#include <bits/stdc++.h>

#define FOR(i,a,b) for(int i= (a); i<((int)b); ++i)
#define RFOR(i,a) for(int i=(a); i >= 0; --i)
#define FOE(i,a) for(auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define DUMP(x)  cerr << #x << " = " << (x) << endl;
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v,x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT(n) (1LL<<(n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

typedef long long LL;
template<typename T> using V = std::vector<T>;
template<typename T> using VV = std::vector<std::vector<T>>;
template<typename T> using VVV = std::vector<std::vector<std::vector<T>>>;

template<class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
template<class T> inline void print(T x) { std::cout << x << std::endl; }
template<class T> inline void print_vec(const std::vector<T> &v) { for (int i = 0; i < v.size(); ++i) {  if (i != 0) {std::cout << " ";} std::cout << v[i];} std::cout << "\n"; }
template<class T> inline bool inside(T y, T x, T H, T W) {return 0 <= y and y < H and 0 <= x and x < W; }
template<class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); }
template<class T> inline double manhattan_distance(T y1, T x1, T y2, T x2) { return abs(x1 - x2) + abs(y1 - y2); }

const int INF = 1L << 30;
const double EPS = 1e-9;
const std::string YES = "YES", Yes = "Yes", NO = "NO", No = "No";
const std::vector<int> dy4 = { 0, 1, 0, -1 }, dx4 = { 1, 0, -1, 0 };    // 4近傍（右, 下, 左, 上）
const std::vector<int> dy8 = { 0, -1, 0, 1, 1, -1, -1, 1 }, dx8 = { 1, 0, -1, 0, 1, 1, -1, -1 };

using namespace std;


int main() {
    cin.tie(0);
	ios::sync_with_stdio(false);

	while (true) {
        int N;
        char S, T, B;
        cin >> N;
        if (N == 0) {
            break;
        }
        cin >> S >> T >> B;

        map<char, pair<int, int>> d;
        FOR(y, 0, 3) {
            FOR(x, 0, 3) {
                d['A' + 3 * y + x] = make_pair(y, x);
            }
        }
        int sy = d[S].first, sx = d[S].second;
        int ey = d[T].first, ex = d[T].second;
        int by = d[B].first, bx = d[B].second;

        vector<vector<vector<double>>> dp(N + 1, vector<vector<double>>(3, vector<double>(3)));
        dp[N][sy][sx] = 1;

        for (int n = N; n > 0; --n) {
            FOR(y, 0, 3) {
                FOR(x, 0, 3) {
                    if (dp[n][y][x] == 0) {
                        continue;
                    }

                    FOR(i, 0, 4) {
                        int ny = dy4[i] + y;
                        int nx = dx4[i] + x;

                        if (not inside(ny, nx, 3, 3) or (ny == by and nx == bx)) {
                            dp[n - 1][y][x] += dp[n][y][x] * 0.25;
                        }
                        else {
                            dp[n - 1][ny][nx] += dp[n][y][x] * 0.25;
                        }
                    }
                }
            }
        }

        cout << fixed << setprecision(7) << dp[0][ey][ex] << endl;
    }
	return 0;
}


Measured memory_bytes: 3224