#include <cstdio>
#define rep(i, n) for(int i = 0; i < n; ++i)
#define ck(a) (0 <= (a) && (a) < 9)

int di[] = {-3, -1, 1, 3};

int main() {
    int n, s, t, b; char cs, ct, cb;
    while(scanf("%d", &n)) {
        if(n == 0) break;
        getchar();
        scanf("%c %c %c", &cs, &ct, &cb);
        s = cs - 'A', t = ct - 'A', b = cb - 'A';
        double p[9] = {0}; p[s] = 1.0;


        while(n--) {
            double q[9] = {0};
            rep(i, 9) rep(d, 4) {
                if(ck(i + di[d]) && !(i % 3 == 0 && di[d] == -1) &&
                   !(i % 3 == 2 && di[d] == 1) &&
                   !(i / 3 == 0 && di[d] == -3) &&
                   !(i / 3 == 2 && di[d] == 3) && i + di[d] != b)
                    q[i + di[d]] += p[i] / 4;
                else q[i] += p[i] / 4;
            }
            rep(i, 9) p[i] = q[i];
        }
        printf("%.8lf\n", p[t]);
    }
    return 0;
}