#include <iostream>
#include <vector>
#include <cstring>
#include <cstdio>

using namespace std;

int main(int argc, char *argv[]) {
  int n;
  char s, t, b;
  long double *rooms, *r;
  vector<long double> result;
  rooms = new long double[9];
  r = new long double[9];
  while (true) {
    cin >> n;
    if (n == 0)
      break;
    memset(rooms, 0, 9 * sizeof(long double));
    cin >> s >> t >> b;

    rooms[s-'A'] = 1;
    b -= 'A';
    for (int i = 0; i < n; i++) {
      memset(r, 0, 9 * sizeof(long double));
      long double *tmp = rooms;
      rooms = r;
      r = tmp;
      if (b != 0) {
        rooms[0] += r[0] * 0.5 + r[1] * 0.25 + r[3] * 0.25;
      } else {
        rooms[1] += r[1] * 0.25;
        rooms[3] += r[3] * 0.25;
      }
      if (b != 1) {
        rooms[1] += (r[0] + r[1] + r[2] + r[4]) * 0.25;
      } else {
        rooms[0] += r[0] * 0.25;
        rooms[2] += r[2] * 0.25;
        rooms[4] += r[4] * 0.25;
      }
      if (b != 2) {
        rooms[2] += r[1] * 0.25 + r[2] * 0.5 + r[5] * 0.25;
      } else {
        rooms[1] += r[1] * 0.25;
        rooms[5] += r[5] * 0.25;
      }
      if (b != 3) {
        rooms[3] += (r[0] + r[3] + r[4] + r[6]) * 0.25;
      } else {
        rooms[0] += r[0] * 0.25;
        rooms[4] += r[4] * 0.25;
        rooms[6] += r[6] * 0.25;
      }
      if (b != 4) {
        rooms[4] += (r[1] + r[3] + r[5] + r[7]) * 0.25;
      } else {
        rooms[1] += r[1] * 0.25;
        rooms[3] += r[3] * 0.25;
        rooms[5] += r[5] * 0.25;
        rooms[7] += r[7] * 0.25;
      }
      if (b != 5) {
        rooms[5] += (r[2] + r[4] + r[5] + r[8]) * 0.25;
      } else {
        rooms[2] += r[2] * 0.25;
        rooms[4] += r[4] * 0.25;
        rooms[8] += r[8] * 0.25;
      }
      if (b != 6) {
        rooms[6] += r[3] * 0.25 + r[6] * 0.5 + r[7] * 0.25;
      } else {
        rooms[3] += r[3] * 0.25;
        rooms[7] += r[7] * 0.25;
      }
      if (b != 7) {
        rooms[7] += (r[4] + r[6] + r[7] + r[8]) * 0.25;
      } else {
        rooms[4] += r[4] * 0.25;
        rooms[6] += r[6] * 0.25;
        rooms[8] += r[8] * 0.25;
      }
      if (b != 8) {
        rooms[8] += r[5] * 0.25 + r[7] * 0.25 + r[8] * 0.5;
      } else {
        rooms[5] += r[5] * 0.25;
        rooms[7] += r[7] * 0.25;
      }
      /*                                                                                                                                                                                                                                                                                                                                            
      for (int i = 0; i < 9; i++)                                                                                                                                                                                                                                                                                                                   
        printf("%c: %lf\n",(char)('A'+i), rooms[i]);                                                                                                                                                                                                                                                                                                
      cout << endl;                                                                                                                                                                                                                                                                                                                                 
      */
    }
    result.push_back(rooms[t-'A']);
  }

  for (int i = 0; i < result.size(); i++)
    printf("%.8Lf\n", result[i]);
  return 0;
}

Measured memory_bytes: 1236