Remove unused bigint from runtime

diff --git a/configure b/configure
index f2afa2d26ef8d7f13471e8d8c038597b5db941fb..1e1b725ff47e9ac23147e9fd33aef9c7c7fc1af5 100755 (executable)
--- a/configure
+++ b/configure
@@ -578,7 +578,7 @@ for t in $CFG_TARGET_TRIPLES
 do
   make_dir rt/$t
   for i in                                          \
-    isaac linenoise bigint sync test arch/i386 arch/x86_64    \
+    isaac linenoise sync test arch/i386 arch/x86_64    \
     libuv libuv/src/ares libuv/src/eio libuv/src/ev
   do
     make_dir rt/$t/$i

diff --git a/src/rt/bigint/bigint.h b/src/rt/bigint/bigint.h
deleted file mode 100644 (file)
index b4c48f0..0000000
--- a/src/rt/bigint/bigint.h
+++ /dev/null
@@ -1,294 +0,0 @@
-/* bigint.h - include file for bigint package
-**
-** This library lets you do math on arbitrarily large integers.  It's
-** pretty fast - compared with the multi-precision routines in the "bc"
-** calculator program, these routines are between two and twelve times faster,
-** except for division which is maybe half as fast.
-**
-** The calling convention is a little unusual.  There's a basic problem
-** with writing a math library in a language that doesn't do automatic
-** garbage collection - what do you do about intermediate results?
-** You'd like to be able to write code like this:
-**
-**     d = bi_sqrt( bi_add( bi_multiply( x, x ), bi_multiply( y, y ) ) );
-**
-** That works fine when the numbers being passed back and forth are
-** actual values - ints, floats, or even fixed-size structs.  However,
-** when the numbers can be any size, as in this package, then you have
-** to pass them around as pointers to dynamically-allocated objects.
-** Those objects have to get de-allocated after you are done with them.
-** But how do you de-allocate the intermediate results in a complicated
-** multiple-call expression like the above?
-**
-** There are two common solutions to this problem.  One, switch all your
-** code to a language that provides automatic garbage collection, for
-** example Java.  This is a fine idea and I recommend you do it wherever
-** it's feasible.  Two, change your routines to use a calling convention
-** that prevents people from writing multiple-call expressions like that.
-** The resulting code will be somewhat clumsy-looking, but it will work
-** just fine.
-**
-** This package uses a third method, which I haven't seen used anywhere
-** before.  It's simple: each number can be used precisely once, after
-** which it is automatically de-allocated.  This handles the anonymous
-** intermediate values perfectly.  Named values still need to be copied
-** and freed explicitly.  Here's the above example using this convention:
-**
-**     d = bi_sqrt( bi_add(
-**             bi_multiply( bi_copy( x ), bi_copy( x ) ),
-**             bi_multiply( bi_copy( y ), bi_copy( y ) ) ) );
-**     bi_free( x );
-**     bi_free( y );
-**
-** Or, since the package contains a square routine, you could just write:
-**
-**     d = bi_sqrt( bi_add( bi_square( x ), bi_square( y ) ) );
-**
-** This time the named values are only being used once, so you don't
-** have to copy and free them.
-**
-** This really works, however you do have to be very careful when writing
-** your code.  If you leave out a bi_copy() and use a value more than once,
-** you'll get a runtime error about "zero refs" and a SIGFPE.  Run your
-** code in a debugger, get a backtrace to see where the call was, and then
-** eyeball the code there to see where you need to add the bi_copy().
-**
-**
-** Copyright © 2000 by Jef Poskanzer <jef@mail.acme.com>.
-** All rights reserved.
-**
-** Redistribution and use in source and binary forms, with or without
-** modification, are permitted provided that the following conditions
-** are met:
-** 1. Redistributions of source code must retain the above copyright
-**    notice, this list of conditions and the following disclaimer.
-** 2. Redistributions in binary form must reproduce the above copyright
-**    notice, this list of conditions and the following disclaimer in the
-**    documentation and/or other materials provided with the distribution.
-**
-** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
-** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-** SUCH DAMAGE.
-*/
-
-
-/* Type definition for bigints - it's an opaque type, the real definition
-** is in bigint.c.
-*/
-typedef void* bigint;
-
-
-/* Some convenient pre-initialized numbers.  These are all permanent,
-** so you can use them as many times as you want without calling bi_copy().
-*/
-extern bigint bi_0, bi_1, bi_2, bi_10, bi_m1, bi_maxint, bi_minint;
-
-
-/* Initialize the bigint package.  You must call this when your program
-** starts up.
-*/
-void bi_initialize( void );
-
-/* Shut down the bigint package.  You should call this when your program
-** exits.  It's not actually required, but it does do some consistency
-** checks which help keep your program bug-free, so you really ought
-** to call it.
-*/
-void bi_terminate( void );
-
-/* Run in unsafe mode, skipping most runtime checks.  Slightly faster.
-** Once your code is debugged you can add this call after bi_initialize().
-*/
-void bi_no_check( void );
-
-/* Make a copy of a bigint.  You must call this if you want to use a
-** bigint more than once.  (Or you can make the bigint permanent.)
-** Note that this routine is very cheap - all it actually does is
-** increment a reference counter.
-*/
-bigint bi_copy( bigint bi );
-
-/* Make a bigint permanent, so it doesn't get automatically freed when
-** used as an operand.
-*/
-void bi_permanent( bigint bi );
-
-/* Undo bi_permanent().  The next use will free the bigint. */
-void bi_depermanent( bigint bi );
-
-/* Explicitly free a bigint.  Normally bigints get freed automatically
-** when they are used as an operand.  This routine lets you free one
-** without using it.  If the bigint is permanent, this doesn't do
-** anything, you have to depermanent it first.
-*/
-void bi_free( bigint bi );
-
-/* Compare two bigints.  Returns -1, 0, or 1. */
-int bi_compare( bigint bia, bigint bib );
-
-/* Convert an int to a bigint. */
-bigint int_to_bi( int i );
-
-/* Convert a string to a bigint. */
-bigint str_to_bi( char* str );
-
-/* Convert a bigint to an int.  SIGFPE on overflow. */
-int bi_to_int( bigint bi );
-
-/* Write a bigint to a file. */
-void bi_print( FILE* f, bigint bi );
-
-/* Read a bigint from a file. */
-bigint bi_scan( FILE* f );
-
-
-/* Operations on a bigint and a regular int. */
-
-/* Add an int to a bigint. */
-bigint bi_int_add( bigint bi, int i );
-
-/* Subtract an int from a bigint. */
-bigint bi_int_subtract( bigint bi, int i );
-
-/* Multiply a bigint by an int. */
-bigint bi_int_multiply( bigint bi, int i );
-
-/* Divide a bigint by an int.  SIGFPE on divide-by-zero. */
-bigint bi_int_divide( bigint binumer, int denom );
-
-/* Take the remainder of a bigint by an int, with an int result.
-** SIGFPE if m is zero.
-*/
-int bi_int_rem( bigint bi, int m );
-
-/* Take the modulus of a bigint by an int, with an int result.
-** Note that mod is not rem: mod is always within [0..m), while
-** rem can be negative.  SIGFPE if m is zero or negative.
-*/
-int bi_int_mod( bigint bi, int m );
-
-
-/* Basic operations on two bigints. */
-
-/* Add two bigints. */
-bigint bi_add( bigint bia, bigint bib );
-
-/* Subtract bib from bia. */
-bigint bi_subtract( bigint bia, bigint bib );
-
-/* Multiply two bigints. */
-bigint bi_multiply( bigint bia, bigint bib );
-
-/* Divide one bigint by another.  SIGFPE on divide-by-zero. */
-bigint bi_divide( bigint binumer, bigint bidenom );
-
-/* Binary division of one bigint by another.  SIGFPE on divide-by-zero.
-** This is here just for testing.  It's about five times slower than
-** regular division.
-*/
-bigint bi_binary_divide( bigint binumer, bigint bidenom );
-
-/* Take the remainder of one bigint by another.  SIGFPE if bim is zero. */
-bigint bi_rem( bigint bia, bigint bim );
-
-/* Take the modulus of one bigint by another.  Note that mod is not rem:
-** mod is always within [0..bim), while rem can be negative.  SIGFPE if
-** bim is zero or negative.
-*/
-bigint bi_mod( bigint bia, bigint bim );
-
-
-/* Some less common operations. */
-
-/* Negate a bigint. */
-bigint bi_negate( bigint bi );
-
-/* Absolute value of a bigint. */
-bigint bi_abs( bigint bi );
-
-/* Divide a bigint in half. */
-bigint bi_half( bigint bi );
-
-/* Multiply a bigint by two. */
-bigint bi_double( bigint bi );
-
-/* Square a bigint. */
-bigint bi_square( bigint bi );
-
-/* Raise bi to the power of biexp.  SIGFPE if biexp is negative. */
-bigint bi_power( bigint bi, bigint biexp );
-
-/* Integer square root. */
-bigint bi_sqrt( bigint bi );
-
-/* Factorial. */
-bigint bi_factorial( bigint bi );
-
-
-/* Some predicates. */
-
-/* 1 if the bigint is odd, 0 if it's even. */
-int bi_is_odd( bigint bi );
-
-/* 1 if the bigint is even, 0 if it's odd. */
-int bi_is_even( bigint bi );
-
-/* 1 if the bigint equals zero, 0 if it's nonzero. */
-int bi_is_zero( bigint bi );
-
-/* 1 if the bigint equals one, 0 otherwise. */
-int bi_is_one( bigint bi );
-
-/* 1 if the bigint is less than zero, 0 if it's zero or greater. */
-int bi_is_negative( bigint bi );
-
-
-/* Now we get into the esoteric number-theory stuff used for cryptography. */
-
-/* Modular exponentiation.  Much faster than bi_mod(bi_power(bi,biexp),bim).
-** Also, biexp can be negative.
-*/
-bigint bi_mod_power( bigint bi, bigint biexp, bigint bim );
-
-/* Modular inverse.  mod( bi * modinv(bi), bim ) == 1.  SIGFPE if bi is not
-** relatively prime to bim.
-*/
-bigint bi_mod_inverse( bigint bi, bigint bim );
-
-/* Produce a random number in the half-open interval [0..bi).  You need
-** to have called srandom() before using this.
-*/
-bigint bi_random( bigint bi );
-
-/* Greatest common divisor of two bigints.  Euclid's algorithm. */
-bigint bi_gcd( bigint bim, bigint bin );
-
-/* Greatest common divisor of two bigints, plus the corresponding multipliers.
-** Extended Euclid's algorithm.
-*/
-bigint bi_egcd( bigint bim, bigint bin, bigint* bim_mul, bigint* bin_mul );
-
-/* Least common multiple of two bigints. */
-bigint bi_lcm( bigint bia, bigint bib );
-
-/* The Jacobi symbol.  SIGFPE if bib is even. */
-bigint bi_jacobi( bigint bia, bigint bib );
-
-/* Probabalistic prime checking.  A non-zero return means the probability
-** that bi is prime is at least 1 - 1/2 ^ certainty.
-*/
-int bi_is_probable_prime( bigint bi, int certainty );
-
-/* Random probabilistic prime with the specified number of bits. */
-bigint bi_generate_prime( int bits, int certainty );
-
-/* Number of bits in the number.  The log base 2, approximately. */
-int bi_bits( bigint bi );

diff --git a/src/rt/bigint/bigint_ext.cpp b/src/rt/bigint/bigint_ext.cpp
deleted file mode 100644 (file)
index 66d7910..0000000
--- a/src/rt/bigint/bigint_ext.cpp
+++ /dev/null
@@ -1,553 +0,0 @@
-/* bigint_ext - external portion of large integer package
-**
-** Copyright © 2000 by Jef Poskanzer <jef@mail.acme.com>.
-** All rights reserved.
-**
-** Redistribution and use in source and binary forms, with or without
-** modification, are permitted provided that the following conditions
-** are met:
-** 1. Redistributions of source code must retain the above copyright
-**    notice, this list of conditions and the following disclaimer.
-** 2. Redistributions in binary form must reproduce the above copyright
-**    notice, this list of conditions and the following disclaimer in the
-**    documentation and/or other materials provided with the distribution.
-**
-** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
-** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-** SUCH DAMAGE.
