#include <bits/stdc++.h>
int m[4] = {3, -3, 1, -1}, s, t, b, dp[9][16];
int d(int p, int n) {
  int i, r = 0;
  if (dp[p][n] != -1) return dp[p][n];
  if (n == 0 && p == t)
    return 1;
  else if (n > 0 && (abs(p / 3 - t / 3) + abs(p % 3 - t % 3)) <= n) {
    for (i = 0; i < 4; i++) {
      if (p + m[i] >= 0 && p + m[i] < 9 && p + m[i] != b)
        r += d(p + m[i], n - 1);
      else
        r += d(p, n - 1);
    }
  }
  return dp[p][n] = r;
}
int main() {
  int n, ans, tmp1;
  double tmp2;
  for (; scanf("%d", &n); ans = 0) {
    if (n == 0) return 0;
    scanf("\n%c %c %c", &s, &t, &b);
    memset(dp, -1, sizeof(dp));
    s -= 65;
    t -= 65;
    b -= 65;
    ans = d(s, n);
    tmp1 = 1 << (n * 2);
    tmp2 = (double)ans / tmp1;
    printf("%lf\n", tmp2);
  }
}
