#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <algorithm>
#include <vector>
#include <utility>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <functional>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cassert>
 
using namespace std;
 
#define REP(i,s,e) for(int i=(s); i<(int)(e); i++)
#define rep(i,n) REP(i, 0, n)
#define pb push_back
#define mp make_pair
#define all(r) (r).begin(),(r).end()
#define rall(r) (r).rbegin(),(r).rend()
#define fi first
#define se second
 
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<ll> vl;
typedef vector<vl> vll;
typedef pair<int, int> pii;
typedef pair<double, int> pdi;
typedef pair<ll, ll> pll;
 

 
const int INF = 1000000;
const double EPS = 1e-8;
const int mod = 1e9 + 7;
const ll LINF = 1e18;
const double PI = acos(-1);

struct Input
{
	int n;
	char c;
	char str[1024];
	int nextInt(){
		scanf("%d", &n);
		return n;
	}
	char nextChar(){
		scanf("%c", &c);
		return c;
	}
	string next(){
		scanf("%s", str);
		return string(str);
	}
	bool hasNext(){
		return !cin.eof();
	}
};
Input in;

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

bool isOutofRange(int x, int y, int b){
	return x < 0 || x >= 3 || y < 0 || y >= 3 || y*3+x==b;
}

int dp[20][3][3];

int main(){
	while(in.hasNext()){
		int n = in.nextInt();
		if(n == 0) break;
		rep(i, 20) rep(j, 3) rep(k, 3) dp[i][j][k] = 0;
		int s = in.next()[0]-'A', t = in.next()[0]-'A', b = in.next()[0]-'A';
		//cout<<s<<" "<<t<<" "<<b<<endl;
		//int x = s % 3, y = s / 3;
		dp[0][s / 3][s % 3] = 1;

		rep(i, n){
			rep(x, 3) rep(y, 3)
				rep(j, 4){
					int nx = x + dx[j], ny = y + dy[j];
					if(isOutofRange(nx, ny, b)) dp[i+1][y][x] += dp[i][y][x];
					else dp[i+1][ny][nx] += dp[i][y][x];
				}
		}

		ll ans = 0LL;
		rep(i, 3) rep(j, 3) ans += dp[n][i][j];

		printf("%.15lf\n", (double)dp[n][t/3][t%3]/ans);
	}
}