,

     51,    52,    52,    52,    53,    53,    53,    54,    54,    54,

     54,    55,    55,    55,    56,    56,    56,    57,    57,    57,

     57,    58,    58,    58,    59,    59,    59,    60,    60,    60,

     60,    61,    61,    61,    62,    62,    62,    63,    63,    63,

     63,    64,    64,    64,    65,    65,    65,    66,    66,    66,

     66,    67,    67,    67,    68,    68,    68,    69,    69,    69,

     69,    70,    70,    70,    71,    71,    71,    72,    72,    72,

     72,    73,    73,    73,    74,    74,    74,    75,    75,    75,

     75,    76,    76,    76,    77,    77,    77,    78,    78,    78,

     78,    79,    79,    79,    80,    80,    80,    81,    81,    81,

     82,    82,    82,    82,    83,    83,    83,    84,    84,    84,

     85,    85,    85,    85,    86,    86,    86,    87,    87,    87,

     88,    88,    88,    88,    89,    89,    89,    90,    90,    90,

     91,    91,    91,    91,    92,    92,    92,    93,    93,    93,

     94,    94,    94,    94,    95,    95,    95,    96,    96,    96,

     97,    97,    97,    97,    98,    98,    98,    99,    99,    99,

    100,   100,   100,   100,   101,   101,   101,   102,   102,   102,

    103,   103,   103,   103,   104,   104,   104,   105,   105,   105,

    106,   106,   106,   106,   107,   107,   107,   108,   108,   108,

    109,   109,   109,   110,   110,   110,   110,   111,   111,   111,

    112,   112,   112,   113,   113,   113,   113,   114,   114,   114,

    115,   115,   115,   116,   116,   116,   116,   117,   117,   117,

    118,   118,   118,   119,   119,   119,   119,   120,   120,   120,

    121,   121,   121,   122,   122,   122,   122,   123,   123,   123,

    124,   124,   124,   125,   125,   125,   125,   126,   126,   126,

    127,   127,   127,   128,   128,   128,   128,   129,   129,   129,

    130,   130,   130,   131,   131,   131,   131,   132,   132,   132,

    133,   133,   133,   134,   134,   134,   134,   135,   135,   135,

    136,   136,   136,   137,   137,   137,   137,   138,   138,   138,

    139,   139,   139,   140,   140,   140,   141,   141,   141,   141,

    142,   142,   142,   143,   143,   143,   144,   144,   144,   144,

    145,   145,   145,   146,   146,   146,   147,   147,   147,   147,

    148,   148,   148,   149,   149,   149,   150,   150,   150,   150,

    151,   151,   151,   152,   152,   152,   153,   153,   153,   153,

    154,   154,   154,   155,   155,   155,   156,   156,   156,   156,

    157,   157,   157,   158,   158,   158,   159,   159,   159,   159,

    160,   160,   160,   161,   161,   161,   162,   162,   162,   162,

    163,   163,   163,   164,   164,   164,   165,   165,   165,   165,

    166,   166,   166,   167,   167,   167,   168,   168,   168,   169,

    169,   169,   169,   170,   170,   170,   171,   171,   171,   172,

    172,   172,   172,   173,   173,   173,   174,   174,   174,   175,

    175,   175,   175,   176,   176,   176,   177,   177,   177,   178,

    178,   178,   178,   179,   179,   179,   180,   180,   180,   181,

    181,   181,   181,   182,   182,   182,   183,   183,   183,   184,

    184,   184,   184,   185,   185,   185,   186,   186,   186,   187,

    187,   187,   187,   188,   188,   188,   189,   189,   189,   190,

    190,   190,   190,   191,   191,   191,   192,   192,   192,   193,

    193,   193,   193,   194,   194,   194,   195,   195,   195,   196,

    196,   196,   197,   197,   197,   197,   198,   198,   198,   199,

    199,   199,   200,   200,   200,   200,   201,   201,   201,   202,

    202,   202,   203,   203,   203,   203,   204,   204,   204,   205,

    205,   205,   206,   206,   206,   206,   207,   207,   207,   208,

    208,   208,   209,   209,   209,   209,   210,   210,   210,   211,

    211,   211,   212,   212,   212,   212,   213,   213,   213,   214,

    214,   214,   215,   215,   215,   215,   216,   216,   216,   217,

    217,   217,   218,   218,   218,   218,   219,   219,   219,   220,

    220,   220,   221,   221,   221,   221,   222,   222,   222,   223,

    223,   223,   224,   224,   224,   224,   225,   225,   225,   226,

    226,   226,   227,   227,   227,   228,   228,   228,   228,   229,

    229,   229,   230,   230,   230,   231,   231,   231,   231,   232,

    232,   232,   233,   233,   233,   234,   234,   234,   234,   235,

    235,   235,   236,   236,   236,   237,   237,   237,   237,   238,

    238,   238,   239,   239,   239,   240,   240,   240,   240,   241,

    241,   241,   242,   242,   242,   243,   243,   243,   243,   244,

    244,   244,   245,   245,   245,   246,   246,   246,   246,   247,

    247,   247,   248,   248,   248,   249,   249,   249,   249,   250,

    250,   250,   251,   251,   251,   252,   252,   252,   252,   253,

    253,   253,   254,   254,   254,   255,   255,   255,   256,   256,

    256,   256,   257,   257,   257,   258,   258,   258,   259,   259,

    259,   259,   260,   260,   260,   261,   261,   261,   262,   262,

    262,   262,   263,   263,   263,   264,   264,   264,   265,   265,

    265,   265,   266,   266,   266,   267,   267,   267,   268,   268,

    268,   268,   269,   269,   269,   270,   270,   270,   271,   271,

    271,   271,   272,   272,   272,   273,   273,   273,   274,   274,