#include <stdio.h>
#include <stdlib.h>

int solutions[480][7];
int symmetry[480];

#define X_AXIS 0
#define Y_AXIS 1
#define Z_AXIS 2

int symmetrize(int c, int axis)
{
  int cube[3][3][3];
  int bit;
  int ret;
  int x, y, z;
  /* change representation of the solution, put it in the 3x3x3 cube */
  for (x = 0; x < 3; x++) for (y = 0; y < 3; y++) for (z = 0; z < 3; z++) {
    bit = x * 9 + y * 3 + z;
    if (c & (1 << bit)) cube[x][y][z] = 1; else cube[x][y][z] = 0;
  }
  /* collect the bits again, but with a symmetry around given axis */
  ret = 0;
  for (x = 0; x < 3; x++) for (y = 0; y < 3; y++) for (z = 0; z < 3; z++) {
    bit = x * 9 + y * 3 + z;
    switch (axis) {
    case X_AXIS: if (cube[2-x][y][z]) ret |= 1 << bit; break;
    case Y_AXIS: if (cube[x][2-y][z]) ret |= 1 << bit; break;
    case Z_AXIS: if (cube[x][y][2-z]) ret |= 1 << bit; break;
    }
  }
  /* note: we could do this in one loop, but it would be maybe less readable */
  return ret;
}

void compute_symmetry(int i, int axis)
{
  int pieces_symmetry[7];
  int j;
  pieces_symmetry[0] = symmetrize(solutions[i][0], axis);
  pieces_symmetry[1] = symmetrize(solutions[i][1], axis);
  pieces_symmetry[2] = symmetrize(solutions[i][2], axis);
  pieces_symmetry[3] = symmetrize(solutions[i][3], axis);
  pieces_symmetry[4] = symmetrize(solutions[i][6], axis);  /* piece 7 -> 5 */
  pieces_symmetry[5] = symmetrize(solutions[i][5], axis);
  pieces_symmetry[6] = symmetrize(solutions[i][4], axis);  /* piece 5 -> 7 */
  /* look for the symmetrical solution, it has to exist! */
  for (j = 0; j < 480; j++) {
    int k;
    for (k = 0; k < 7; k++) if (solutions[j][k] != pieces_symmetry[k]) break;
    if (k == 7) { symmetry[i] = j; break; }
  }
  if (j == 480) { printf("what? no symmetry found for solution %d?\n", i); exit(1); }
}

void read_solutions(void)
{
  int i;
  int j;
  int x;

  for (i = 0; i < 480; i++) for (j = 0; j < 7; j++) {
    if (scanf("%x", &x) != 1) { printf("error\n"); exit(1); }
    solutions[i][j] = x;
  }
}

void check_symmetry(int i)
{
  int j = symmetry[i];
  if (symmetry[j] != i) { printf("uh oh, symmetry fails!\n"); exit(1); }
}

int main(void)
{
  int i;
  read_solutions();
  /* verify with X axis */
  printf("x\n");
  for (i = 0; i < 480; i++) compute_symmetry(i, X_AXIS);
  for (i = 0; i < 480; i++) check_symmetry(i);
  /* verify with Y axis */
  printf("y\n");
  for (i = 0; i < 480; i++) compute_symmetry(i, Y_AXIS);
  for (i = 0; i < 480; i++) check_symmetry(i);
  /* verify with Z axis */
  printf("z\n");
  for (i = 0; i < 480; i++) compute_symmetry(i, Z_AXIS);
  for (i = 0; i < 480; i++) check_symmetry(i);

  return 0;
}