#include <bits/stdc++.h>

using namespace std;

typedef pair<int, int> pii;

pii get_pos(int x)
{
    return pii(x / 3, x % 3);
}

bool inField(int x, int y)
{
    return (0 <= x && x < 3 && 0 <= y && y < 3);
}

int main()
{
    int N;
    while (cin >> N, N) {
        string S = "ABCDEFGHI";
        char a[3];
        for (int i = 0; i < 3; i++) {
            cin >> a[i];
        }
        int s = S.find(a[0]);
        int t = S.find(a[1]);
        int b = S.find(a[2]);

        double dp[25][9] = {{}};
        pii p = get_pos(b);

        dp[0][s] = 1;
        
        const int di[] = {-1, +0, +1, +0};
        const int dj[] = {+0, -1, +0, +1};
        
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < 9; j++) {
                if (dp[i][j] == 0) continue;
                pii n = get_pos(j);
                for (int k = 0; k < 4; k++) {
                    int ni = n.first + di[k];
                    int nj = n.second + dj[k];
                    if (!inField(nj, ni) || (pii(ni, nj) == p)) {
                        dp[i+1][j] += dp[i][j] / 4;
                    } else {
                        dp[i+1][ni*3+nj] += dp[i][j] / 4;
                    }
                }
            }
        }
        printf("%.10f\n", dp[N][t]);            
    }    
    return 0;
}