# include <iostream>
# include <algorithm>
# include <vector>
# include <string>
# include <set>
# include <map>
# include <cmath>
# include <iomanip>
# include <functional>
# include <utility>
# include <stack>
# include <queue>
# include <list>
using namespace std;
using LL = long long;
constexpr int MOD = 1000000000 + 7;
constexpr int INF = 2000000000;
const double PI = acos(-1);


int n;
char s, t, b;
pair<int, int> S, T, B;
double dp[16][3][3];

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

int main() {
	while (cin >> n&&n) {
		cin >> s >> t >> b;
		S = make_pair((s - 'A') / 3, (s - 'A') % 3);
		T = make_pair((t - 'A') / 3, (t - 'A') % 3);
		B = make_pair((b - 'A') / 3, (b - 'A') % 3);
		for (int i = 0; i < 16; i++) {
			for (int j = 0; j < 3; j++) {
				for (int k = 0; k < 3; k++) {
					dp[i][j][k] = 0;
				}
			}
		}
		dp[0][S.first][S.second] = 1;
		for (int i = 0; i < n; i++) {
			for (int y = 0; y < 3; y++) {
				for (int x = 0; x < 3; x++) {
					if (dp[i][y][x] == 0)continue;
					for (int d = 0; d < 4; d++) {
						int ny = y + dy[d], nx = x + dx[d];
						if (0 <= nx&&nx < 3 && 0 <= ny&&ny < 3 && make_pair(ny, nx) != B)dp[i + 1][ny][nx] += dp[i][y][x] * 0.25;
						else dp[i + 1][y][x] += dp[i][y][x] * 0.25;
					}
				}
			}
		}
		cout << fixed << setprecision(10) << dp[n][T.first][T.second] << endl;
	}
}