#include <iostream>
#include <cstdio>
using namespace std;

int dx[] = {-1,0,1,0},dy[] = {0,1,0,-1};

int main(){
	int n;
	char s,t,b;
	while(cin >> n,n){
		cin >> s >> t >> b;
		double dp[16][3][3] = {};
		int sn = s - 'A',tn = t - 'A',bn = b - 'A';
		dp[0][sn / 3][sn % 3] = 1;
		for(int i = 0;i < n;i++){
			for(int j = 0;j < 3;j++){
				for(int k = 0;k < 3;k++){
					for(int l = 0;l < 4;l++){
						int x = j + dx[l],y = k + dy[l];
						if(x >= 0 && x < 3 && y >= 0 && y < 3 && x * 3 + y != bn){
							dp[i + 1][x][y] += dp[i][j][k] / 4.0;
						}
						else dp[i + 1][j][k] += dp[i][j][k] / 4.0;
					}
				}
			}
		}
		printf("%.9f\n",dp[n][tn / 3][tn % 3]);
	}
	return 0;
}