#include<bits/stdc++.h>
using namespace std;

double dp[16][9];
int k, x, y, z;
int b[9][4]={
	{1,3,-1,-1},
	{ 0,2,4,-1 },
	{ 1,5,-1,-1 },
	{ 0,4,6,-1 },
	{ 1,3,5,7 },
	{ 2,4,8,-1 },
	{ 3,7,-1,-1 },
	{ 4,6,8,-1 },
	{ 5,7,-1,-1 }
};
int main() {
	while (cin >> k, k) {
		memset(dp, 0, sizeof(dp));
		char a, b, c; cin >> a >> b >> c;
		dp[0][a - 'A'] = 1;
	    y = b - 'A'; z = c - 'A';
		double S = 0;
		for (int i = 0; i < k; i++) {
			for (int j = 0; j < 9; j++) {
				for (int l = 0; l < 4; l++) {
					if (::b[j][l] == -1 || ::b[j][l] == z) {
						dp[i + 1][j] += dp[i][j] * 0.25;
					}
					else {
						dp[i + 1][::b[j][l]] += dp[i][j] * 0.25;
					}
				}
			}
		}
		printf("%.10lf\n", dp[k][y]);
	}
}