#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  int dx[] = {1, 0, -1, 0};
  int dy[] = {0, 1, 0, -1};
  double nxt[5][5], cur[5][5];
  while (cin >> n, n) {
    memset(cur, 0, sizeof(cur));
    int xs[3], ys[3];
    for (int i = 0; i < 3; i++) {
      char c;
      int a;
      cin >> c;
      a = c - 'A';
      xs[i] = a % 3 + 1;
      ys[i] = a / 3 + 1;
    }
    cur[xs[0]][ys[0]] = 1;
    for (int i = 0; i < n; i++) {
      memset(nxt, 0, sizeof(nxt));
      for (int x = 1; x <= 3; x++) {
        for (int y = 1; y <= 3; y++) {
          for (int i = 0; i < 4; i++) {
            if (x + dx[i] == xs[2] && y + dy[i] == ys[2])
              nxt[x][y] += cur[x][y] / 4;
            else
              nxt[x + dx[i]][y + dy[i]] += cur[x][y] / 4;
          }
        }
      }
      memcpy(cur, nxt, sizeof(cur));
    }
    printf("%.8f\n", cur[xs[1]][ys[1]]);
  }
  return 0;
}