-*/
-
-#include <sys/types.h>
-#include <signal.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <unistd.h>
-#include <time.h>
-
-#include "bigint.h"
-#include "low_primes.h"
-
-
-bigint bi_0, bi_1, bi_2, bi_10, bi_m1, bi_maxint, bi_minint;
-
-
-/* Forwards. */
-static void print_pos( FILE* f, bigint bi );
-
-
-bigint
-str_to_bi( char* str )
-    {
-    int sign;
-    bigint biR;
-
-    sign = 1;
-    if ( *str == '-' )
-       {
-       sign = -1;
-       ++str;
-       }
-    for ( biR = bi_0; *str >= '0' && *str <= '9'; ++str )
-       biR = bi_int_add( bi_int_multiply( biR, 10 ), *str - '0' );
-    if ( sign == -1 )
-       biR = bi_negate( biR );
-    return biR;
-    }
-
-
-void
-bi_print( FILE* f, bigint bi )
-    {
-    if ( bi_is_negative( bi_copy( bi ) ) )
-       {
-       putc( '-', f );
-       bi = bi_negate( bi );
-       }
-    print_pos( f, bi );
-    }
-
-
-bigint
-bi_scan( FILE* f )
-    {
-    int sign;
-    int c;
-    bigint biR;
-
-    sign = 1;
-    c = getc( f );
-    if ( c == '-' )
-       sign = -1;
-    else
-       ungetc( c, f );
-
-    biR = bi_0;
-    for (;;)
-       {
-       c = getc( f );
-       if ( c < '0' || c > '9' )
-           break;
-       biR = bi_int_add( bi_int_multiply( biR, 10 ), c - '0' );
-       }
-
-    if ( sign == -1 )
-       biR = bi_negate( biR );
-    return biR;
-    }
-
-
-static void
-print_pos( FILE* f, bigint bi )
-    {
-    if ( bi_compare( bi_copy( bi ), bi_10 ) >= 0 )
-       print_pos( f, bi_int_divide( bi_copy( bi ), 10 ) );
-    putc( bi_int_mod( bi, 10 ) + '0', f );
-    }
-
-
-int
-bi_int_mod( bigint bi, int m )
-    {
-    int r;
-
-    if ( m <= 0 )
-       {
-       (void) fprintf( stderr, "bi_int_mod: zero or negative modulus\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    r = bi_int_rem( bi, m );
-    if ( r < 0 )
-       r += m;
-    return r;
-    }
-
-
-bigint
-bi_rem( bigint bia, bigint bim )
-    {
-    return bi_subtract(
-       bia, bi_multiply( bi_divide( bi_copy( bia ), bi_copy( bim ) ), bim ) );
-    }
-
-
-bigint
-bi_mod( bigint bia, bigint bim )
-    {
-    bigint biR;
-
-    if ( bi_compare( bi_copy( bim ), bi_0 ) <= 0 )
-       {
-       (void) fprintf( stderr, "bi_mod: zero or negative modulus\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    biR = bi_rem( bia, bi_copy( bim ) );
-    if ( bi_is_negative( bi_copy( biR ) ) )
-       biR = bi_add( biR, bim );
-    else
-       bi_free( bim );
-    return biR;
-    }
-
-
-bigint
-bi_square( bigint bi )
-    {
-    bigint biR;
-
-    biR = bi_multiply( bi_copy( bi ), bi_copy( bi ) );
-    bi_free( bi );
-    return biR;
-    }
-
-
-bigint
-bi_power( bigint bi, bigint biexp )
-    {
-    bigint biR;
-
-    if ( bi_is_negative( bi_copy( biexp ) ) )
-       {
-       (void) fprintf( stderr, "bi_power: negative exponent\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    biR = bi_1;
-    for (;;)
-       {
-       if ( bi_is_odd( bi_copy( biexp ) ) )
-           biR = bi_multiply( biR, bi_copy( bi ) );
-       biexp = bi_half( biexp );
-       if ( bi_compare( bi_copy( biexp ), bi_0 ) <= 0 )
-           break;
-       bi = bi_multiply( bi_copy( bi ), bi );
-       }
-    bi_free( bi );
-    bi_free( biexp );
-    return biR;
-    }
-
-
-bigint
-bi_factorial( bigint bi )
-    {
-    bigint biR;
-
-    biR = bi_1;
-    while ( bi_compare( bi_copy( bi ), bi_1 ) > 0 )
-       {
-       biR = bi_multiply( biR, bi_copy( bi ) );
-       bi = bi_int_subtract( bi, 1 );
-       }
-    bi_free( bi );
-    return biR;
-    }
-
-
-int
-bi_is_even( bigint bi )
-    {
-    return ! bi_is_odd( bi );
-    }
-
-
-bigint
-bi_mod_power( bigint bi, bigint biexp, bigint bim )
-    {
-    int invert;
-    bigint biR;
-
-    invert = 0;
-    if ( bi_is_negative( bi_copy( biexp ) ) )
-       {
-       biexp = bi_negate( biexp );
-       invert = 1;
-       }
-
-    biR = bi_1;
-    for (;;)
-       {
-       if ( bi_is_odd( bi_copy( biexp ) ) )
-           biR = bi_mod( bi_multiply( biR, bi_copy( bi ) ), bi_copy( bim ) );
-       biexp = bi_half( biexp );
-       if ( bi_compare( bi_copy( biexp ), bi_0 ) <= 0 )
-           break;
-       bi = bi_mod( bi_multiply( bi_copy( bi ), bi ), bi_copy( bim ) );
-       }
-    bi_free( bi );
-    bi_free( biexp );
-
-    if ( invert )
-       biR = bi_mod_inverse( biR, bim );
-    else
-       bi_free( bim );
-    return biR;
-    }
-
-
-bigint
-bi_mod_inverse( bigint bi, bigint bim )
-    {
-    bigint gcd, mul0, mul1;
-
-    gcd = bi_egcd( bi_copy( bim ), bi, &mul0, &mul1 );
-
-    /* Did we get gcd == 1? */
-    if ( ! bi_is_one( gcd ) )
-       {
-       (void) fprintf( stderr, "bi_mod_inverse: not relatively prime\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-
-    bi_free( mul0 );
-    return bi_mod( mul1, bim );
-    }
-
-
-/* Euclid's algorithm. */
-bigint
-bi_gcd( bigint bim, bigint bin )
-    {
-    bigint bit;
-
-    bim = bi_abs( bim );
-    bin = bi_abs( bin );
-    while ( ! bi_is_zero( bi_copy( bin ) ) )
-       {
-       bit = bi_mod( bim, bi_copy( bin ) );
-       bim = bin;
-       bin = bit;
-       }
-    bi_free( bin );
-    return bim;
-    }
-
-
-/* Extended Euclidean algorithm. */
-bigint
-bi_egcd( bigint bim, bigint bin, bigint* bim_mul, bigint* bin_mul )
-    {
-    bigint a0, b0, c0, a1, b1, c1, q, t;
-
-    if ( bi_is_negative( bi_copy( bim ) ) )
-       {
-       bigint biR;
-
-       biR = bi_egcd( bi_negate( bim ), bin, &t, bin_mul );
-       *bim_mul = bi_negate( t );
-       return biR;
-       }
-    if ( bi_is_negative( bi_copy( bin ) ) )
-       {
-       bigint biR;
-
-       biR = bi_egcd( bim, bi_negate( bin ), bim_mul, &t );
-       *bin_mul = bi_negate( t );
-       return biR;
-       }
-
-    a0 = bi_1;  b0 = bi_0;  c0 = bim;
-    a1 = bi_0;  b1 = bi_1;  c1 = bin;
-
-    while ( ! bi_is_zero( bi_copy( c1 ) ) )
-       {
-       q = bi_divide( bi_copy( c0 ), bi_copy( c1 ) );
-       t = a0;
-       a0 = bi_copy( a1 );
-       a1 = bi_subtract( t, bi_multiply( bi_copy( q ), a1 ) );
-       t = b0;
-       b0 = bi_copy( b1 );
-       b1 = bi_subtract( t, bi_multiply( bi_copy( q ), b1 ) );
-       t = c0;
-       c0 = bi_copy( c1 );
-       c1 = bi_subtract( t, bi_multiply( bi_copy( q ), c1 ) );
-       bi_free( q );
-       }
-
-    bi_free( a1 );
-    bi_free( b1 );
-    bi_free( c1 );
-    *bim_mul = a0;
-    *bin_mul = b0;
-    return c0;
-    }
-
-
-bigint
-bi_lcm( bigint bia, bigint bib )
-    {
-    bigint biR;
-
-    biR = bi_divide(
-       bi_multiply( bi_copy( bia ), bi_copy( bib ) ),
-       bi_gcd( bi_copy( bia ), bi_copy( bib ) ) );
-    bi_free( bia );
-    bi_free( bib );
-    return biR;
-    }
-
-
-/* The Jacobi symbol. */
-bigint
-bi_jacobi( bigint bia, bigint bib )
-    {
-    bigint biR;
-
-    if ( bi_is_even( bi_copy( bib ) ) )
-       {
-       (void) fprintf( stderr, "bi_jacobi: don't know how to compute Jacobi(n, even)\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-
-    if ( bi_compare( bi_copy( bia ), bi_copy( bib ) ) >= 0 )
-       return bi_jacobi( bi_mod( bia, bi_copy( bib ) ), bib );
-
-    if ( bi_is_zero( bi_copy( bia ) ) || bi_is_one( bi_copy( bia ) ) )
-       {
-       bi_free( bib );
-       return bia;
-       }
-
-    if ( bi_compare( bi_copy( bia ), bi_2 ) == 0 )
-       {
-       bi_free( bia );
-       switch ( bi_int_mod( bib, 8 ) )
-           {
-           case 1: case 7:
-           return bi_1;
-           case 3: case 5:
-           return bi_m1;
-           }
-       }
-
-    if ( bi_is_even( bi_copy( bia ) ) )
-       {
-       biR = bi_multiply(
-           bi_jacobi( bi_2, bi_copy( bib ) ),
-           bi_jacobi( bi_half( bia ), bi_copy( bib ) ) );
-       bi_free( bib );
-       return biR;
-       }
-
-    if ( bi_int_mod( bi_copy( bia ), 4 ) == 3 &&
-         bi_int_mod( bi_copy( bib ), 4 ) == 3 )
-       return bi_negate( bi_jacobi( bib, bia ) );
-    else
-       return bi_jacobi( bib, bia );
-    }
-
-
-/* Probabalistic prime checking. */
-int
-bi_is_probable_prime( bigint bi, int certainty )
-    {
-    int i, p;
-    bigint bim1;
-
-    /* First do trial division by a list of small primes.  This eliminates
-    ** many candidates.
-    */
-    for ( i = 0; i < sizeof(low_primes)/sizeof(*low_primes); ++i )
-       {
-       p = low_primes[i];
-       switch ( bi_compare( int_to_bi( p ), bi_copy( bi ) ) )
-           {
-           case 0:
-           bi_free( bi );
-           return 1;
-           case 1:
-           bi_free( bi );
-           return 0;
-           }
-       if ( bi_int_mod( bi_copy( bi ), p ) == 0 )
-           {
-           bi_free( bi );
-           return 0;
-           }
-       }
-
-    /* Now do the probabilistic tests. */
-    bim1 = bi_int_subtract( bi_copy( bi ), 1 );
-    for ( i = 0; i < certainty; ++i )
-       {
-       bigint a, j, jac;
-
-       /* Pick random test number. */
-       a = bi_random( bi_copy( bi ) );
-
-       /* Decide whether to run the Fermat test or the Solovay-Strassen
-       ** test.  The Fermat test is fast but lets some composite numbers
-       ** through.  Solovay-Strassen runs slower but is more certain.
-       ** So the compromise here is we run the Fermat test a couple of
-       ** times to quickly reject most composite numbers, and then do
-       ** the rest of the iterations with Solovay-Strassen so nothing
-       ** slips through.
-       */
-       if ( i < 2 && certainty >= 5 )
-           {
-           /* Fermat test.  Note that this is not state of the art.  There's a
-           ** class of numbers called Carmichael numbers which are composite
-           ** but look prime to this test - it lets them slip through no
-           ** matter how many reps you run.  However, it's nice and fast so
-           ** we run it anyway to help quickly reject most of the composites.
-           */
-           if ( ! bi_is_one( bi_mod_power( bi_copy( a ), bi_copy( bim1 ), bi_copy( bi ) ) ) )
-               {
-               bi_free( bi );
-               bi_free( bim1 );
-               bi_free( a );
-               return 0;
-               }
-           }
-       else
-           {
-           /* GCD test.  This rarely hits, but we need it for Solovay-Strassen. */
-           if ( ! bi_is_one( bi_gcd( bi_copy( bi ), bi_copy( a ) ) ) )
-               {
-               bi_free( bi );
-               bi_free( bim1 );
-               bi_free( a );
-               return 0;
-               }
-
-           /* Solovay-Strassen test.  First compute pseudo Jacobi. */
-           j = bi_mod_power(
-                   bi_copy( a ), bi_half( bi_copy( bim1 ) ), bi_copy( bi ) );
-           if ( bi_compare( bi_copy( j ), bi_copy( bim1 ) ) == 0 )
-               {
-               bi_free( j );
-               j = bi_m1;
-               }
-
-           /* Now compute real Jacobi. */
-           jac = bi_jacobi( bi_copy( a ), bi_copy( bi ) );
-
-           /* If they're not equal, the number is definitely composite. */
-           if ( bi_compare( j, jac ) != 0 )
-               {
-               bi_free( bi );
-               bi_free( bim1 );
-               bi_free( a );
-               return 0;
-               }
-           }
-
-       bi_free( a );
-       }
-
-    bi_free( bim1 );
-
-    bi_free( bi );
-    return 1;
-    }
-
-
-bigint
-bi_generate_prime( int bits, int certainty )
-    {
-    bigint bimo2, bip;
-    int i, inc = 0;
-
-    bimo2 = bi_power( bi_2, int_to_bi( bits - 1 ) );
-    for (;;)
-       {
-       bip = bi_add( bi_random( bi_copy( bimo2 ) ), bi_copy( bimo2 ) );
-       /* By shoving the candidate numbers up to the next highest multiple
-       ** of six plus or minus one, we pre-eliminate all multiples of
-       ** two and/or three.
-       */
-       switch ( bi_int_mod( bi_copy( bip ), 6 ) )
-           {
-           case 0: inc = 4; bip = bi_int_add( bip, 1 ); break;
-           case 1: inc = 4;                             break;
-           case 2: inc = 2; bip = bi_int_add( bip, 3 ); break;
-           case 3: inc = 2; bip = bi_int_add( bip, 2 ); break;
-           case 4: inc = 2; bip = bi_int_add( bip, 1 ); break;
-           case 5: inc = 2;                             break;
-           }
-       /* Starting from the generated random number, check a bunch of
-       ** numbers in sequence.  This is just to avoid calls to bi_random(),
-       ** which is more expensive than a simple add.
-       */
-       for ( i = 0; i < 1000; ++i )    /* arbitrary */
-           {
-           if ( bi_is_probable_prime( bi_copy( bip ), certainty ) )
-               {
-               bi_free( bimo2 );
-               return bip;
-               }
-           bip = bi_int_add( bip, inc );
-           inc = 6 - inc;
-           }
-       /* We ran through the whole sequence and didn't find a prime.
-       ** Shrug, just try a different random starting point.
-       */
-       bi_free( bip );
-       }
-    }

diff --git a/src/rt/bigint/bigint_int.cpp b/src/rt/bigint/bigint_int.cpp
deleted file mode 100644 (file)
index 194ddcb..0000000
--- a/src/rt/bigint/bigint_int.cpp
+++ /dev/null
@@ -1,1428 +0,0 @@
-/* bigint - internal portion of large integer package
-**
-** Copyright © 2000 by Jef Poskanzer <jef@mail.acme.com>.
-** All rights reserved.
-**
-** Redistribution and use in source and binary forms, with or without
-** modification, are permitted provided that the following conditions
-** are met:
-** 1. Redistributions of source code must retain the above copyright
-**    notice, this list of conditions and the following disclaimer.
-** 2. Redistributions in binary form must reproduce the above copyright
-**    notice, this list of conditions and the following disclaimer in the
-**    documentation and/or other materials provided with the distribution.
-**
-** THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
-** ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-** IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
-** ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
-** FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-** DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
-** OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
-** HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
-** OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
-** SUCH DAMAGE.
-*/
-
-#include <sys/types.h>
-#include <signal.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <unistd.h>
-#include <time.h>
-
-#include "bigint.h"
-
-#define max(a,b) ((a)>(b)?(a):(b))
-#define min(a,b) ((a)<(b)?(a):(b))
-
-/* MAXINT and MININT extracted from <values.h>, which gives a warning
-** message if included.
-*/
-#define BITSPERBYTE 8
-#define BITS(type)  (BITSPERBYTE * (int)sizeof(type))
-#define INTBITS     BITS(int)
-#define MININT      (1 << (INTBITS - 1))
-#define MAXINT      (~MININT)
-
-
-/* The package represents arbitrary-precision integers as a sign and a sum
-** of components multiplied by successive powers of the basic radix, i.e.:
-**
-**   sign * ( comp0 + comp1 * radix + comp2 * radix^2 + comp3 * radix^3 )
-**
-** To make good use of the computer's word size, the radix is chosen
-** to be a power of two.  It could be chosen to be the full word size,
-** however this would require a lot of finagling in the middle of the
-** algorithms to get the inter-word overflows right.  That would slow things
-** down.  Instead, the radix is chosen to be *half* the actual word size.
-** With just a little care, this means the words can hold all intermediate
-** values, and the overflows can be handled all at once at the end, in a
-** normalization step.  This simplifies the coding enormously, and is probably
-** somewhat faster to run.  The cost is that numbers use twice as much
-** storage as they would with the most efficient representation, but storage
-** is cheap.
-**
-** A few more notes on the representation:
-**
-**  - The sign is always 1 or -1, never 0.  The number 0 is represented
-**    with a sign of 1.
-**  - The components are signed numbers, to allow for negative intermediate
-**    values.  After normalization, all components are >= 0 and the sign is
-**    updated.
-*/
-
-/* Type definition for bigints. */
-typedef int64_t comp;  /* should be the largest signed int type you have */
-struct _real_bigint {
-    int refs;
-    struct _real_bigint* next;
-    int num_comps, max_comps;
-    int sign;
-    comp* comps;
-    };
-typedef struct _real_bigint* real_bigint;
-
-
-#undef DUMP
-
-
-#define PERMANENT 123456789
-
-static comp bi_radix, bi_radix_o2;
-static int bi_radix_sqrt, bi_comp_bits;
-
-static real_bigint active_list, free_list;
-static int active_count, free_count;
-static int check_level;
-
-
-/* Forwards. */
-static bigint regular_multiply( real_bigint bia, real_bigint bib );
-static bigint multi_divide( bigint binumer, real_bigint bidenom );
-static bigint multi_divide2( bigint binumer, real_bigint bidenom );
-static void more_comps( real_bigint bi, int n );
-static real_bigint alloc( int num_comps );
-static real_bigint clone( real_bigint bi );
-static void normalize( real_bigint bi );
-static void check( real_bigint bi );
-static void double_check( void );
-static void triple_check( void );
-#ifdef DUMP
-static void dump( char* str, bigint bi );
-#endif /* DUMP */
-static int csqrt( comp c );
-static int cbits( comp c );
-
-
-void
-bi_initialize( void )
-    {
-    /* Set the radix.  This does not actually have to be a power of
-    ** two, that's just the most efficient value.  It does have to
-    ** be even for bi_half() to work.
