#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <cfloat>
#include <ctime>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <numeric>
#include <list>

using namespace std;

#ifdef _MSC_VER
#define __typeof__ decltype

template <class T>
int __builtin_popcount(T n) { return n ? 1 + __builtin_popcount(n & (n - 1)) : 0; }
#endif

#define foreach(it, c) for (__typeof__((c).begin()) it=(c).begin(); it != (c).end(); ++it)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define popcount __builtin_popcount
	
#define rep(i, n) for (int i = 0; i < n; ++i)

template <class T> void max_swap(T& a, const T b) { a = max(a, b); }
template <class T> void min_swap(T& a, const T b) { a = min(a, b); }

const double EPS = 1e-10;
typedef long long ll;
typedef pair<int, int> pint;


int main()
{
	int n;
	char s, t, b;
	while (cin >> n, n)
	{
		cin >> s >> t >> b;
		s -= 'A';
		t -= 'A';
		b -= 'A';

		int sx = s % 3, sy = s / 3;
		int tx = t % 3, ty = t / 3;
		int bx = b % 3, by = b / 3;

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

		double dp[20][3][3];
		memset(dp, 0, sizeof(dp));
		dp[0][sy][sx] = 1;
		rep (i, n)
		{
			rep (y, 3)
			{
				rep (x, 3)
				{
					rep (j, 4)
					{
						int nx = x + dx[j], ny = y + dy[j];
						if (0 <= nx && nx < 3 && 0 <= ny && ny < 3
							&& !(nx == bx && ny == by))
							dp[i + 1][ny][nx] += dp[i][y][x] / 4;
						else
							dp[i + 1][y][x] += dp[i][y][x] / 4;
					}
				}
			}
		}

		printf("%.8f\n", dp[n][ty][tx]);
	}
}