#include <iostream>
#include <iomanip>
#include <cstring>

using namespace std;

int main() {
	int n;
	while (cin >> n, n) {
		long double room[3][3][n+1];
		memset(room, 0, sizeof(room));

		char s, t, b;
		cin >> s >> t >> b;

		int y = (s-'A') / 3;
		int x = (s-'A') % 3;
		int by = (b-'A') / 3;
		int bx = (b-'A') % 3;
		int gy = (t-'A') / 3;
		int gx = (t-'A') % 3;

		room[y][x][0] = 1.0;

		int dx[] = {-1, 0, 0, 1};
		int dy[] = {0, -1, 1, 0};
		for (int i = 0; i < n; i++) {
			for (int k = 0; k < 3; k++) {
				for (int l = 0; l < 3; l++) {
					for (int j = 0; j < 4; j++) {
						int nx = l + dx[j];
						int ny = k + dy[j];
						if (nx < 0 || 2 < nx || ny < 0 || 2 < ny || (bx == nx && by == ny)) {
							room[k][l][i+1] += room[k][l][i] * 0.25;
						} else {
							room[ny][nx][i+1] += room[k][l][i] * 0.25;
						}
					}
				}
			}
		}
		cout.precision(9);
		cout << fixed << room[gy][gx][n] << endl;
	}
	return 0;
}