-    */
-    bi_radix = 1;
-    bi_radix <<= BITS(comp) / 2 - 1;
-
-    /* Halve the radix.  Only used by bi_half(). */
-    bi_radix_o2 = bi_radix >> 1;
-
-    /* Take the square root of the radix.  Only used by bi_divide(). */
-    bi_radix_sqrt = csqrt( bi_radix );
-
-    /* Figure out how many bits in a component.  Only used by bi_bits(). */
-    bi_comp_bits = cbits( bi_radix - 1 );
-
-    /* Init various globals. */
-    active_list = (real_bigint) 0;
-    active_count = 0;
-    free_list = (real_bigint) 0;
-    free_count = 0;
-
-    /* This can be 0 through 3. */
-    check_level = 3;
-
-    /* Set up some convenient bigints. */
-    bi_0 = int_to_bi( 0 ); bi_permanent( bi_0 );
-    bi_1 = int_to_bi( 1 ); bi_permanent( bi_1 );
-    bi_2 = int_to_bi( 2 ); bi_permanent( bi_2 );
-    bi_10 = int_to_bi( 10 ); bi_permanent( bi_10 );
-    bi_m1 = int_to_bi( -1 ); bi_permanent( bi_m1 );
-    bi_maxint = int_to_bi( MAXINT ); bi_permanent( bi_maxint );
-    bi_minint = int_to_bi( MININT ); bi_permanent( bi_minint );
-    }
-
-
-void
-bi_terminate( void )
-    {
-    real_bigint p, pn;
-
-    bi_depermanent( bi_0 ); bi_free( bi_0 );
-    bi_depermanent( bi_1 ); bi_free( bi_1 );
-    bi_depermanent( bi_2 ); bi_free( bi_2 );
-    bi_depermanent( bi_10 ); bi_free( bi_10 );
-    bi_depermanent( bi_m1 ); bi_free( bi_m1 );
-    bi_depermanent( bi_maxint ); bi_free( bi_maxint );
-    bi_depermanent( bi_minint ); bi_free( bi_minint );
-
-    if ( active_count != 0 )
-       (void) fprintf(
-           stderr, "bi_terminate: there were %d un-freed bigints\n",
-           active_count );
-    if ( check_level >= 2 )
-       double_check();
-    if ( check_level >= 3 )
-       {
-       triple_check();
-       for ( p = active_list; p != (bigint) 0; p = pn )
-           {
-           pn = p->next;
-           free( p->comps );
-           free( p );
-           }
-       }
-    for ( p = free_list; p != (bigint) 0; p = pn )
-       {
-       pn = p->next;
-       free( p->comps );
-       free( p );
-       }
-    }
-
-
-void
-bi_no_check( void )
-    {
-    check_level = 0;
-    }
-
-
-bigint
-bi_copy( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-
-    check( bi );
-    if ( bi->refs != PERMANENT )
-       ++bi->refs;
-    return bi;
-    }
-
-
-void
-bi_permanent( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-
-    check( bi );
-    if ( check_level >= 1 && bi->refs != 1 )
-       {
-       (void) fprintf( stderr, "bi_permanent: refs was not 1\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    bi->refs = PERMANENT;
-    }
-
-
-void
-bi_depermanent( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-
-    check( bi );
-    if ( check_level >= 1 && bi->refs != PERMANENT )
-       {
-       (void) fprintf( stderr, "bi_depermanent: bigint was not permanent\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    bi->refs = 1;
-    }
-
-
-void
-bi_free( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-
-    check( bi );
-    if ( bi->refs == PERMANENT )
-       return;
-    --bi->refs;
-    if ( bi->refs > 0 )
-       return;
-    if ( check_level >= 3 )
-       {
-       /* The active list only gets maintained at check levels 3 or higher. */
-       real_bigint* nextP;
-       for ( nextP = &active_list; *nextP != (real_bigint) 0; nextP = &((*nextP)->next) )
-           if ( *nextP == bi )
-               {
-               *nextP = bi->next;
-               break;
-               }
-       }
-    --active_count;
-    bi->next = free_list;
-    free_list = bi;
-    ++free_count;
-    if ( check_level >= 1 && active_count < 0 )
-       {
-       (void) fprintf( stderr,
-           "bi_free: active_count went negative - double-freed bigint?\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    }
-
-
-int
-bi_compare( bigint obia, bigint obib )
-    {
-    real_bigint bia = (real_bigint) obia;
-    real_bigint bib = (real_bigint) obib;
-    int r, c;
-
-    check( bia );
-    check( bib );
-
-    /* First check for pointer equality. */
-    if ( bia == bib )
-       r = 0;
-    else
-       {
-       /* Compare signs. */
-       if ( bia->sign > bib->sign )
-           r = 1;
-       else if ( bia->sign < bib->sign )
-           r = -1;
-       /* Signs are the same.  Check the number of components. */
-       else if ( bia->num_comps > bib->num_comps )
-           r = bia->sign;
-       else if ( bia->num_comps < bib->num_comps )
-           r = -bia->sign;
-       else
-           {
-           /* Same number of components.  Compare starting from the high end
-           ** and working down.
-           */
-           r = 0;      /* if we complete the loop, the numbers are equal */
-           for ( c = bia->num_comps - 1; c >= 0; --c )
-               {
-               if ( bia->comps[c] > bib->comps[c] )
-                   { r = bia->sign; break; }
-               else if ( bia->comps[c] < bib->comps[c] )
-                   { r = -bia->sign; break; }
-               }
-           }
-       }
-
-    bi_free( bia );
-    bi_free( bib );
-    return r;
-    }
-
-
-bigint
-int_to_bi( int i )
-    {
-    real_bigint biR;
-
-    biR = alloc( 1 );
-    biR->sign = 1;
-    biR->comps[0] = i;
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-int
-bi_to_int( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    comp v, m;
-    int c, r;
-
-    check( bi );
-    if ( bi_compare( bi_copy( bi ), bi_maxint ) > 0 ||
-        bi_compare( bi_copy( bi ), bi_minint ) < 0 )
-       {
-       (void) fprintf( stderr, "bi_to_int: overflow\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    v = 0;
-    m = 1;
-    for ( c = 0; c < bi->num_comps; ++c )
-       {
-       v += bi->comps[c] * m;
-       m *= bi_radix;
-       }
-    r = (int) ( bi->sign * v );
-    bi_free( bi );
-    return r;
-    }
-
-
-bigint
-bi_int_add( bigint obi, int i )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-
-    check( bi );
-    biR = clone( bi );
-    if ( biR->sign == 1 )
-       biR->comps[0] += i;
-    else
-       biR->comps[0] -= i;
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_int_subtract( bigint obi, int i )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-
-    check( bi );
-    biR = clone( bi );
-    if ( biR->sign == 1 )
-       biR->comps[0] -= i;
-    else
-       biR->comps[0] += i;
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_int_multiply( bigint obi, int i )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-    int c;
-
-    check( bi );
-    biR = clone( bi );
-    if ( i < 0 )
-       {
-       i = -i;
-       biR->sign = -biR->sign;
-       }
-    for ( c = 0; c < biR->num_comps; ++c )
-       biR->comps[c] *= i;
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_int_divide( bigint obinumer, int denom )
-    {
-    real_bigint binumer = (real_bigint) obinumer;
-    real_bigint biR;
-    int c;
-    comp r;
-
-    check( binumer );
-    if ( denom == 0 )
-       {
-       (void) fprintf( stderr, "bi_int_divide: divide by zero\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    biR = clone( binumer );
-    if ( denom < 0 )
-       {
-       denom = -denom;
-       biR->sign = -biR->sign;
-       }
-    r = 0;
-    for ( c = biR->num_comps - 1; c >= 0; --c )
-       {
-       r = r * bi_radix + biR->comps[c];
-       biR->comps[c] = r / denom;
-       r = r % denom;
-       }
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-int
-bi_int_rem( bigint obi, int m )
-    {
-    real_bigint bi = (real_bigint) obi;
-    comp rad_r, r;
-    int  c;
-
-    check( bi );
-    if ( m == 0 )
-       {
-       (void) fprintf( stderr, "bi_int_rem: divide by zero\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    if ( m < 0 )
-       m = -m;
-    rad_r = 1;
-    r = 0;
-    for ( c = 0; c < bi->num_comps; ++c )
-       {
-       r = ( r + bi->comps[c] * rad_r ) % m;
-       rad_r = ( rad_r * bi_radix ) % m;
-       }
-    if ( bi->sign < 1 )
-       r = -r;
-    bi_free( bi );
-    return (int) r;
-    }
-
-
-bigint
-bi_add( bigint obia, bigint obib )
-    {
-    real_bigint bia = (real_bigint) obia;
-    real_bigint bib = (real_bigint) obib;
-    real_bigint biR;
-    int c;
-
-    check( bia );
-    check( bib );
-    biR = clone( bia );
-    more_comps( biR, max( biR->num_comps, bib->num_comps ) );
-    for ( c = 0; c < bib->num_comps; ++c )
-       if ( biR->sign == bib->sign )
-           biR->comps[c] += bib->comps[c];
-       else
-           biR->comps[c] -= bib->comps[c];
-    bi_free( bib );
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_subtract( bigint obia, bigint obib )
-    {
-    real_bigint bia = (real_bigint) obia;
-    real_bigint bib = (real_bigint) obib;
-    real_bigint biR;
-    int c;
-
-    check( bia );
-    check( bib );
-    biR = clone( bia );
-    more_comps( biR, max( biR->num_comps, bib->num_comps ) );
-    for ( c = 0; c < bib->num_comps; ++c )
-       if ( biR->sign == bib->sign )
-           biR->comps[c] -= bib->comps[c];
-       else
-           biR->comps[c] += bib->comps[c];
-    bi_free( bib );
-    normalize( biR );
-    check( biR );
-    return biR;
-    }
-
-
-/* Karatsuba multiplication.  This is supposedly O(n^1.59), better than
-** regular multiplication for large n.  The define below sets the crossover
-** point - below that we use regular multiplication, above it we
-** use Karatsuba.  Note that Karatsuba is a recursive algorithm, so
-** all Karatsuba calls involve regular multiplications as the base
-** steps.
-*/
-#define KARATSUBA_THRESH 12
-bigint
-bi_multiply( bigint obia, bigint obib )
-    {
-    real_bigint bia = (real_bigint) obia;
-    real_bigint bib = (real_bigint) obib;
-
-    check( bia );
-    check( bib );
-    if ( min( bia->num_comps, bib->num_comps ) < KARATSUBA_THRESH )
-       return regular_multiply( bia, bib );
-    else
-       {
-       /* The factors are large enough that Karatsuba multiplication
-       ** is a win.  The basic idea here is you break each factor up
-       ** into two parts, like so:
-       **     i * r^n + j        k * r^n + l
-       ** r is the radix we're representing numbers with, so this
-       ** breaking up just means shuffling components around, no
-       ** math required.  With regular multiplication the product
-       ** would be:
-       **     ik * r^(n*2) + ( il + jk ) * r^n + jl
-       ** That's four sub-multiplies and one addition, not counting the
-       ** radix-shifting.  With Karatsuba, you instead do:
-       **     ik * r^(n*2) + ( (i+j)(k+l) - ik - jl ) * r^n  + jl
-       ** This is only three sub-multiplies.  The number of adds
-       ** (and subtracts) increases to four, but those run in linear time
-       ** so they are cheap.  The sub-multiplies are accomplished by
-       ** recursive calls, eventually reducing to regular multiplication.
-       */
-       int n, c;
-       real_bigint bi_i, bi_j, bi_k, bi_l;
-       real_bigint bi_ik, bi_mid, bi_jl;
-
-       n = ( max( bia->num_comps, bib->num_comps ) + 1 ) / 2;
-       bi_i = alloc( n );
-       bi_j = alloc( n );
-       bi_k = alloc( n );
-       bi_l = alloc( n );
-       for ( c = 0; c < n; ++c )
-           {
-           if ( c + n < bia->num_comps )
-               bi_i->comps[c] = bia->comps[c + n];
-           else
-               bi_i->comps[c] = 0;
-           if ( c < bia->num_comps )
-               bi_j->comps[c] = bia->comps[c];
-           else
-               bi_j->comps[c] = 0;
-           if ( c + n < bib->num_comps )
-               bi_k->comps[c] = bib->comps[c + n];
-           else
-               bi_k->comps[c] = 0;
-           if ( c < bib->num_comps )
-               bi_l->comps[c] = bib->comps[c];
-           else
-               bi_l->comps[c] = 0;
-           }
-       bi_i->sign = bi_j->sign = bi_k->sign = bi_l->sign = 1;
-       normalize( bi_i );
-       normalize( bi_j );
-       normalize( bi_k );
-       normalize( bi_l );
-       bi_ik = bi_multiply( bi_copy( bi_i ), bi_copy( bi_k ) );
-       bi_jl = bi_multiply( bi_copy( bi_j ), bi_copy( bi_l ) );
-       bi_mid = bi_subtract(
-           bi_subtract(
-               bi_multiply( bi_add( bi_i, bi_j ), bi_add( bi_k, bi_l ) ),
-               bi_copy( bi_ik ) ),
-           bi_copy( bi_jl ) );
-       more_comps(
-           bi_jl, max( bi_mid->num_comps + n, bi_ik->num_comps + n * 2 ) );
-       for ( c = 0; c < bi_mid->num_comps; ++c )
-           bi_jl->comps[c + n] += bi_mid->comps[c];
-       for ( c = 0; c < bi_ik->num_comps; ++c )
-           bi_jl->comps[c + n * 2] += bi_ik->comps[c];
-       bi_free( bi_ik );
-       bi_free( bi_mid );
-       bi_jl->sign = bia->sign * bib->sign;
-       bi_free( bia );
-       bi_free( bib );
-       normalize( bi_jl );
-       check( bi_jl );
-       return bi_jl;
-       }
-    }
-
-
-/* Regular O(n^2) multiplication. */
-static bigint
-regular_multiply( real_bigint bia, real_bigint bib )
-    {
-    real_bigint biR;
-    int new_comps, c1, c2;
-
-    check( bia );
-    check( bib );
-    biR = clone( bi_0 );
-    new_comps = bia->num_comps + bib->num_comps;
-    more_comps( biR, new_comps );
-    for ( c1 = 0; c1 < bia->num_comps; ++c1 )
-       {
-       for ( c2 = 0; c2 < bib->num_comps; ++c2 )
-           biR->comps[c1 + c2] += bia->comps[c1] * bib->comps[c2];
-       /* Normalize after each inner loop to avoid overflowing any
-       ** components.  But be sure to reset biR's components count,
-       ** in case a previous normalization lowered it.
-       */
-       biR->num_comps = new_comps;
-       normalize( biR );
-       }
-    check( biR );
-    if ( ! bi_is_zero( bi_copy( biR ) ) )
-       biR->sign = bia->sign * bib->sign;
-    bi_free( bia );
-    bi_free( bib );
-    return biR;
-    }
-
-
-/* The following three routines implement a multi-precision divide method
-** that I haven't seen used anywhere else.  It is not quite as fast as
-** the standard divide method, but it is a lot simpler.  In fact it's
-** about as simple as the binary shift-and-subtract method, which goes
-** about five times slower than this.
-**
-** The method assumes you already have multi-precision multiply and subtract
-** routines, and also a multi-by-single precision divide routine.  The latter
-** is used to generate approximations, which are then checked and corrected
-** using the former.  The result converges to the correct value by about
-** 16 bits per loop.
-*/
-
-/* Public routine to divide two arbitrary numbers. */
-bigint
-bi_divide( bigint binumer, bigint obidenom )
-    {
-    real_bigint bidenom = (real_bigint) obidenom;
-    int sign;
-    bigint biquotient;
-
-    /* Check signs and trivial cases. */
-    sign = 1;
-    switch ( bi_compare( bi_copy( bidenom ), bi_0 ) )
-       {
-       case 0:
-       (void) fprintf( stderr, "bi_divide: divide by zero\n" );
-       (void) kill( getpid(), SIGFPE );
-       case -1:
-       sign *= -1;
-       bidenom = bi_negate( bidenom );
-       break;
-       }
-    switch ( bi_compare( bi_copy( binumer ), bi_0 ) )
-       {
-       case 0:
-       bi_free( binumer );
-       bi_free( bidenom );
-       return bi_0;
-       case -1:
-       sign *= -1;
-       binumer = bi_negate( binumer );
-       break;
-       }
-    switch ( bi_compare( bi_copy( binumer ), bi_copy( bidenom ) ) )
-       {
-       case -1:
-       bi_free( binumer );
-       bi_free( bidenom );
-       return bi_0;
-       case 0:
-       bi_free( binumer );
-       bi_free( bidenom );
-       if ( sign == 1 )
-           return bi_1;
-       else
-           return bi_m1;
-       }
-
-    /* Is the denominator small enough to do an int divide? */
-    if ( bidenom->num_comps == 1 )
-       {
-       /* Win! */
-       biquotient = bi_int_divide( binumer, bidenom->comps[0] );
-       bi_free( bidenom );
-       }
-    else
-       {
-       /* No, we have to do a full multi-by-multi divide. */
-       biquotient = multi_divide( binumer, bidenom );
-       }
-
-    if ( sign == -1 )
-       biquotient = bi_negate( biquotient );
-    return biquotient;
-    }
-
-
-/* Divide two multi-precision positive numbers. */
-static bigint
-multi_divide( bigint binumer, real_bigint bidenom )
-    {
-    /* We use a successive approximation method that is kind of like a
-    ** continued fraction.  The basic approximation is to do an int divide
-    ** by the high-order component of the denominator.  Then we correct
-    ** based on the remainder from that.
