#include <vector>
#include <list>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <utility>
#include <functional>
#include <sstream>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <climits>
#include <cassert>
using namespace std;
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define REP(i,n) FOR(i,0,(n)-1)
const double EPS = 1e-10;
const double PI  = acos(-1.0);
const int INF = INT_MAX/10;

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

int main() {
	int n;
	char s, t, b;

	while(cin >> n, n) {
		cin >> s >> t >> b;

		int sx = (s-'A')%3, sy = (s-'A')/3;
		int tx = (t-'A')%3, ty = (t-'A')/3;
		int bx = (b-'A')%3, by = (b-'A')/3;

		vector<vvi> dp(3, vvi(3, vi(n+1)));
		dp[sy][sx][0] = 1;
		FOR(i, 1, n) {
			REP(x, 3) {
				REP(y, 3) {
					REP(d, 4) {
						int nx = x + dx[d];
						int ny = y + dy[d];
						if(nx < 0 || 2 < nx || ny < 0 || 2 < ny) {
							nx = x;
							ny = y;
						}
						if(nx == bx && ny == by) {
							nx = x;
							ny = y;
						}

						dp[ny][nx][i] += dp[y][x][i-1];
					}
				}
			}
		}

		double ans = (double)dp[ty][tx][n]/(1<<(2*n));
		printf("%.8f\n", ans);
	}

	return 0;
}