#include <stdio.h>
#include <stdlib.h>
typedef unsigned short us;
typedef long long int cf;
us const p[] = {0xffff, 0x039f, 0xf2f2, 0xf9c8, 0xf900, 0xb0f0};
// 16+8+10+9+6+7 = 56
cf const o = 1;
char rn[] = {0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15};

// Next four lines are only for debugging.
typedef unsigned long uint32;
int gcount(uint32 x)
   {int c=0; while(x){++c; x &= x-1;} return c;}
int bc(cf x){return gcount(x) + gcount(x>>32);}

cf twist(cf x){cf s = 0;
  {int i=4; while(i--) {int j=4; while(j--) {int k=4; while(k--)
    if(x&(o<<(i+4*j+16*k))) s |= o<<(j+4*k+16*i);}}}
  return s;}

us turn(us px){
  return ((px     &0xf)<< 4) //1302 rotate piece 90 about long axis
      | (((px>> 4)    )<<12)
      |  ((px>> 8)&0xf)
      | (((px>>12)&0xf)<< 8);}

us tb(us px){
  return ((us)rn[ px     &0xf]<< 8) //2301 rotate piece 180 about short axis
      |  ((us)rn[(px>> 4)&0xf]<<12)
      |   (us)rn[(px>> 8)&0xf]
      |  ((us)rn[(px>>12)    ]<< 4);}

cf place(us x){
  return ((cf)(x      &0xf) <<  4)
       | ((cf)((x>> 4)&0xf) <<  8)
       | ((cf)((x>> 8)&0xf) << 20)
       | ((cf)((x>>12)    ) << 24);}

cf pz[6][6][8];
char L[] = {0,1,2,3,4,5}; // last 5 totally permuted by perm
char oa[6];
int cnt=0;
void x(){cf arena = pz[0][0][0];
  void add(char piece){++cnt;
   if(piece>5) {int j; for(j=0; j<piece; ++j) printf("%d %d, ", L[j], oa[j]);
       printf("xt %016llx\n", arena);
       if(piece==6){int p; for(p=0; p<6; ++p)
          printf("so %d %d %d %016llx\n", p, L[p], oa[p], pz[p][L[p]][oa[p]]);}}
   if(piece<6) {int j=8; while(j--) {
     cf * ppz = &pz[piece][L[piece]][j];
     oa[piece] = j;
     if(!(arena & *ppz)) {arena |= *ppz; add(piece+1); arena &= ~*ppz;}
     else if(0) printf("t%d %d %d %016llx\n", piece, L[piece], j, arena & *ppz);
    }}}
add(1);
}

void perm(char * a, int n){
  // This routine permutes the n characters starting at a and for
  // each permutation, calls x.
  // The characters are left as they were found.
  char t = *a; int j=n; while(j--) {
    char u = *(a+j); *a = u; *(a+j) = t;
    if(n<3) x(); else perm(a+1, n-1);
    *(a+j) = u;} *a = t;}

int main(){
{int pi = 6; while(pi--)
      {char pzi[] = {0, 0, 0, 0, 0, 0};
  void put (cf x, int li) {pz[pi][li][pzi[li]++] = x;}
  void puta(cf x, int w) {
     cf y = twist(x); put(x, w); put(y, w+1); put(twist(y), w+2);}
  void putb(us q){cf x = place(q); puta (x, 0); puta(x<<32, 3);}
  
  {us px = p[pi]; int q = 4; while(q--) {putb(px); putb(tb(px));  px = turn(px);}
    if (px != p[pi]) exit(printf("fratz! px=%04x, p[pi]=%04x\n", px, p[pi]));}
  {int y=6; while(y-- )if (pzi[y] != 8)
       {int j=6; while(j--) printf("gz %d ", pzi[j]); exit(0);}}}}

  {cf q = 0x2649c387e3a3b1d7LL; if(q != twist(twist(twist(q))))
     exit(printf ("goic\n"));}
  if(0) {int i=6; cf ss=0; while(i--) {int k=6; while(k--)
     {int j=8; while(j--)
        {printf("pz[%d][%d][%d] = %016llx\n",
           i, k, j, pz[i][k][j]); ss |= pz[i][k][j];}}}
      printf(" union = %016llx %d\n", ss, bc(ss)); // should be 6ff6ffffffff6ff6
      }
perm(L+1, 5); 
{int j; for(j=0; j<6; ++j) printf("%d ", gcount(p[j])); printf("pc\n");}
printf("%d Bye\n", cnt);

return 0;}
/* Output on 2008, Jan 31:
0 0, 4 1, 1 3, 5 0, 2 1, 3 7, xt 6ff6ffffffff6ff6
so 0 0 0 000000000ff00ff0
so 1 4 1 6200220020006000
so 2 1 3 0006006600060006
so 3 5 0 0000cc88c0080000
so 4 2 1 0000111110010000
so 5 3 7 0df0000000000000
0 0, 1 5, 4 7, 2 1, 5 0, 3 2, xt 6ff6ffffffff6ff6
so 0 0 0 000000000ff00ff0
so 1 1 5 0046004400040006
so 2 4 7 6000660060006000
so 3 2 1 0000113310030000
so 4 5 0 0000888880080000
so 5 3 2 0fb0000000000000
16 8 10 9 6 7 pc
606 Bye
*/