-    **
-    ** However, if the high-order component is too small, this doesn't
-    ** work well.  In particular, if the high-order component is 1 it
-    ** doesn't work at all.  Easily fixed, though - if the component
-    ** is too small, increase it!
-    */
-    if ( bidenom->comps[bidenom->num_comps-1] < bi_radix_sqrt )
-       {
-       /* We use the square root of the radix as the threshhold here
-       ** because that's the largest value guaranteed to not make the
-       ** high-order component overflow and become too small again.
-       **
-       ** We increase binumer along with bidenom to keep the end result
-       ** the same.
-       */
-       binumer = bi_int_multiply( binumer, bi_radix_sqrt );
-       bidenom = bi_int_multiply( bidenom, bi_radix_sqrt );
-       }
-
-    /* Now start the recursion. */
-    return multi_divide2( binumer, bidenom );
-    }
-
-
-/* Divide two multi-precision positive conditioned numbers. */
-static bigint
-multi_divide2( bigint binumer, real_bigint bidenom )
-    {
-    real_bigint biapprox;
-    bigint birem, biquotient;
-    int c, o;
-
-    /* Figure out the approximate quotient.   Since we're dividing by only
-    ** the top component of the denominator, which is less than or equal to
-    ** the full denominator, the result is guaranteed to be greater than or
-    ** equal to the correct quotient.
-    */
-    o = bidenom->num_comps - 1;
-    biapprox = bi_int_divide( bi_copy( binumer ), bidenom->comps[o] );
-    /* And downshift the result to get the approximate quotient. */
-    for ( c = o; c < biapprox->num_comps; ++c )
-       biapprox->comps[c - o] = biapprox->comps[c];
-    biapprox->num_comps -= o;
-
-    /* Find the remainder from the approximate quotient. */
-    birem = bi_subtract(
-       bi_multiply( bi_copy( biapprox ), bi_copy( bidenom ) ), binumer );
-
-    /* If the remainder is negative, zero, or in fact any value less
-    ** than bidenom, then we have the correct quotient and we're done.
-    */
-    if ( bi_compare( bi_copy( birem ), bi_copy( bidenom ) ) < 0 )
-       {
-       biquotient = biapprox;
-       bi_free( birem );
-       bi_free( bidenom );
-       }
-    else
-       {
-       /* The real quotient is now biapprox - birem / bidenom.  We still
-       ** have to do a divide.  However, birem is smaller than binumer,
-       ** so the next divide will go faster.  We do the divide by
-       ** recursion.  Since this is tail-recursion or close to it, we
-       ** could probably re-arrange things and make it a non-recursive
-       ** loop, but the overhead of recursion is small and the bookkeeping
-       ** is simpler this way.
-       **
-       ** Note that since the sub-divide uses the same denominator, it
-       ** doesn't have to adjust the values again - the high-order component
-       ** will still be good.
-       */
-       biquotient = bi_subtract( biapprox, multi_divide2( birem, bidenom ) );
-       }
-
-    return biquotient;
-    }
-
-
-/* Binary division - about five times slower than the above. */
-bigint
-bi_binary_divide( bigint binumer, bigint obidenom )
-    {
-    real_bigint bidenom = (real_bigint) obidenom;
-    int sign;
-    bigint biquotient;
-
-    /* Check signs and trivial cases. */
-    sign = 1;
-    switch ( bi_compare( bi_copy( bidenom ), bi_0 ) )
-       {
-       case 0:
-       (void) fprintf( stderr, "bi_divide: divide by zero\n" );
-       (void) kill( getpid(), SIGFPE );
-       case -1:
-       sign *= -1;
-       bidenom = bi_negate( bidenom );
-       break;
-       }
-    switch ( bi_compare( bi_copy( binumer ), bi_0 ) )
-       {
-       case 0:
-       bi_free( binumer );
-       bi_free( bidenom );
-       return bi_0;
-       case -1:
-       sign *= -1;
-       binumer = bi_negate( binumer );
-       break;
-       }
-    switch ( bi_compare( bi_copy( binumer ), bi_copy( bidenom ) ) )
-       {
-       case -1:
-       bi_free( binumer );
-       bi_free( bidenom );
-       return bi_0;
-       case 0:
-       bi_free( binumer );
-       bi_free( bidenom );
-       if ( sign == 1 )
-           return bi_1;
-       else
-           return bi_m1;
-       }
-
-    /* Is the denominator small enough to do an int divide? */
-    if ( bidenom->num_comps == 1 )
-       {
-       /* Win! */
-       biquotient = bi_int_divide( binumer, bidenom->comps[0] );
-       bi_free( bidenom );
-       }
-    else
-       {
-       /* No, we have to do a full multi-by-multi divide. */
-       int num_bits, den_bits, i;
-
-       num_bits = bi_bits( bi_copy( binumer ) );
-       den_bits = bi_bits( bi_copy( bidenom ) );
-       bidenom = bi_multiply( bidenom, bi_power( bi_2, int_to_bi( num_bits - den_bits ) ) );
-       biquotient = bi_0;
-       for ( i = den_bits; i <= num_bits; ++i )
-           {
-           biquotient = bi_double( biquotient );
-           if ( bi_compare( bi_copy( binumer ), bi_copy( bidenom ) ) >= 0 )
-               {
-               biquotient = bi_int_add( biquotient, 1 );
-               binumer = bi_subtract( binumer, bi_copy( bidenom ) );
-               }
-           bidenom = bi_half( bidenom );
-           }
-       bi_free( binumer );
-       bi_free( bidenom );
-       }
-
-    if ( sign == -1 )
-       biquotient = bi_negate( biquotient );
-    return biquotient;
-    }
-
-
-bigint
-bi_negate( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-
-    check( bi );
-    biR = clone( bi );
-    biR->sign = -biR->sign;
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_abs( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-
-    check( bi );
-    biR = clone( bi );
-    biR->sign = 1;
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_half( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-    int c;
-
-    check( bi );
-    /* This depends on the radix being even. */
-    biR = clone( bi );
-    for ( c = 0; c < biR->num_comps; ++c )
-       {
-       if ( biR->comps[c] & 1 )
-           if ( c > 0 )
-               biR->comps[c - 1] += bi_radix_o2;
-       biR->comps[c] = biR->comps[c] >> 1;
-       }
-    /* Avoid normalization. */
-    if ( biR->num_comps > 1 && biR->comps[biR->num_comps-1] == 0 )
-       --biR->num_comps;
-    check( biR );
-    return biR;
-    }
-
-
-bigint
-bi_double( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    real_bigint biR;
-    int c;
-
-    check( bi );
-    biR = clone( bi );
-    for ( c = biR->num_comps - 1; c >= 0; --c )
-       {
-       biR->comps[c] = biR->comps[c] << 1;
-       if ( biR->comps[c] >= bi_radix )
-           {
-           if ( c + 1 >= biR->num_comps )
-               more_comps( biR, biR->num_comps + 1 );
-           biR->comps[c] -= bi_radix;
-           biR->comps[c + 1] += 1;
-           }
-       }
-    check( biR );
-    return biR;
-    }
-
-
-/* Find integer square root by Newton's method. */
-bigint
-bi_sqrt( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    bigint biR, biR2, bidiff;
-
-    switch ( bi_compare( bi_copy( bi ), bi_0 ) )
-       {
-       case -1:
-       (void) fprintf( stderr, "bi_sqrt: imaginary result\n" );
-       (void) kill( getpid(), SIGFPE );
-       case 0:
-       return bi;
-       }
-    if ( bi_is_one( bi_copy( bi ) ) )
-       return bi;
-
-    /* Newton's method converges reasonably fast, but it helps to have
-    ** a good initial guess.  We can make a *very* good initial guess
-    ** by taking the square root of the top component times the square
-    ** root of the radix part.  Both of those are easy to compute.
-    */
-    biR = bi_int_multiply(
-       bi_power( int_to_bi( bi_radix_sqrt ), int_to_bi( bi->num_comps - 1 ) ),
-       csqrt( bi->comps[bi->num_comps - 1] ) );
-
-    /* Now do the Newton loop until we have the answer. */
-    for (;;)
-       {
-       biR2 = bi_divide( bi_copy( bi ), bi_copy( biR ) );
-       bidiff = bi_subtract( bi_copy( biR ), bi_copy( biR2 ) );
-       if ( bi_is_zero( bi_copy( bidiff ) ) ||
-            bi_compare( bi_copy( bidiff ), bi_m1 ) == 0 )
-           {
-           bi_free( bi );
-           bi_free( bidiff );
-           bi_free( biR2 );
-           return biR;
-           }
-       if ( bi_is_one( bi_copy( bidiff ) ) )
-           {
-           bi_free( bi );
-           bi_free( bidiff );
-           bi_free( biR );
-           return biR2;
-           }
-       bi_free( bidiff );
-       biR = bi_half( bi_add( biR, biR2 ) );
-       }
-    }
-
-
-int
-bi_is_odd( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    int r;
-
-    check( bi );
-    r = bi->comps[0] & 1;
-    bi_free( bi );
-    return r;
-    }
-
-
-int
-bi_is_zero( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    int r;
-
-    check( bi );
-    r = ( bi->sign == 1 && bi->num_comps == 1 && bi->comps[0] == 0 );
-    bi_free( bi );
-    return r;
-    }
-
-
-int
-bi_is_one( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    int r;
-
-    check( bi );
-    r = ( bi->sign == 1 && bi->num_comps == 1 && bi->comps[0] == 1 );
-    bi_free( bi );
-    return r;
-    }
-
-
-int
-bi_is_negative( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    int r;
-
-    check( bi );
-    r = ( bi->sign == -1 );
-    bi_free( bi );
-    return r;
-    }
-
-
-bigint
-bi_random( bigint bi )
-    {
-    real_bigint biR;
-    int c;
-
-    biR = bi_multiply( bi_copy( bi ), bi_copy( bi ) );
-    for ( c = 0; c < biR->num_comps; ++c )
-       biR->comps[c] = random();
-    normalize( biR );
-    biR = bi_mod( biR, bi );
-    return biR;
-    }
-
-
-int
-bi_bits( bigint obi )
-    {
-    real_bigint bi = (real_bigint) obi;
-    int bits;
-
-    bits =
-       bi_comp_bits * ( bi->num_comps - 1 ) +
-       cbits( bi->comps[bi->num_comps - 1] );
-    bi_free( bi );
-    return bits;
-    }
-
-
-/* Allocate and zero more components.  Does not consume bi, of course. */
-static void
-more_comps( real_bigint bi, int n )
-    {
-    if ( n > bi->max_comps )
-       {
-       bi->max_comps = max( bi->max_comps * 2, n );
-       bi->comps = (comp*) realloc(
-           (void*) bi->comps, bi->max_comps * sizeof(comp) );
-       if ( bi->comps == (comp*) 0 )
-           {
-           (void) fprintf( stderr, "out of memory\n" );
-           exit( 1 );
-           }
-       }
-    for ( ; bi->num_comps < n; ++bi->num_comps )
-       bi->comps[bi->num_comps] = 0;
-    }
-
-
-/* Make a new empty bigint.  Fills in everything except sign and the
-** components.
-*/
-static real_bigint
-alloc( int num_comps )
-    {
-    real_bigint biR;
-
-    /* Can we recycle an old bigint? */
-    if ( free_list != (real_bigint) 0 )
-       {
-       biR = free_list;
-       free_list = biR->next;
-       --free_count;
-       if ( check_level >= 1 && biR->refs != 0 )
-           {
-           (void) fprintf( stderr, "alloc: refs was not 0\n" );
-           (void) kill( getpid(), SIGFPE );
-           }
-       more_comps( biR, num_comps );
-       }
-    else
-       {
-       /* No free bigints available - create a new one. */
-       biR = (real_bigint) malloc( sizeof(struct _real_bigint) );
-       if ( biR == (real_bigint) 0 )
-           {
-           (void) fprintf( stderr, "out of memory\n" );
-           exit( 1 );
-           }
-       biR->comps = (comp*) malloc( num_comps * sizeof(comp) );
-       if ( biR->comps == (comp*) 0 )
-           {
-           (void) fprintf( stderr, "out of memory\n" );
-           exit( 1 );
-           }
-       biR->max_comps = num_comps;
-       }
-    biR->num_comps = num_comps;
-    biR->refs = 1;
-    if ( check_level >= 3 )
-       {
-       /* The active list only gets maintained at check levels 3 or higher. */
-       biR->next = active_list;
-       active_list = biR;
-       }
-    else
-       biR->next = (real_bigint) 0;
-    ++active_count;
-    return biR;
-    }
-
-
-/* Make a modifiable copy of bi.  DOES consume bi. */
-static real_bigint
-clone( real_bigint bi )
-    {
-    real_bigint biR;
-    int c;
-
-    /* Very clever optimization. */
-    if ( bi->refs != PERMANENT && bi->refs == 1 )
-       return bi;
-
-    biR = alloc( bi->num_comps );
-    biR->sign = bi->sign;
-    for ( c = 0; c < bi->num_comps; ++c )
-       biR->comps[c] = bi->comps[c];
-    bi_free( bi );
-    return biR;
-    }
-
-
-/* Put bi into normal form.  Does not consume bi, of course.
-**
-** Normal form is:
-**  - All components >= 0 and < bi_radix.
-**  - Leading 0 components removed.
-**  - Sign either 1 or -1.
-**  - The number zero represented by a single 0 component and a sign of 1.
-*/
-static void
-normalize( real_bigint bi )
-    {
-    int c;
-
-    /* Borrow for negative components.  Got to be careful with the math here:
-    **   -9 / 10 == 0    -9 % 10 == -9
-    **   -10 / 10 == -1  -10 % 10 == 0
-    **   -11 / 10 == -1  -11 % 10 == -1
-    */
-    for ( c = 0; c < bi->num_comps - 1; ++c )
-       if ( bi->comps[c] < 0 )
-           {
-           bi->comps[c+1] += bi->comps[c] / bi_radix - 1;
-           bi->comps[c] = bi->comps[c] % bi_radix;
-           if ( bi->comps[c] != 0 )
-               bi->comps[c] += bi_radix;
-           else
-               bi->comps[c+1] += 1;
-           }
-    /* Is the top component negative? */
-    if ( bi->comps[bi->num_comps - 1] < 0 )
-       {
-       /* Switch the sign of the number, and fix up the components. */
-       bi->sign = -bi->sign;
-       for ( c = 0; c < bi->num_comps - 1; ++c )
-           {
-           bi->comps[c] =  bi_radix - bi->comps[c];
-           bi->comps[c + 1] += 1;
-           }
-       bi->comps[bi->num_comps - 1] = -bi->comps[bi->num_comps - 1];
-       }
-
-    /* Carry for components larger than the radix. */
-    for ( c = 0; c < bi->num_comps; ++c )
-       if ( bi->comps[c] >= bi_radix )
-           {
-           if ( c + 1 >= bi->num_comps )
-               more_comps( bi, bi->num_comps + 1 );
-           bi->comps[c+1] += bi->comps[c] / bi_radix;
-           bi->comps[c] = bi->comps[c] % bi_radix;
-           }
-
-    /* Trim off any leading zero components. */
-    for ( ; bi->num_comps > 1 && bi->comps[bi->num_comps-1] == 0; --bi->num_comps )
-       ;
-
-    /* Check for -0. */
-    if ( bi->num_comps == 1 && bi->comps[0] == 0 && bi->sign == -1 )
-       bi->sign = 1;
-    }
-
-
-static void
-check( real_bigint bi )
-    {
-    if ( check_level == 0 )
-       return;
-    if ( bi->refs == 0 )
-       {
-       (void) fprintf( stderr, "check: zero refs in bigint\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    if ( bi->refs < 0 )
-       {
-       (void) fprintf( stderr, "check: negative refs in bigint\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-    if ( check_level < 3 )
-       {
-       /* At check levels less than 3, active bigints have a zero next. */
-       if ( bi->next != (real_bigint) 0 )
-           {
-           (void) fprintf(
-               stderr, "check: attempt to use a bigint from the free list\n" );
-           (void) kill( getpid(), SIGFPE );
-           }
-       }
-    else
-       {
-       /* At check levels 3 or higher, active bigints must be on the active
-       ** list.
