#include <bits/stdc++.h>
using namespace std;
double dp[16][3][3];
int n, dx[] = {0, -1, 0, 1}, dy[] = {-1, 0, 1, 0};
char cs, ct, cb;
int s, t, b;
int main() {
  while (scanf("%d", &n) && n) {
    memset(dp, 0.0, sizeof(dp));
    scanf("\n%c %c %c", &cs, &ct, &cb);
    s = cs - 'A';
    t = ct - 'A';
    b = cb - 'A';
    dp[0][s / 3][s % 3] = 1;
    for (int(i) = (0); ((i)) < ((n)); ++(i))
      for (int(y) = (0); ((y)) < ((3)); ++(y))
        for (int(x) = (0); ((x)) < ((3)); ++(x)) {
          for (int(d) = (0); ((d)) < ((4)); ++(d)) {
            int ny = y + dy[d], nx = x + dx[d];
            if (ny < 0 || nx < 0 || ny >= 3 || nx >= 3 || ny * 3 + nx == b)
              continue;
            dp[i + 1][ny][nx] += dp[i][y][x] * 0.25;
          }
        }
    printf("%.8lf\n", dp[n][t / 3][t % 3]);
  }
  return 0;
}
