#include <bits/stdc++.h>
#define REP(i,n) for (int i=0;i<(n);i++)
#define ALL(a) (a).begin(),(a).end()
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) for (int i=0;i<(n);i++)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#define ll long long
#define ull unsigned long long
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

using namespace std;

typedef pair<int, int> P;

P nukumori(char a) {
    if (a == 'A') {
        return P(0, 0);
    } else if (a == 'B') {
        return P(1, 0);
    } else if (a == 'C') {
        return P(2, 0);
    } else if (a == 'D') {
        return P(0, 1);
    } else if (a == 'E') {
        return P(1, 1);
    } else if (a == 'F') {
        return P(2, 1);
    } else if (a == 'G') {
        return P(0, 2);
    } else if (a == 'H') {
        return P(1, 2);
    } else {
        return P(2, 2);
    }
}

int sx, sy, gx, gy, ox, oy;
double memo[3][3][20];

double rec(int x, int y, int times) {
    if (memo[x][y][times] >= 0.0) return memo[x][y][times];

    if (times == 0) {
        if (x == gx && y == gy) {
            return 1.0;
        } else {
            return 0.0;
        }
    }

    double res = 0.0;
    for (int i = 0; i < 4; i++) {
        int nx = x + dx[i], ny = y + dy[i];
        if (nx >= 0 && nx < 3 && ny >= 0 && ny < 3 &&
                !(nx == ox && ny == oy)) {
            res += rec(nx, ny, times - 1) / 4.0;
        } else {
            res += rec(x, y, times - 1) / 4.0;
        }
    }
    return memo[x][y][times] = res;
}

int main(){
    int n;
    char s, t, b;
    while (scanf("%d", &n), n) {
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                for (int k = 0; k < 20; k++) {
                    memo[i][j][k] = -1.0;
                }
            }
        }
        cin >> s >> t >> b;

        P temps = nukumori(s),
          tempt = nukumori(t),
          tempb = nukumori(b);

        sx = temps.first; sy = temps.second;
        gx = tempt.first; gy = tempt.second;
        ox = tempb.first; oy = tempb.second;

        printf("%.10f\n", rec(sx, sy, n));
    }

    return 0;
}