-       */
-       real_bigint p;
-
-       for ( p = active_list; p != (real_bigint) 0; p = p->next )
-           if ( p == bi )
-               break;
-       if ( p == (real_bigint) 0 )
-           {
-           (void) fprintf( stderr,
-               "check: attempt to use a bigint not on the active list\n" );
-           (void) kill( getpid(), SIGFPE );
-           }
-       }
-    if ( check_level >= 2 )
-       double_check();
-    if ( check_level >= 3 )
-       triple_check();
-    }
-
-
-static void
-double_check( void )
-    {
-    real_bigint p;
-    int c;
-
-    for ( p = free_list, c = 0; p != (real_bigint) 0; p = p->next, ++c )
-       if ( p->refs != 0 )
-           {
-           (void) fprintf( stderr,
-               "double_check: found a non-zero ref on the free list\n" );
-           (void) kill( getpid(), SIGFPE );
-           }
-    if ( c != free_count )
-       {
-       (void) fprintf( stderr,
-           "double_check: free_count is %d but the free list has %d items\n",
-           free_count, c );
-       (void) kill( getpid(), SIGFPE );
-       }
-    }
-
-
-static void
-triple_check( void )
-    {
-    real_bigint p;
-    int c;
-
-    for ( p = active_list, c = 0; p != (real_bigint) 0; p = p->next, ++c )
-       if ( p->refs == 0 )
-           {
-           (void) fprintf( stderr,
-               "triple_check: found a zero ref on the active list\n" );
-           (void) kill( getpid(), SIGFPE );
-           }
-    if ( c != active_count )
-       {
-       (void) fprintf( stderr,
-           "triple_check: active_count is %d but active_list has %d items\n",
-           free_count, c );
-       (void) kill( getpid(), SIGFPE );
-       }
-    }
-
-
-#ifdef DUMP
-/* Debug routine to dump out a complete bigint.  Does not consume bi. */
-static void
-dump( char* str, bigint obi )
-    {
-    int c;
-    real_bigint bi = (real_bigint) obi;
-
-    (void) fprintf( stdout, "dump %s at 0x%08x:\n", str, (unsigned int) bi );
-    (void) fprintf( stdout, "  refs: %d\n", bi->refs );
-    (void) fprintf( stdout, "  next: 0x%08x\n", (unsigned int) bi->next );
-    (void) fprintf( stdout, "  num_comps: %d\n", bi->num_comps );
-    (void) fprintf( stdout, "  max_comps: %d\n", bi->max_comps );
-    (void) fprintf( stdout, "  sign: %d\n", bi->sign );
-    for ( c = bi->num_comps - 1; c >= 0; --c )
-       (void) fprintf( stdout, "    comps[%d]: %11lld (0x%016llx)\n", c, (long long) bi->comps[c], (long long) bi->comps[c] );
-    (void) fprintf( stdout, "  print: " );
-    bi_print( stdout, bi_copy( bi ) );
-    (void) fprintf( stdout, "\n" );
-    }
-#endif /* DUMP */
-
-
-/* Trivial square-root routine so that we don't have to link in the math lib. */
-static int
-csqrt( comp c )
-    {
-    comp r, r2, diff;
-
-    if ( c < 0 )
-       {
-       (void) fprintf( stderr, "csqrt: imaginary result\n" );
-       (void) kill( getpid(), SIGFPE );
-       }
-
-    r = c / 2;
-    for (;;)
-       {
-       r2 = c / r;
-       diff = r - r2;
-       if ( diff == 0 || diff == -1 )
-           return (int) r;
-       if ( diff == 1 )
-           return (int) r2;
-       r = ( r + r2 ) / 2;
-       }
-    }
-
-
-/* Figure out how many bits are in a number. */
-static int
-cbits( comp c )
-    {
-    int b;
-
-    for ( b = 0; c != 0; ++b )
-       c >>= 1;
-    return b;
-    }

diff --git a/src/rt/bigint/low_primes.h b/src/rt/bigint/low_primes.h
deleted file mode 100644 (file)
index c9d3df0..0000000
--- a/src/rt/bigint/low_primes.h
+++ /dev/null
@@ -1,1069 +0,0 @@
-/* Primes up to 100000. */
-static long low_primes[] = {
-        2,     3,     5,     7,    11,    13,    17,    19,    23,
-       29,    31,    37,    41,    43,    47,    53,    59,    61,
-       67,    71,    73,    79,    83,    89,    97,   101,   103,
-      107,   109,   113,   127,   131,   137,   139,   149,   151,
-      157,   163,   167,   173,   179,   181,   191,   193,   197,
-      199,   211,   223,   227,   229,   233,   239,   241,   251,
-      257,   263,   269,   271,   277,   281,   283,   293,   307,
-      311,   313,   317,   331,   337,   347,   349,   353,   359,
-      367,   373,   379,   383,   389,   397,   401,   409,   419,
-      421,   431,   433,   439,   443,   449,   457,   461,   463,
-      467,   479,   487,   491,   499,   503,   509,   521,   523,
-      541,   547,   557,   563,   569,   571,   577,   587,   593,
-      599,   601,   607,   613,   617,   619,   631,   641,   643,
-      647,   653,   659,   661,   673,   677,   683,   691,   701,
-      709,   719,   727,   733,   739,   743,   751,   757,   761,
-      769,   773,   787,   797,   809,   811,   821,   823,   827,
-      829,   839,   853,   857,   859,   863,   877,   881,   883,
-      887,   907,   911,   919,   929,   937,   941,   947,   953,
-      967,   971,   977,   983,   991,   997,  1009,  1013,  1019,
-     1021,  1031,  1033,  1039,  1049,  1051,  1061,  1063,  1069,
-     1087,  1091,  1093,  1097,  1103,  1109,  1117,  1123,  1129,
-     1151,  1153,  1163,  1171,  1181,  1187,  1193,  1201,  1213,
-     1217,  1223,  1229,  1231,  1237,  1249,  1259,  1277,  1279,
-     1283,  1289,  1291,  1297,  1301,  1303,  1307,  1319,  1321,
-     1327,  1361,  1367,  1373,  1381,  1399,  1409,  1423,  1427,
-     1429,  1433,  1439,  1447,  1451,  1453,  1459,  1471,  1481,
-     1483,  1487,  1489,  1493,  1499,  1511,  1523,  1531,  1543,
-     1549,  1553,  1559,  1567,  1571,  1579,  1583,  1597,  1601,
-     1607,  1609,  1613,  1619,  1621,  1627,  1637,  1657,  1663,
-     1667,  1669,  1693,  1697,  1699,  1709,  1721,  1723,  1733,
-     1741,  1747,  1753,  1759,  1777,  1783,  1787,  1789,  1801,
-     1811,  1823,  1831,  1847,  1861,  1867,  1871,  1873,  1877,
-     1879,  1889,  1901,  1907,  1913,  1931,  1933,  1949,  1951,
-     1973,  1979,  1987,  1993,  1997,  1999,  2003,  2011,  2017,
-     2027,  2029,  2039,  2053,  2063,  2069,  2081,  2083,  2087,
-     2089,  2099,  2111,  2113,  2129,  2131,  2137,  2141,  2143,
-     2153,  2161,  2179,  2203,  2207,  2213,  2221,  2237,  2239,
-     2243,  2251,  2267,  2269,  2273,  2281,  2287,  2293,  2297,
-     2309,  2311,  2333,  2339,  2341,  2347,  2351,  2357,  2371,
-     2377,  2381,  2383,  2389,  2393,  2399,  2411,  2417,  2423,
-     2437,  2441,  2447,  2459,  2467,  2473,  2477,  2503,  2521,
-     2531,  2539,  2543,  2549,  2551,  2557,  2579,  2591,  2593,
-     2609,  2617,  2621,  2633,  2647,  2657,  2659,  2663,  2671,
-     2677,  2683,  2687,  2689,  2693,  2699,  2707,  2711,  2713,
-     2719,  2729,  2731,  2741,  2749,  2753,  2767,  2777,  2789,
-     2791,  2797,  2801,  2803,  2819,  2833,  2837,  2843,  2851,
-     2857,  2861,  2879,  2887,  2897,  2903,  2909,  2917,  2927,
-     2939,  2953,  2957,  2963,  2969,  2971,  2999,  3001,  3011,
-     3019,  3023,  3037,  3041,  3049,  3061,  3067,  3079,  3083,
-     3089,  3109,  3119,  3121,  3137,  3163,  3167,  3169,  3181,
-     3187,  3191,  3203,  3209,  3217,  3221,  3229,  3251,  3253,
-     3257,  3259,  3271,  3299,  3301,  3307,  3313,  3319,  3323,
-     3329,  3331,  3343,  3347,  3359,  3361,  3371,  3373,  3389,
-     3391,  3407,  3413,  3433,  3449,  3457,  3461,  3463,  3467,
-     3469,  3491,  3499,  3511,  3517,  3527,  3529,  3533,  3539,
-     3541,  3547,  3557,  3559,  3571,  3581,  3583,  3593,  3607,
-     3613,  3617,  3623,  3631,  3637,  3643,  3659,  3671,  3673,
-     3677,  3691,  3697,  3701,  3709,  3719,  3727,  3733,  3739,
-     3761,  3767,  3769,  3779,  3793,  3797,  3803,  3821,  3823,
-     3833,  3847,  3851,  3853,  3863,  3877,  3881,  3889,  3907,
-     3911,  3917,  3919,  3923,  3929,  3931,  3943,  3947,  3967,
-     3989,  4001,  4003,  4007,  4013,  4019,  4021,  4027,  4049,
-     4051,  4057,  4073,  4079,  4091,  4093,  4099,  4111,  4127,
-     4129,  4133,  4139,  4153,  4157,  4159,  4177,  4201,  4211,
-     4217,  4219,  4229,  4231,  4241,  4243,  4253,  4259,  4261,
-     4271,  4273,  4283,  4289,  4297,  4327,  4337,  4339,  4349,
-     4357,  4363,  4373,  4391,  4397,  4409,  4421,  4423,  4441,
-     4447,  4451,  4457,  4463,  4481,  4483,  4493,  4507,  4513,
-     4517,  4519,  4523,  4547,  4549,  4561,  4567,  4583,  4591,
-     4597,  4603,  4621,  4637,  4639,  4643,  4649,  4651,  4657,
-     4663,  4673,  4679,  4691,  4703,  4721,  4723,  4729,  4733,
-     4751,  4759,  4783,  4787,  4789,  4793,  4799,  4801,  4813,
-     4817,  4831,  4861,  4871,  4877,  4889,  4903,  4909,  4919,
-     4931,  4933,  4937,  4943,  4951,  4957,  4967,  4969,  4973,
-     4987,  4993,  4999,  5003,  5009,  5011,  5021,  5023,  5039,
-     5051,  5059,  5077,  5081,  5087,  5099,  5101,  5107,  5113,
-     5119,  5147,  5153,  5167,  5171,  5179,  5189,  5197,  5209,
-     5227,  5231,  5233,  5237,  5261,  5273,  5279,  5281,  5297,
-     5303,  5309,  5323,  5333,  5347,  5351,  5381,  5387,  5393,
-     5399,  5407,  5413,  5417,  5419,  5431,  5437,  5441,  5443,
-     5449,  5471,  5477,  5479,  5483,  5501,  5503,  5507,  5519,
-     5521,  5527,  5531,  5557,  5563,  5569,  5573,  5581,  5591,
-     5623,  5639,  5641,  5647,  5651,  5653,  5657,  5659,  5669,
-     5683,  5689,  5693,  5701,  5711,  5717,  5737,  5741,  5743,
-     5749,  5779,  5783,  5791,  5801,  5807,  5813,  5821,  5827,
-     5839,  5843,  5849,  5851,  5857,  5861,  5867,  5869,  5879,
-     5881,  5897,  5903,  5923,  5927,  5939,  5953,  5981,  5987,
-     6007,  6011,  6029,  6037,  6043,  6047,  6053,  6067,  6073,
-     6079,  6089,  6091,  6101,  6113,  6121,  6131,  6133,  6143,
-     6151,  6163,  6173,  6197,  6199,  6203,  6211,  6217,  6221,
-     6229,  6247,  6257,  6263,  6269,  6271,  6277,  6287,  6299,
-     6301,  6311,  6317,  6323,  6329,  6337,  6343,  6353,  6359,
-     6361,  6367,  6373,  6379,  6389,  6397,  6421,  6427,  6449,
-     6451,  6469,  6473,  6481,  6491,  6521,  6529,  6547,  6551,
-     6553,  6563,  6569,  6571,  6577,  6581,  6599,  6607,  6619,
-     6637,  6653,  6659,  6661,  6673,  6679,  6689,  6691,  6701,
-     6703,  6709,  6719,  6733,  6737,  6761,  6763,  6779,  6781,
-     6791,  6793,  6803,  6823,  6827,  6829,  6833,  6841,  6857,
-     6863,  6869,  6871,  6883,  6899,  6907,  6911,  6917,  6947,
-     6949,  6959,  6961,  6967,  6971,  6977,  6983,  6991,  6997,
-     7001,  7013,  7019,  7027,  7039,  7043,  7057,  7069,  7079,
-     7103,  7109,  7121,  7127,  7129,  7151,  7159,  7177,  7187,
-     7193,  7207,  7211,  7213,  7219,  7229,  7237,  7243,  7247,
-     7253,  7283,  7297,  7307,  7309,  7321,  7331,  7333,  7349,
-     7351,  7369,  7393,  7411,  7417,  7433,  7451,  7457,  7459,
-     7477,  7481,  7487,  7489,  7499,  7507,  7517,  7523,  7529,
-     7537,  7541,  7547,  7549,  7559,  7561,  7573,  7577,  7583,
-     7589,  7591,  7603,  7607,  7621,  7639,  7643,  7649,  7669,
-     7673,  7681,  7687,  7691,  7699,  7703,  7717,  7723,  7727,
-     7741,  7753,  7757,  7759,  7789,  7793,  7817,  7823,  7829,
-     7841,  7853,  7867,  7873,  7877,  7879,  7883,  7901,  7907,
-     7919,  7927,  7933,  7937,  7949,  7951,  7963,  7993,  8009,
-     8011,  8017,  8039,  8053,  8059,  8069,  8081,  8087,  8089,
-     8093,  8101,  8111,  8117,  8123,  8147,  8161,  8167,  8171,
-     8179,  8191,  8209,  8219,  8221,  8231,  8233,  8237,  8243,
-     8263,  8269,  8273,  8287,  8291,  8293,  8297,  8311,  8317,
-     8329,  8353,  8363,  8369,  8377,  8387,  8389,  8419,  8423,
-     8429,  8431,  8443,  8447,  8461,  8467,  8501,  8513,  8521,
-     8527,  8537,  8539,  8543,  8563,  8573,  8581,  8597,  8599,
-     8609,  8623,  8627,  8629,  8641,  8647,  8663,  8669,  8677,
-     8681,  8689,  8693,  8699,  8707,  8713,  8719,  8731,  8737,
-     8741,  8747,  8753,  8761,  8779,  8783,  8803,  8807,  8819,
-     8821,  8831,  8837,  8839,  8849,  8861,  8863,  8867,  8887,
-     8893,  8923,  8929,  8933,  8941,  8951,  8963,  8969,  8971,
-     8999,  9001,  9007,  9011,  9013,  9029,  9041,  9043,  9049,
-     9059,  9067,  9091,  9103,  9109,  9127,  9133,  9137,  9151,
-     9157,  9161,  9173,  9181,  9187,  9199,  9203,  9209,  9221,
-     9227,  9239,  9241,  9257,  9277,  9281,  9283,  9293,  9311,
-     9319,  9323,  9337,  9341,  9343,  9349,  9371,  9377,  9391,
-     9397,  9403,  9413,  9419,  9421,  9431,  9433,  9437,  9439,
-     9461,  9463,  9467,  9473,  9479,  9491,  9497,  9511,  9521,
-     9533,  9539,  9547,  9551,  9587,  9601,  9613,  9619,  9623,
-     9629,  9631,  9643,  9649,  9661,  9677,  9679,  9689,  9697,
-     9719,  9721,  9733,  9739,  9743,  9749,  9767,  9769,  9781,
-     9787,  9791,  9803,  9811,  9817,  9829,  9833,  9839,  9851,
-     9857,  9859,  9871,  9883,  9887,  9901,  9907,  9923,  9929,
-     9931,  9941,  9949,  9967,  9973, 10007, 10009, 10037, 10039,
-    10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111,
-    10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181,
-    10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271,
-    10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337,
-    10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453,
-    10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529,
-    10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627,
-    10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709,
-    10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789,
-    10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883,
-    10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973,
-    10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069,
-    11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149,
-    11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243,
-    11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317,
-    11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411,
-    11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491,
-    11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593,
-    11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699,
-    11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789,
-    11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863,
-    11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939,
-    11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011,
-    12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107,
-    12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197,
-    12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269,
-    12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373,
-    12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437,
-    12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511,
-    12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583,
-    12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653,
-    12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743,
-    12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829,
-    12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919,
-    12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001,
-    13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093,
-    13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163,
-    13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249,
-    13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337,
-    13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441,
-    13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523,
-    13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627,
-    13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697,
-    13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763,
-    13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873,
-    13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931,
-    13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033,
-    14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149,
-    14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249,
-    14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347,
-    14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431,
-    14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533,
-    14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593,
-    14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683,
-    14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753,
-    14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827,
-    14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897,
-    14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013,
-    15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101,
-    15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187,
-    15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269,
-    15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329,
-    15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401,
-    15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493,
-    15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583,
-    15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661,
-    15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739,
-    15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809,
-    15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907,
-    15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001,
-    16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087,
-    16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187,
-    16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267,
-    16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369,
-    16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453,
-    16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561,
-    16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651,
-    16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741,
-    16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843,
-    16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931,
-    16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021,
-    17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099,
-    17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191,
-    17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299,
-    17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383,
-    17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449,
-    17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519,
-    17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609,
-    17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713,
-    17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807,
