#include <bits/stdc++.h>
using namespace std;
struct Point {
  int y, x;
};
int nari[3][3];
int bfs(int, int, int, int);
int y11(int);
int x11(int);
int main() {
  int n, j, i;
  char s, t, b;
  double ans;
  while (1) {
    cin >> n;
    if (n == 0) break;
    cin >> s >> t >> b;
    bfs(s, t, b, n);
    printf("%lf\n", (double)bfs(s, t, b, n) / pow(4, n));
  }
}
int bfs(int s, int t, int b, int n) {
  Point u, v;
  queue<Point> Q;
  int ny, nx, count = 0, nn = 0;
  int dy[4] = {0, -1, 0, 1};
  int dx[4] = {1, 0, -1, 0};
  for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 3; j++) nari[i][j] = INT_MAX;
  }
  u.y = y11(s);
  u.x = x11(s);
  nari[y11(b)][x11(b)] = -1;
  nari[u.y][u.x] = 1;
  Q.push(u);
  while (!Q.empty()) {
    nn++;
    u = Q.front();
    Q.pop();
    for (int r = 0; r < 4; r++) {
      nx = u.x + dx[r];
      ny = u.y + dy[r];
      if (nx < 0 || ny < 0 || ny >= 3 || nx >= 3) {
        nx = u.x;
        ny = u.y;
      }
      if (ny == y11(t) && nx == x11(t) && pow(4, n - 1) >= nn) count++;
      if (nari[ny][nx] != INT_MAX) continue;
      nari[ny][nx] = nari[u.y][u.x] + 1;
      v.x = nx;
      v.y = ny;
      Q.push(v);
    }
  }
  return count;
}
int y11(int s) {
  if (s == 'A') return 0;
  if (s == 'B') return 0;
  if (s == 'C') return 0;
  if (s == 'D') return 1;
  if (s == 'E') return 1;
  if (s == 'F') return 1;
  if (s == 'G') return 2;
  if (s == 'H') return 2;
  if (s == 'I') return 2;
}
int x11(int s) {
  if (s == 'A') return 0;
  if (s == 'B') return 1;
  if (s == 'C') return 2;
  if (s == 'D') return 0;
  if (s == 'E') return 1;
  if (s == 'F') return 2;
  if (s == 'G') return 0;
  if (s == 'H') return 1;
  if (s == 'I') return 2;
}
