#include <iostream>
#include<cstdio>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
const int dx[] ={ 0,1,0,-1};
const int dy[] ={-1,0,1, 0};

int main(){
  int n;
  while(cin >> n , n){
    long double dp[16][5][5] = {{{0.0}}};
    char map[5][5];
    rep(i,5)rep(j,5)map[i][j] = 'X';
    rep(i,3)rep(j,3)map[i+1][j+1] = ' ';
    int sx, sy, gx, gy, bx, by;
    char s,t,b;
    cin >> s >> t >> b ;
    sy = (s-'A')/3 +1 , sx = (s-'A')%3 +1;
    gy = (t-'A')/3 +1 , gx = (t-'A')%3 +1;
    by = (b-'A')/3 +1 , bx = (b-'A')%3 +1;
    
    map[by][bx] = 'X';
    dp[n][sy][sx] = 1.0;
    
    while(n){
      for(int y=1;y<=3;y++){
	for(int x=1;x<=3;x++){
	  rep(i,4){
	    int tx = x+dx[i], ty = y+dy[i] ;
	    if(map[ty][tx] == 'X')ty = y , tx = x;
	    dp[n-1][ty][tx] += dp[n][y][x] / 4.0;
	  }
	}
      }
      n--;
    }
    printf("%.8Lf\n",dp[0][gy][gx]);
  }
}