-    17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909,
-    17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977,
-    17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059,
-    18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133,
-    18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223,
-    18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301,
-    18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379,
-    18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457,
-    18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541,
-    18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679,
-    18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773,
-    18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911,
-    18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009,
-    19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087,
-    19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211,
-    19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289,
-    19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391,
-    19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447,
-    19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507,
-    19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597,
-    19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717,
-    19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801,
-    19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891,
-    19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979,
-    19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051,
-    20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129,
-    20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219,
-    20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327,
-    20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393,
-    20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483,
-    20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593,
-    20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707,
-    20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771,
-    20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887,
-    20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963,
-    20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031,
-    21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143,
-    21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211,
-    21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319,
-    21323, 21341, 21347, 21377, 21379, 21383, 21391, 21397, 21401,
-    21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499,
-    21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569,
-    21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647,
-    21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739,
-    21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821,
-    21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911,
-    21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013,
-    22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079,
-    22091, 22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153,
-    22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271,
-    22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349,
-    22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447,
-    22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543,
-    22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639,
-    22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717,
-    22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787,
-    22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901,
-    22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, 23003,
-    23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057,
-    23059, 23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143,
-    23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227,
-    23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327,
-    23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447,
-    23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557,
-    23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623,
-    23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689,
-    23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789,
-    23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873,
-    23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957,
-    23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029,
-    24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103,
-    24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 24179,
-    24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281,
-    24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407,
-    24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499,
-    24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611,
-    24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709,
-    24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821,
-    24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 24919,
-    24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, 25013,
-    25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117,
-    25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189,
-    25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303,
-    25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373,
-    25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463,
-    25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583,
-    25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657,
-    25667, 25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747,
-    25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847,
-    25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933,
-    25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, 26017,
-    26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113,
-    26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203,
-    26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293,
-    26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387,
-    26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459,
-    26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573,
-    26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683,
-    26687, 26693, 26699, 26701, 26711, 26713, 26717, 26723, 26729,
-    26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833,
-    26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903,
-    26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993,
-    27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077,
-    27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197,
-    27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283,
-    27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409, 27427,
-    27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527,
-    27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631,
-    27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737,
-    27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791,
-    27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 27851,
-    27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953,
-    27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051,
-    28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123,
-    28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277,
-    28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351,
-    28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447,
-    28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547,
-    28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607,
-    28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663,
-    28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753,
-    28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843,
-    28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933,
-    28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033,
-    29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147,
-    29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221,
-    29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327,
-    29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401,
-    29411, 29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501,
-    29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599,
-    29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717,
-    29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833,
-    29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921,
-    29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047,
-    30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119,
-    30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203,
-    30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307,
-    30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403,
-    30427, 30431, 30449, 30467, 30469, 30491, 30493, 30497, 30509,
-    30517, 30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631,
-    30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703,
-    30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809,
-    30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871,
-    30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977,
-    30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079,
-    31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159,
-    31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237,
-    31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319,
-    31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393,
-    31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531,
-    31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627,
-    31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723,
-    31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817,
-    31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963,
-    31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057,
-    32059, 32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119,
-    32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213,
-    32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309,
-    32321, 32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371,
-    32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441, 32443,
-    32467, 32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537,
-    32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611,
-    32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717,
-    32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803,
-    32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917,
-    32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993,
-    32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073,
-    33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, 33179,
-    33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289,
-    33301, 33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353,
-    33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457, 33461,
-    33469, 33479, 33487, 33493, 33503, 33521, 33529, 33533, 33547,
-    33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613,
-    33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703,
-    33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773,
-    33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863,
-    33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961,
-    33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123,
-    34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, 34211,
-    34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283,
-    34297, 34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361,
-    34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 34469,
-    34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537,
-    34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631,
-    34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721,
-    34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819,
-    34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913,
-    34919, 34939, 34949, 34961, 34963, 34981, 35023, 35027, 35051,
-    35053, 35059, 35069, 35081, 35083, 35089, 35099, 35107, 35111,
-    35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221,
-    35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317,
-    35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407,
-    35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509,
-    35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591,
-    35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747,
-    35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837,
-    35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923,
-    35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999, 36007,
-    36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097,
-    36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209,
-    36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299,
-    36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389,
-    36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497,
-    36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583,
-    36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677,
-    36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761,
-    36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833,
-    36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919,
-    36923, 36929, 36931, 36943, 36947, 36973, 36979, 36997, 37003,
-    37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097,
-    37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201,
-    37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313,
-    37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397,
-    37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501,
-    37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567,
-    37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643,
-    37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781,
-    37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871,
-    37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987,
-    37991, 37993, 37997, 38011, 38039, 38047, 38053, 38069, 38083,
-    38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197,
-    38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287,
-    38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371,
-    38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501,
-    38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611,
-    38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699,
-    38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767,
-    38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867,
-    38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959,
-    38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079,
-    39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157,
-    39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229,
-    39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323,
-    39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409,
-    39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511,
-    39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623,
-    39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727,
-    39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821, 39827,
-    39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883,
-    39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989,
-    40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099,
-    40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177,
-    40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283,
-    40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429,
-    40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519,
-    40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609,
-    40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751,
-    40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823, 40829,
-    40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903,
-    40927, 40933, 40939, 40949, 40961, 40973, 40993, 41011, 41017,
-    41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117,
-    41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189,
-    41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257,
-    41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381,
-    41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479,
-    41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579,
-    41593, 41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641,
-    41647, 41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737,
-    41759, 41761, 41771, 41777, 41801, 41809, 41813, 41843, 41849,
-    41851, 41863, 41879, 41887, 41893, 41897, 41903, 41911, 41927,
-    41941, 41947, 41953, 41957, 41959, 41969, 41981, 41983, 41999,
-    42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083,
-    42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187,
-    42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257, 42281,
-    42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359,
-    42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433, 42437,
-    42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, 42491,
-    42499, 42509, 42533, 42557, 42569, 42571, 42577, 42589, 42611,
-    42641, 42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701,
-    42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773,
-    42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 42859,
-    42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961,
-    42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051,
-    43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177,
-    43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291,
-    43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411,
-    43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541,
-    43543, 43573, 43577, 43579, 43591, 43597, 43607, 43609, 43613,
-    43627, 43633, 43649, 43651, 43661, 43669, 43691, 43711, 43717,
-    43721, 43753, 43759, 43777, 43781, 43783, 43787, 43789, 43793,
-    43801, 43853, 43867, 43889, 43891, 43913, 43933, 43943, 43951,
-    43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 44021,
-    44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101,
-    44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189,
-    44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269,
