#include<stdio.h>
#include <iostream>
using namespace std;

int main() {
	while (1) {
		int n, s, t, b, sum = 0;
		int ai[16][3][3] = { 0 };
		char a, d, c;
		scanf("%d", &n);
		if (n == 0) break;
		cin >> a >> d >> c;
		s = a - 'A';  t = d - 'A'; b = c - 'A';
		ai[0][s / 3][s % 3] = 1;
		for (int i = 1; i <= n; ++i) {
			for (int j = 0; j < 3; ++j) {
				for (int l = 0; l < 3; ++l) {
					if (j - 1 >= 0 && (j-1) * 3 + l != b) ai[i][j - 1][l] += ai[i - 1][j][l];
					else ai[i][j][l] += ai[i - 1][j][l];
					if (j + 1 < 3 && (j + 1) * 3 + l != b) ai[i][j + 1][l] += ai[i - 1][j][l];
					else ai[i][j][l] += ai[i - 1][j][l];

					if (l - 1 >= 0 && j * 3 + l - 1 != b) ai[i][j][l - 1] += ai[i - 1][j][l];
					else ai[i][j][l] += ai[i - 1][j][l];
					if (l + 1 < 3 && j * 3 + l + 1 != b) ai[i][j][l + 1] += ai[i - 1][j][l];
					else ai[i][j][l] += ai[i - 1][j][l];					
				}
			}
		}
		for (int i = 0; i < 3; ++i) {
			for (int j = 0; j < 3; ++j) {
				sum += ai[n][i][j];
			}
		}
		printf("%f\n", (double)ai[n][t / 3][t % 3] / sum);
	}

}