#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
// Wikipedia: http://en.wikipedia.org/wiki/Binary_Golay_code
// Roberts: http://mathcs.pugetsound.edu/~bryans/Current/Journal_Spring_2006/ARoberts_LeechLattice.pdf
int W[12] = { // From Wikipedia:
  0x8009F1, 0x4004FA, 0x20027D, 0x10093E,
  0x080C9D, 0x040E4E, 0x020F25, 0x010F92,
  0x0087C9, 0x0043E6, 0x002557, 0x001AAB};
int r[12] = { // Roberts Page 13
  0x800FFD, 0x4000FE, 0x20071E, 0x100B66,
  0x080DAA, 0x040ED2, 0x0203CB, 0x010573,
  0x0086A7, 0x004997, 0x002A3B, 0x001C4F};
int R[12] = { // Roberts Page 14
  0xFF0000, 0xF0F000, 0xCCCC00, 0xAAAA00,
  0x999900, 0xA9C0C0, 0x9ACAA0, 0xCA9090,
  0x788888, 0x00CCCC, 0x00AAAA, 0x005555};
typedef signed char co;
static int weight(int x) {int c=0; while(x){++c; x &= x-1;} return c;}
static int vtm(int v, int * m){int p=0;
   for(int j=0; j<12; ++j) if((v>>j)&1) p ^= m[11-j]; return p;}
// Gq is a test of membership in Golay codes.
int Gq(int x){return x == vtm(x>>12, W);}
static int ew(co * x, int s){int w=0; for(int j=0; j<24; ++j) w=(w<<1)|(x[j]>>s)&1; return w;}
// Lq is a test for membership in Leech lattice.
int Lq(co * x){
  return (ew(x, 0) == (weight(ew(x, 2))&1?0xffffff:0)) && Gq(ew(x, 1));}

#if 0
int main(){
  for(int j=0; j<12; ++j) assert(Gq(W[j])); assert(Gq(W[3]^W[6]));
  {co x[24]; for(int i=0; i<24; ++i) x[i] = 0; assert(Lq(x));
    x[0] = 8; assert(Lq(x));
    x[6] = -8; assert(Lq(x));
    x[0] = 0; assert(Lq(x));}
  {co x[24]; for(int i=0; i<24; ++i) x[i] = i<2?4:0; assert(Lq(x));}
  {co x[24]; for(int i=0; i<24; ++i) x[i] = i==11?3:-1; assert(Lq(x));}
  printf("Good\n");
  return 0;}
#endif