-    44273, 44279, 44281, 44293, 44351, 44357, 44371, 44381, 44383,
-    44389, 44417, 44449, 44453, 44483, 44491, 44497, 44501, 44507,
-    44519, 44531, 44533, 44537, 44543, 44549, 44563, 44579, 44587,
-    44617, 44621, 44623, 44633, 44641, 44647, 44651, 44657, 44683,
-    44687, 44699, 44701, 44711, 44729, 44741, 44753, 44771, 44773,
-    44777, 44789, 44797, 44809, 44819, 44839, 44843, 44851, 44867,
-    44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 44959,
-    44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077,
-    45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179,
-    45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289,
-    45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361,
-    45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491,
-    45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587,
-    45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677,
-    45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, 45779,
-    45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869,
-    45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989,
-    46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099,
-    46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187,
-    46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301,
-    46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411,
-    46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499,
-    46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591,
-    46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681,
-    46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769,
-    46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861,
-    46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997,
-    47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119,
-    47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207,
-    47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303,
-    47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389,
-    47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501,
-    47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581,
-    47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 47659,
-    47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743,
-    47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843,
-    47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947,
-    47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049,
-    48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163,
-    48179, 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271,
-    48281, 48299, 48311, 48313, 48337, 48341, 48353, 48371, 48383,
-    48397, 48407, 48409, 48413, 48437, 48449, 48463, 48473, 48479,
-    48481, 48487, 48491, 48497, 48523, 48527, 48533, 48539, 48541,
-    48563, 48571, 48589, 48593, 48611, 48619, 48623, 48647, 48649,
-    48661, 48673, 48677, 48679, 48731, 48733, 48751, 48757, 48761,
-    48767, 48779, 48781, 48787, 48799, 48809, 48817, 48821, 48823,
-    48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 48947,
-    48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033,
-    49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121,
-    49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201,
-    49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307,
-    49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409,
-    49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481,
-    49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597,
-    49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681,
-    49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787,
-    49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871,
-    49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957,
-    49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, 50053,
-    50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129,
-    50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231,
-    50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333,
-    50341, 50359, 50363, 50377, 50383, 50387, 50411, 50417, 50423,
-    50441, 50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543,
-    50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647,
-    50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773,
-    50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50873,
-    50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971,
-    50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071,
-    51109, 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197,
-    51199, 51203, 51217, 51229, 51239, 51241, 51257, 51263, 51283,
-    51287, 51307, 51329, 51341, 51343, 51347, 51349, 51361, 51383,
-    51407, 51413, 51419, 51421, 51427, 51431, 51437, 51439, 51449,
-    51461, 51473, 51479, 51481, 51487, 51503, 51511, 51517, 51521,
-    51539, 51551, 51563, 51577, 51581, 51593, 51599, 51607, 51613,
-    51631, 51637, 51647, 51659, 51673, 51679, 51683, 51691, 51713,
-    51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 51817,
-    51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899,
-    51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991,
-    52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103,
-    52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189,
-    52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291,
-    52301, 52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391,
-    52433, 52453, 52457, 52489, 52501, 52511, 52517, 52529, 52541,
-    52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627,
-    52631, 52639, 52667, 52673, 52691, 52697, 52709, 52711, 52721,
-    52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817,
-    52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919,
-    52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999, 53003,
-    53017, 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101,
-    53113, 53117, 53129, 53147, 53149, 53161, 53171, 53173, 53189,
-    53197, 53201, 53231, 53233, 53239, 53267, 53269, 53279, 53281,
-    53299, 53309, 53323, 53327, 53353, 53359, 53377, 53381, 53401,
-    53407, 53411, 53419, 53437, 53441, 53453, 53479, 53503, 53507,
-    53527, 53549, 53551, 53569, 53591, 53593, 53597, 53609, 53611,
-    53617, 53623, 53629, 53633, 53639, 53653, 53657, 53681, 53693,
-    53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 53791,
-    53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891,
-    53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987,
-    53993, 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091,
-    54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193,
-    54217, 54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323,
-    54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, 54409,
-    54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497,
-    54499, 54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563,
-    54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 54647,
-    54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 54767,
-    54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877,
-    54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979,
-    54983, 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073,
-    55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201,
-    55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291,
-    55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381,
-    55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 55511,
-    55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621,
-    55631, 55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691,
-    55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793, 55799,
-    55807, 55813, 55817, 55819, 55823, 55829, 55837, 55843, 55849,
-    55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933,
-    55949, 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053,
-    56081, 56087, 56093, 56099, 56101, 56113, 56123, 56131, 56149,
-    56167, 56171, 56179, 56197, 56207, 56209, 56237, 56239, 56249,
-    56263, 56267, 56269, 56299, 56311, 56333, 56359, 56369, 56377,
-    56383, 56393, 56401, 56417, 56431, 56437, 56443, 56453, 56467,
-    56473, 56477, 56479, 56489, 56501, 56503, 56509, 56519, 56527,
-    56531, 56533, 56543, 56569, 56591, 56597, 56599, 56611, 56629,
-    56633, 56659, 56663, 56671, 56681, 56687, 56701, 56711, 56713,
-    56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807, 56809,
-    56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897,
-    56909, 56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963,
-    56983, 56989, 56993, 56999, 57037, 57041, 57047, 57059, 57073,
-    57077, 57089, 57097, 57107, 57119, 57131, 57139, 57143, 57149,
-    57163, 57173, 57179, 57191, 57193, 57203, 57221, 57223, 57241,
-    57251, 57259, 57269, 57271, 57283, 57287, 57301, 57329, 57331,
-    57347, 57349, 57367, 57373, 57383, 57389, 57397, 57413, 57427,
-    57457, 57467, 57487, 57493, 57503, 57527, 57529, 57557, 57559,
-    57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 57667,
-    57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737,
-    57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809, 57829,
-    57839, 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923,
-    57943, 57947, 57973, 57977, 57991, 58013, 58027, 58031, 58043,
-    58049, 58057, 58061, 58067, 58073, 58099, 58109, 58111, 58129,
-    58147, 58151, 58153, 58169, 58171, 58189, 58193, 58199, 58207,
-    58211, 58217, 58229, 58231, 58237, 58243, 58271, 58309, 58313,
-    58321, 58337, 58363, 58367, 58369, 58379, 58391, 58393, 58403,
-    58411, 58417, 58427, 58439, 58441, 58451, 58453, 58477, 58481,
-    58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, 58603,
-    58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711,
-    58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831,
-    58889, 58897, 58901, 58907, 58909, 58913, 58921, 58937, 58943,
-    58963, 58967, 58979, 58991, 58997, 59009, 59011, 59021, 59023,
-    59029, 59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107,
-    59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197,
-    59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273,
-    59281, 59333, 59341, 59351, 59357, 59359, 59369, 59377, 59387,
-    59393, 59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453,
-    59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557, 59561,
-    59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, 59659,
-    59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743,
-    59747, 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863,
-    59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999,
-    60013, 60017, 60029, 60037, 60041, 60077, 60083, 60089, 60091,
-    60101, 60103, 60107, 60127, 60133, 60139, 60149, 60161, 60167,
-    60169, 60209, 60217, 60223, 60251, 60257, 60259, 60271, 60289,
-    60293, 60317, 60331, 60337, 60343, 60353, 60373, 60383, 60397,
-    60413, 60427, 60443, 60449, 60457, 60493, 60497, 60509, 60521,
-    60527, 60539, 60589, 60601, 60607, 60611, 60617, 60623, 60631,
-    60637, 60647, 60649, 60659, 60661, 60679, 60689, 60703, 60719,
-    60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779, 60793,
-    60811, 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913,
-    60917, 60919, 60923, 60937, 60943, 60953, 60961, 61001, 61007,
-    61027, 61031, 61043, 61051, 61057, 61091, 61099, 61121, 61129,
-    61141, 61151, 61153, 61169, 61211, 61223, 61231, 61253, 61261,
-    61283, 61291, 61297, 61331, 61333, 61339, 61343, 61357, 61363,
-    61379, 61381, 61403, 61409, 61417, 61441, 61463, 61469, 61471,
-    61483, 61487, 61493, 61507, 61511, 61519, 61543, 61547, 61553,
-    61559, 61561, 61583, 61603, 61609, 61613, 61627, 61631, 61637,
-    61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 61717,
-    61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843,
-    61861, 61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967,
-    61979, 61981, 61987, 61991, 62003, 62011, 62017, 62039, 62047,
-    62053, 62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137,
-    62141, 62143, 62171, 62189, 62191, 62201, 62207, 62213, 62219,
-    62233, 62273, 62297, 62299, 62303, 62311, 62323, 62327, 62347,
-    62351, 62383, 62401, 62417, 62423, 62459, 62467, 62473, 62477,
-    62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581,
-    62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 62659,
-    62683, 62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773,
-    62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873, 62897,
-    62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983,
-    62987, 62989, 63029, 63031, 63059, 63067, 63073, 63079, 63097,
-    63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211,
-    63241, 63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331,
-    63337, 63347, 63353, 63361, 63367, 63377, 63389, 63391, 63397,
-    63409, 63419, 63421, 63439, 63443, 63463, 63467, 63473, 63487,
-    63493, 63499, 63521, 63527, 63533, 63541, 63559, 63577, 63587,
-    63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649,
-    63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719,
-    63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799, 63803,
-    63809, 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907,
-    63913, 63929, 63949, 63977, 63997, 64007, 64013, 64019, 64033,
-    64037, 64063, 64067, 64081, 64091, 64109, 64123, 64151, 64153,
-    64157, 64171, 64187, 64189, 64217, 64223, 64231, 64237, 64271,
-    64279, 64283, 64301, 64303, 64319, 64327, 64333, 64373, 64381,
-    64399, 64403, 64433, 64439, 64451, 64453, 64483, 64489, 64499,
-    64513, 64553, 64567, 64577, 64579, 64591, 64601, 64609, 64613,
-    64621, 64627, 64633, 64661, 64663, 64667, 64679, 64693, 64709,
-    64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849,
-    64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927,
-    64937, 64951, 64969, 64997, 65003, 65011, 65027, 65029, 65033,
-    65053, 65063, 65071, 65089, 65099, 65101, 65111, 65119, 65123,
-    65129, 65141, 65147, 65167, 65171, 65173, 65179, 65183, 65203,
-    65213, 65239, 65257, 65267, 65269, 65287, 65293, 65309, 65323,
-    65327, 65353, 65357, 65371, 65381, 65393, 65407, 65413, 65419,
-    65423, 65437, 65447, 65449, 65479, 65497, 65519, 65521, 65537,
-    65539, 65543, 65551, 65557, 65563, 65579, 65581, 65587, 65599,
-    65609, 65617, 65629, 65633, 65647, 65651, 65657, 65677, 65687,
-    65699, 65701, 65707, 65713, 65717, 65719, 65729, 65731, 65761,
-    65777, 65789, 65809, 65827, 65831, 65837, 65839, 65843, 65851,
-    65867, 65881, 65899, 65921, 65927, 65929, 65951, 65957, 65963,
-    65981, 65983, 65993, 66029, 66037, 66041, 66047, 66067, 66071,
-    66083, 66089, 66103, 66107, 66109, 66137, 66161, 66169, 66173,
-    66179, 66191, 66221, 66239, 66271, 66293, 66301, 66337, 66343,
-    66347, 66359, 66361, 66373, 66377, 66383, 66403, 66413, 66431,
-    66449, 66457, 66463, 66467, 66491, 66499, 66509, 66523, 66529,
-    66533, 66541, 66553, 66569, 66571, 66587, 66593, 66601, 66617,
-    66629, 66643, 66653, 66683, 66697, 66701, 66713, 66721, 66733,
-    66739, 66749, 66751, 66763, 66791, 66797, 66809, 66821, 66841,
-    66851, 66853, 66863, 66877, 66883, 66889, 66919, 66923, 66931,
-    66943, 66947, 66949, 66959, 66973, 66977, 67003, 67021, 67033,
-    67043, 67049, 67057, 67061, 67073, 67079, 67103, 67121, 67129,
-    67139, 67141, 67153, 67157, 67169, 67181, 67187, 67189, 67211,
-    67213, 67217, 67219, 67231, 67247, 67261, 67271, 67273, 67289,
-    67307, 67339, 67343, 67349, 67369, 67391, 67399, 67409, 67411,
-    67421, 67427, 67429, 67433, 67447, 67453, 67477, 67481, 67489,
-    67493, 67499, 67511, 67523, 67531, 67537, 67547, 67559, 67567,
-    67577, 67579, 67589, 67601, 67607, 67619, 67631, 67651, 67679,
-    67699, 67709, 67723, 67733, 67741, 67751, 67757, 67759, 67763,
-    67777, 67783, 67789, 67801, 67807, 67819, 67829, 67843, 67853,
-    67867, 67883, 67891, 67901, 67927, 67931, 67933, 67939, 67943,
-    67957, 67961, 67967, 67979, 67987, 67993, 68023, 68041, 68053,
-    68059, 68071, 68087, 68099, 68111, 68113, 68141, 68147, 68161,
-    68171, 68207, 68209, 68213, 68219, 68227, 68239, 68261, 68279,
-    68281, 68311, 68329, 68351, 68371, 68389, 68399, 68437, 68443,
-    68447, 68449, 68473, 68477, 68483, 68489, 68491, 68501, 68507,
-    68521, 68531, 68539, 68543, 68567, 68581, 68597, 68611, 68633,
-    68639, 68659, 68669, 68683, 68687, 68699, 68711, 68713, 68729,
-    68737, 68743, 68749, 68767, 68771, 68777, 68791, 68813, 68819,
-    68821, 68863, 68879, 68881, 68891, 68897, 68899, 68903, 68909,
-    68917, 68927, 68947, 68963, 68993, 69001, 69011, 69019, 69029,
-    69031, 69061, 69067, 69073, 69109, 69119, 69127, 69143, 69149,
-    69151, 69163, 69191, 69193, 69197, 69203, 69221, 69233, 69239,
-    69247, 69257, 69259, 69263, 69313, 69317, 69337, 69341, 69371,
-    69379, 69383, 69389, 69401, 69403, 69427, 69431, 69439, 69457,
-    69463, 69467, 69473, 69481, 69491, 69493, 69497, 69499, 69539,
-    69557, 69593, 69623, 69653, 69661, 69677, 69691, 69697, 69709,
-    69737, 69739, 69761, 69763, 69767, 69779, 69809, 69821, 69827,
-    69829, 69833, 69847, 69857, 69859, 69877, 69899, 69911, 69929,
-    69931, 69941, 69959, 69991, 69997, 70001, 70003, 70009, 70019,
-    70039, 70051, 70061, 70067, 70079, 70099, 70111, 70117, 70121,
-    70123, 70139, 70141, 70157, 70163, 70177, 70181, 70183, 70199,
-    70201, 70207, 70223, 70229, 70237, 70241, 70249, 70271, 70289,
-    70297, 70309, 70313, 70321, 70327, 70351, 70373, 70379, 70381,
-    70393, 70423, 70429, 70439, 70451, 70457, 70459, 70481, 70487,
-    70489, 70501, 70507, 70529, 70537, 70549, 70571, 70573, 70583,
-    70589, 70607, 70619, 70621, 70627, 70639, 70657, 70663, 70667,
-    70687, 70709, 70717, 70729, 70753, 70769, 70783, 70793, 70823,
-    70841, 70843, 70849, 70853, 70867, 70877, 70879, 70891, 70901,
-    70913, 70919, 70921, 70937, 70949, 70951, 70957, 70969, 70979,
-    70981, 70991, 70997, 70999, 71011, 71023, 71039, 71059, 71069,
-    71081, 71089, 71119, 71129, 71143, 71147, 71153, 71161, 71167,
-    71171, 71191, 71209, 71233, 71237, 71249, 71257, 71261, 71263,
-    71287, 71293, 71317, 71327, 71329, 71333, 71339, 71341, 71347,
-    71353, 71359, 71363, 71387, 71389, 71399, 71411, 71413, 71419,
-    71429, 71437, 71443, 71453, 71471, 71473, 71479, 71483, 71503,
-    71527, 71537, 71549, 71551, 71563, 71569, 71593, 71597, 71633,
-    71647, 71663, 71671, 71693, 71699, 71707, 71711, 71713, 71719,
-    71741, 71761, 71777, 71789, 71807, 71809, 71821, 71837, 71843,
