#include <iostream>
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]);
	}
}
	