#include<iostream>
#include<iomanip>
#include<cstring>
using namespace std;
char T[3], U[10] = "ABCDEFGHI"; int n, c[3][2], x[5][5]; double p[100][5][5];

void A(int E, int B, int C, double D, int F, int G) { 
	if (x[B][C] == 0) { 
		p[E][B][C] += D; 
	} 
	else {
		p[E][F][G] += D;
	}
}

int main() {
	while (true) {
		memset(p, 0.0, sizeof(p));
		cin >> n;
		if (!n) { break; }
		cin >> T[0] >> T[1] >> T[2];
		for (int i = 0; i < 3; i++) {
			for (int j = 0; j < 9; j++) {
				if (U[j] == (char)T[i]) {
					c[i][0] = j / 3 + 1;
					c[i][1] = j % 3 + 1;
				}
			}
		}
		p[n][c[0][0]][c[0][1]] = 1;
		for (int i = 0; i < 25; i++) {
			x[i / 5][i % 5] = 1;
		}
		for (int i = 1; i <= 3; i++) {
			for (int j = 1; j <= 3; j++) {
				if (i != c[2][0] || j != c[2][1]) {
					x[i][j] = 0;
				}
			}
		}
		for (int i = n - 1; i >= 0; i--) {
			for (int j = 1; j <= 3; j++) {
				for (int k = 1; k <= 3; k++) {
					if (p[i + 1][j][k]>0) {
						A(i, j - 1, k, p[i + 1][j][k] / 4.0, j, k);
						A(i, j + 1, k, p[i + 1][j][k] / 4.0, j, k);
						A(i, j, k + 1, p[i + 1][j][k] / 4.0, j, k);
						A(i, j, k - 1, p[i + 1][j][k] / 4.0, j, k);
					}
				}
			}
		}
		cout << fixed << setprecision(15) << p[0][c[1][0]][c[1][1]] << endl;
	}
}