-    71849, 71861, 71867, 71879, 71881, 71887, 71899, 71909, 71917,
-    71933, 71941, 71947, 71963, 71971, 71983, 71987, 71993, 71999,
-    72019, 72031, 72043, 72047, 72053, 72073, 72077, 72089, 72091,
-    72101, 72103, 72109, 72139, 72161, 72167, 72169, 72173, 72211,
-    72221, 72223, 72227, 72229, 72251, 72253, 72269, 72271, 72277,
-    72287, 72307, 72313, 72337, 72341, 72353, 72367, 72379, 72383,
-    72421, 72431, 72461, 72467, 72469, 72481, 72493, 72497, 72503,
-    72533, 72547, 72551, 72559, 72577, 72613, 72617, 72623, 72643,
-    72647, 72649, 72661, 72671, 72673, 72679, 72689, 72701, 72707,
-    72719, 72727, 72733, 72739, 72763, 72767, 72797, 72817, 72823,
-    72859, 72869, 72871, 72883, 72889, 72893, 72901, 72907, 72911,
-    72923, 72931, 72937, 72949, 72953, 72959, 72973, 72977, 72997,
-    73009, 73013, 73019, 73037, 73039, 73043, 73061, 73063, 73079,
-    73091, 73121, 73127, 73133, 73141, 73181, 73189, 73237, 73243,
-    73259, 73277, 73291, 73303, 73309, 73327, 73331, 73351, 73361,
-    73363, 73369, 73379, 73387, 73417, 73421, 73433, 73453, 73459,
-    73471, 73477, 73483, 73517, 73523, 73529, 73547, 73553, 73561,
-    73571, 73583, 73589, 73597, 73607, 73609, 73613, 73637, 73643,
-    73651, 73673, 73679, 73681, 73693, 73699, 73709, 73721, 73727,
-    73751, 73757, 73771, 73783, 73819, 73823, 73847, 73849, 73859,
-    73867, 73877, 73883, 73897, 73907, 73939, 73943, 73951, 73961,
-    73973, 73999, 74017, 74021, 74027, 74047, 74051, 74071, 74077,
-    74093, 74099, 74101, 74131, 74143, 74149, 74159, 74161, 74167,
-    74177, 74189, 74197, 74201, 74203, 74209, 74219, 74231, 74257,
-    74279, 74287, 74293, 74297, 74311, 74317, 74323, 74353, 74357,
-    74363, 74377, 74381, 74383, 74411, 74413, 74419, 74441, 74449,
-    74453, 74471, 74489, 74507, 74509, 74521, 74527, 74531, 74551,
-    74561, 74567, 74573, 74587, 74597, 74609, 74611, 74623, 74653,
-    74687, 74699, 74707, 74713, 74717, 74719, 74729, 74731, 74747,
-    74759, 74761, 74771, 74779, 74797, 74821, 74827, 74831, 74843,
-    74857, 74861, 74869, 74873, 74887, 74891, 74897, 74903, 74923,
-    74929, 74933, 74941, 74959, 75011, 75013, 75017, 75029, 75037,
-    75041, 75079, 75083, 75109, 75133, 75149, 75161, 75167, 75169,
-    75181, 75193, 75209, 75211, 75217, 75223, 75227, 75239, 75253,
-    75269, 75277, 75289, 75307, 75323, 75329, 75337, 75347, 75353,
-    75367, 75377, 75389, 75391, 75401, 75403, 75407, 75431, 75437,
-    75479, 75503, 75511, 75521, 75527, 75533, 75539, 75541, 75553,
-    75557, 75571, 75577, 75583, 75611, 75617, 75619, 75629, 75641,
-    75653, 75659, 75679, 75683, 75689, 75703, 75707, 75709, 75721,
-    75731, 75743, 75767, 75773, 75781, 75787, 75793, 75797, 75821,
-    75833, 75853, 75869, 75883, 75913, 75931, 75937, 75941, 75967,
-    75979, 75983, 75989, 75991, 75997, 76001, 76003, 76031, 76039,
-    76079, 76081, 76091, 76099, 76103, 76123, 76129, 76147, 76157,
-    76159, 76163, 76207, 76213, 76231, 76243, 76249, 76253, 76259,
-    76261, 76283, 76289, 76303, 76333, 76343, 76367, 76369, 76379,
-    76387, 76403, 76421, 76423, 76441, 76463, 76471, 76481, 76487,
-    76493, 76507, 76511, 76519, 76537, 76541, 76543, 76561, 76579,
-    76597, 76603, 76607, 76631, 76649, 76651, 76667, 76673, 76679,
-    76697, 76717, 76733, 76753, 76757, 76771, 76777, 76781, 76801,
-    76819, 76829, 76831, 76837, 76847, 76871, 76873, 76883, 76907,
-    76913, 76919, 76943, 76949, 76961, 76963, 76991, 77003, 77017,
-    77023, 77029, 77041, 77047, 77069, 77081, 77093, 77101, 77137,
-    77141, 77153, 77167, 77171, 77191, 77201, 77213, 77237, 77239,
-    77243, 77249, 77261, 77263, 77267, 77269, 77279, 77291, 77317,
-    77323, 77339, 77347, 77351, 77359, 77369, 77377, 77383, 77417,
-    77419, 77431, 77447, 77471, 77477, 77479, 77489, 77491, 77509,
-    77513, 77521, 77527, 77543, 77549, 77551, 77557, 77563, 77569,
-    77573, 77587, 77591, 77611, 77617, 77621, 77641, 77647, 77659,
-    77681, 77687, 77689, 77699, 77711, 77713, 77719, 77723, 77731,
-    77743, 77747, 77761, 77773, 77783, 77797, 77801, 77813, 77839,
-    77849, 77863, 77867, 77893, 77899, 77929, 77933, 77951, 77969,
-    77977, 77983, 77999, 78007, 78017, 78031, 78041, 78049, 78059,
-    78079, 78101, 78121, 78137, 78139, 78157, 78163, 78167, 78173,
-    78179, 78191, 78193, 78203, 78229, 78233, 78241, 78259, 78277,
-    78283, 78301, 78307, 78311, 78317, 78341, 78347, 78367, 78401,
-    78427, 78437, 78439, 78467, 78479, 78487, 78497, 78509, 78511,
-    78517, 78539, 78541, 78553, 78569, 78571, 78577, 78583, 78593,
-    78607, 78623, 78643, 78649, 78653, 78691, 78697, 78707, 78713,
-    78721, 78737, 78779, 78781, 78787, 78791, 78797, 78803, 78809,
-    78823, 78839, 78853, 78857, 78877, 78887, 78889, 78893, 78901,
-    78919, 78929, 78941, 78977, 78979, 78989, 79031, 79039, 79043,
-    79063, 79087, 79103, 79111, 79133, 79139, 79147, 79151, 79153,
-    79159, 79181, 79187, 79193, 79201, 79229, 79231, 79241, 79259,
-    79273, 79279, 79283, 79301, 79309, 79319, 79333, 79337, 79349,
-    79357, 79367, 79379, 79393, 79397, 79399, 79411, 79423, 79427,
-    79433, 79451, 79481, 79493, 79531, 79537, 79549, 79559, 79561,
-    79579, 79589, 79601, 79609, 79613, 79621, 79627, 79631, 79633,
-    79657, 79669, 79687, 79691, 79693, 79697, 79699, 79757, 79769,
-    79777, 79801, 79811, 79813, 79817, 79823, 79829, 79841, 79843,
-    79847, 79861, 79867, 79873, 79889, 79901, 79903, 79907, 79939,
-    79943, 79967, 79973, 79979, 79987, 79997, 79999, 80021, 80039,
-    80051, 80071, 80077, 80107, 80111, 80141, 80147, 80149, 80153,
-    80167, 80173, 80177, 80191, 80207, 80209, 80221, 80231, 80233,
-    80239, 80251, 80263, 80273, 80279, 80287, 80309, 80317, 80329,
-    80341, 80347, 80363, 80369, 80387, 80407, 80429, 80447, 80449,
-    80471, 80473, 80489, 80491, 80513, 80527, 80537, 80557, 80567,
-    80599, 80603, 80611, 80621, 80627, 80629, 80651, 80657, 80669,
-    80671, 80677, 80681, 80683, 80687, 80701, 80713, 80737, 80747,
-    80749, 80761, 80777, 80779, 80783, 80789, 80803, 80809, 80819,
-    80831, 80833, 80849, 80863, 80897, 80909, 80911, 80917, 80923,
-    80929, 80933, 80953, 80963, 80989, 81001, 81013, 81017, 81019,
-    81023, 81031, 81041, 81043, 81047, 81049, 81071, 81077, 81083,
-    81097, 81101, 81119, 81131, 81157, 81163, 81173, 81181, 81197,
-    81199, 81203, 81223, 81233, 81239, 81281, 81283, 81293, 81299,
-    81307, 81331, 81343, 81349, 81353, 81359, 81371, 81373, 81401,
-    81409, 81421, 81439, 81457, 81463, 81509, 81517, 81527, 81533,
-    81547, 81551, 81553, 81559, 81563, 81569, 81611, 81619, 81629,
-    81637, 81647, 81649, 81667, 81671, 81677, 81689, 81701, 81703,
-    81707, 81727, 81737, 81749, 81761, 81769, 81773, 81799, 81817,
-    81839, 81847, 81853, 81869, 81883, 81899, 81901, 81919, 81929,
-    81931, 81937, 81943, 81953, 81967, 81971, 81973, 82003, 82007,
-    82009, 82013, 82021, 82031, 82037, 82039, 82051, 82067, 82073,
-    82129, 82139, 82141, 82153, 82163, 82171, 82183, 82189, 82193,
-    82207, 82217, 82219, 82223, 82231, 82237, 82241, 82261, 82267,
-    82279, 82301, 82307, 82339, 82349, 82351, 82361, 82373, 82387,
-    82393, 82421, 82457, 82463, 82469, 82471, 82483, 82487, 82493,
-    82499, 82507, 82529, 82531, 82549, 82559, 82561, 82567, 82571,
-    82591, 82601, 82609, 82613, 82619, 82633, 82651, 82657, 82699,
-    82721, 82723, 82727, 82729, 82757, 82759, 82763, 82781, 82787,
-    82793, 82799, 82811, 82813, 82837, 82847, 82883, 82889, 82891,
-    82903, 82913, 82939, 82963, 82981, 82997, 83003, 83009, 83023,
-    83047, 83059, 83063, 83071, 83077, 83089, 83093, 83101, 83117,
-    83137, 83177, 83203, 83207, 83219, 83221, 83227, 83231, 83233,
-    83243, 83257, 83267, 83269, 83273, 83299, 83311, 83339, 83341,
-    83357, 83383, 83389, 83399, 83401, 83407, 83417, 83423, 83431,
-    83437, 83443, 83449, 83459, 83471, 83477, 83497, 83537, 83557,
-    83561, 83563, 83579, 83591, 83597, 83609, 83617, 83621, 83639,
-    83641, 83653, 83663, 83689, 83701, 83717, 83719, 83737, 83761,
-    83773, 83777, 83791, 83813, 83833, 83843, 83857, 83869, 83873,
-    83891, 83903, 83911, 83921, 83933, 83939, 83969, 83983, 83987,
-    84011, 84017, 84047, 84053, 84059, 84061, 84067, 84089, 84121,
-    84127, 84131, 84137, 84143, 84163, 84179, 84181, 84191, 84199,
-    84211, 84221, 84223, 84229, 84239, 84247, 84263, 84299, 84307,
-    84313, 84317, 84319, 84347, 84349, 84377, 84389, 84391, 84401,
-    84407, 84421, 84431, 84437, 84443, 84449, 84457, 84463, 84467,
-    84481, 84499, 84503, 84509, 84521, 84523, 84533, 84551, 84559,
-    84589, 84629, 84631, 84649, 84653, 84659, 84673, 84691, 84697,
-    84701, 84713, 84719, 84731, 84737, 84751, 84761, 84787, 84793,
-    84809, 84811, 84827, 84857, 84859, 84869, 84871, 84913, 84919,
-    84947, 84961, 84967, 84977, 84979, 84991, 85009, 85021, 85027,
-    85037, 85049, 85061, 85081, 85087, 85091, 85093, 85103, 85109,
-    85121, 85133, 85147, 85159, 85193, 85199, 85201, 85213, 85223,
-    85229, 85237, 85243, 85247, 85259, 85297, 85303, 85313, 85331,
-    85333, 85361, 85363, 85369, 85381, 85411, 85427, 85429, 85439,
-    85447, 85451, 85453, 85469, 85487, 85513, 85517, 85523, 85531,
-    85549, 85571, 85577, 85597, 85601, 85607, 85619, 85621, 85627,
-    85639, 85643, 85661, 85667, 85669, 85691, 85703, 85711, 85717,
-    85733, 85751, 85781, 85793, 85817, 85819, 85829, 85831, 85837,
-    85843, 85847, 85853, 85889, 85903, 85909, 85931, 85933, 85991,
-    85999, 86011, 86017, 86027, 86029, 86069, 86077, 86083, 86111,
-    86113, 86117, 86131, 86137, 86143, 86161, 86171, 86179, 86183,
-    86197, 86201, 86209, 86239, 86243, 86249, 86257, 86263, 86269,
-    86287, 86291, 86293, 86297, 86311, 86323, 86341, 86351, 86353,
-    86357, 86369, 86371, 86381, 86389, 86399, 86413, 86423, 86441,
-    86453, 86461, 86467, 86477, 86491, 86501, 86509, 86531, 86533,
-    86539, 86561, 86573, 86579, 86587, 86599, 86627, 86629, 86677,
-    86689, 86693, 86711, 86719, 86729, 86743, 86753, 86767, 86771,
-    86783, 86813, 86837, 86843, 86851, 86857, 86861, 86869, 86923,
-    86927, 86929, 86939, 86951, 86959, 86969, 86981, 86993, 87011,
-    87013, 87037, 87041, 87049, 87071, 87083, 87103, 87107, 87119,
-    87121, 87133, 87149, 87151, 87179, 87181, 87187, 87211, 87221,
-    87223, 87251, 87253, 87257, 87277, 87281, 87293, 87299, 87313,
-    87317, 87323, 87337, 87359, 87383, 87403, 87407, 87421, 87427,
-    87433, 87443, 87473, 87481, 87491, 87509, 87511, 87517, 87523,
-    87539, 87541, 87547, 87553, 87557, 87559, 87583, 87587, 87589,
-    87613, 87623, 87629, 87631, 87641, 87643, 87649, 87671, 87679,
-    87683, 87691, 87697, 87701, 87719, 87721, 87739, 87743, 87751,
-    87767, 87793, 87797, 87803, 87811, 87833, 87853, 87869, 87877,
-    87881, 87887, 87911, 87917, 87931, 87943, 87959, 87961, 87973,
-    87977, 87991, 88001, 88003, 88007, 88019, 88037, 88069, 88079,
-    88093, 88117, 88129, 88169, 88177, 88211, 88223, 88237, 88241,
-    88259, 88261, 88289, 88301, 88321, 88327, 88337, 88339, 88379,
-    88397, 88411, 88423, 88427, 88463, 88469, 88471, 88493, 88499,
-    88513, 88523, 88547, 88589, 88591, 88607, 88609, 88643, 88651,
-    88657, 88661, 88663, 88667, 88681, 88721, 88729, 88741, 88747,
-    88771, 88789, 88793, 88799, 88801, 88807, 88811, 88813, 88817,
-    88819, 88843, 88853, 88861, 88867, 88873, 88883, 88897, 88903,
-    88919, 88937, 88951, 88969, 88993, 88997, 89003, 89009, 89017,
-    89021, 89041, 89051, 89057, 89069, 89071, 89083, 89087, 89101,
-    89107, 89113, 89119, 89123, 89137, 89153, 89189, 89203, 89209,
-    89213, 89227, 89231, 89237, 89261, 89269, 89273, 89293, 89303,
-    89317, 89329, 89363, 89371, 89381, 89387, 89393, 89399, 89413,
-    89417, 89431, 89443, 89449, 89459, 89477, 89491, 89501, 89513,
-    89519, 89521, 89527, 89533, 89561, 89563, 89567, 89591, 89597,
-    89599, 89603, 89611, 89627, 89633, 89653, 89657, 89659, 89669,
-    89671, 89681, 89689, 89753, 89759, 89767, 89779, 89783, 89797,
-    89809, 89819, 89821, 89833, 89839, 89849, 89867, 89891, 89897,
-    89899, 89909, 89917, 89923, 89939, 89959, 89963, 89977, 89983,
-    89989, 90001, 90007, 90011, 90017, 90019, 90023, 90031, 90053,
-    90059, 90067, 90071, 90073, 90089, 90107, 90121, 90127, 90149,
-    90163, 90173, 90187, 90191, 90197, 90199, 90203, 90217, 90227,
-    90239, 90247, 90263, 90271, 90281, 90289, 90313, 90353, 90359,
-    90371, 90373, 90379, 90397, 90401, 90403, 90407, 90437, 90439,
-    90469, 90473, 90481, 90499, 90511, 90523, 90527, 90529, 90533,
-    90547, 90583, 90599, 90617, 90619, 90631, 90641, 90647, 90659,
-    90677, 90679, 90697, 90703, 90709, 90731, 90749, 90787, 90793,
-    90803, 90821, 90823, 90833, 90841, 90847, 90863, 90887, 90901,
-    90907, 90911, 90917, 90931, 90947, 90971, 90977, 90989, 90997,
-    91009, 91019, 91033, 91079, 91081, 91097, 91099, 91121, 91127,
-    91129, 91139, 91141, 91151, 91153, 91159, 91163, 91183, 91193,
-    91199, 91229, 91237, 91243, 91249, 91253, 91283, 91291, 91297,
-    91303, 91309, 91331, 91367, 91369, 91373, 91381, 91387, 91393,
-    91397, 91411, 91423, 91433, 91453, 91457, 91459, 91463, 91493,
-    91499, 91513, 91529, 91541, 91571, 91573, 91577, 91583, 91591,
-    91621, 91631, 91639, 91673, 91691, 91703, 91711, 91733, 91753,
-    91757, 91771, 91781, 91801, 91807, 91811, 91813, 91823, 91837,
-    91841, 91867, 91873, 91909, 91921, 91939, 91943, 91951, 91957,
-    91961, 91967, 91969, 91997, 92003, 92009, 92033, 92041, 92051,
-    92077, 92083, 92107, 92111, 92119, 92143, 92153, 92173, 92177,
-    92179, 92189, 92203, 92219, 92221, 92227, 92233, 92237, 92243,
-    92251, 92269, 92297, 92311, 92317, 92333, 92347, 92353, 92357,
-    92363, 92369, 92377, 92381, 92383, 92387, 92399, 92401, 92413,
-    92419, 92431, 92459, 92461, 92467, 92479, 92489, 92503, 92507,
-    92551, 92557, 92567, 92569, 92581, 92593, 92623, 92627, 92639,
-    92641, 92647, 92657, 92669, 92671, 92681, 92683, 92693, 92699,
-    92707, 92717, 92723, 92737, 92753, 92761, 92767, 92779, 92789,
-    92791, 92801, 92809, 92821, 92831, 92849, 92857, 92861, 92863,
-    92867, 92893, 92899, 92921, 92927, 92941, 92951, 92957, 92959,
-    92987, 92993, 93001, 93047, 93053, 93059, 93077, 93083, 93089,
-    93097, 93103, 93113, 93131, 93133, 93139, 93151, 93169, 93179,
-    93187, 93199, 93229, 93239, 93241, 93251, 93253, 93257, 93263,
-    93281, 93283, 93287, 93307, 93319, 93323, 93329, 93337, 93371,
-    93377, 93383, 93407, 93419, 93427, 93463, 93479, 93481, 93487,
-    93491, 93493, 93497, 93503, 93523, 93529, 93553, 93557, 93559,
-    93563, 93581, 93601, 93607, 93629, 93637, 93683, 93701, 93703,
-    93719, 93739, 93761, 93763, 93787, 93809, 93811, 93827, 93851,
-    93871, 93887, 93889, 93893, 93901, 93911, 93913, 93923, 93937,
-    93941, 93949, 93967, 93971, 93979, 93983, 93997, 94007, 94009,
-    94033, 94049, 94057, 94063, 94079, 94099, 94109, 94111, 94117,
-    94121, 94151, 94153, 94169, 94201, 94207, 94219, 94229, 94253,
-    94261, 94273, 94291, 94307, 94309, 94321, 94327, 94331, 94343,
-    94349, 94351, 94379, 94397, 94399, 94421, 94427, 94433, 94439,
-    94441, 94447, 94463, 94477, 94483, 94513, 94529, 94531, 94541,
-    94543, 94547, 94559, 94561, 94573, 94583, 94597, 94603, 94613,
-    94621, 94649, 94651, 94687, 94693, 94709, 94723, 94727, 94747,
-    94771, 94777, 94781, 94789, 94793, 94811, 94819, 94823, 94837,
-    94841, 94847, 94849, 94873, 94889, 94903, 94907, 94933, 94949,
-    94951, 94961, 94993, 94999, 95003, 95009, 95021, 95027, 95063,
-    95071, 95083, 95087, 95089, 95093, 95101, 95107, 95111, 95131,
-    95143, 95153, 95177, 95189, 95191, 95203, 95213, 95219, 95231,
-    95233, 95239, 95257, 95261, 95267, 95273, 95279, 95287, 95311,
-    95317, 95327, 95339, 95369, 95383, 95393, 95401, 95413, 95419,
-    95429, 95441, 95443, 95461, 95467, 95471, 95479, 95483, 95507,
-    95527, 95531, 95539, 95549, 95561, 95569, 95581, 95597, 95603,
-    95617, 95621, 95629, 95633, 95651, 95701, 95707, 95713, 95717,
-    95723, 95731, 95737, 95747, 95773, 95783, 95789, 95791, 95801,
-    95803, 95813, 95819, 95857, 95869, 95873, 95881, 95891, 95911,
-    95917, 95923, 95929, 95947, 95957, 95959, 95971, 95987, 95989,
-    96001, 96013, 96017, 96043, 96053, 96059, 96079, 96097, 96137,
-    96149, 96157, 96167, 96179, 96181, 96199, 96211, 96221, 96223,
-    96233, 96259, 96263, 96269, 96281, 96289, 96293, 96323, 96329,
-    96331, 96337, 96353, 96377, 96401, 96419, 96431, 96443, 96451,
-    96457, 96461, 96469, 96479, 96487, 96493, 96497, 96517, 96527,
-    96553, 96557, 96581, 96587, 96589, 96601, 96643, 96661, 96667,
-    96671, 96697, 96703, 96731, 96737, 96739, 96749, 96757, 96763,
-    96769, 96779, 96787, 96797, 96799, 96821, 96823, 96827, 96847,
-    96851, 96857, 96893, 96907, 96911, 96931, 96953, 96959, 96973,
-    96979, 96989, 96997, 97001, 97003, 97007, 97021, 97039, 97073,
-    97081, 97103, 97117, 97127, 97151, 97157, 97159, 97169, 97171,
-    97177, 97187, 97213, 97231, 97241, 97259, 97283, 97301, 97303,
-    97327, 97367, 97369, 97373, 97379, 97381, 97387, 97397, 97423,
-    97429, 97441, 97453, 97459, 97463, 97499, 97501, 97511, 97523,
-    97547, 97549, 97553, 97561, 97571, 97577, 97579, 97583, 97607,
-    97609, 97613, 97649, 97651, 97673, 97687, 97711, 97729, 97771,
-    97777, 97787, 97789, 97813, 97829, 97841, 97843, 97847, 97849,
-    97859, 97861, 97871, 97879, 97883, 97919, 97927, 97931, 97943,
-    97961, 97967, 97973, 97987, 98009, 98011, 98017, 98041, 98047,
-    98057, 98081, 98101, 98123, 98129, 98143, 98179, 98207, 98213,
-    98221, 98227, 98251, 98257, 98269, 98297, 98299, 98317, 98321,
-    98323, 98327, 98347, 98369, 98377, 98387, 98389, 98407, 98411,
-    98419, 98429, 98443, 98453, 98459, 98467, 98473, 98479, 98491,
-    98507, 98519, 98533, 98543, 98561, 98563, 98573, 98597, 98621,
-    98627, 98639, 98641, 98663, 98669, 98689, 98711, 98713, 98717,
-    98729, 98731, 98737, 98773, 98779, 98801, 98807, 98809, 98837,
-    98849, 98867, 98869, 98873, 98887, 98893, 98897, 98899, 98909,
-    98911, 98927, 98929, 98939, 98947, 98953, 98963, 98981, 98993,
-    98999, 99013, 99017, 99023, 99041, 99053, 99079, 99083, 99089,
-    99103, 99109, 99119, 99131, 99133, 99137, 99139, 99149, 99173,
-    99181, 99191, 99223, 99233, 99241, 99251, 99257, 99259, 99277,
-    99289, 99317, 99347, 99349, 99367, 99371, 99377, 99391, 99397,
-    99401, 99409, 99431, 99439, 99469, 99487, 99497, 99523, 99527,
-    99529, 99551, 99559, 99563, 99571, 99577, 99581, 99607, 99611,
-    99623, 99643, 99661, 99667, 99679, 99689, 99707, 99709, 99713,
-    99719, 99721, 99733, 99761, 99767, 99787, 99793, 99809, 99817,
-    99823, 99829, 99833, 99839, 99859, 99871, 99877, 99881, 99901,
-    99907, 99923, 99929, 99961, 99971, 99989, 99991,
-    };