#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <cmath>
#include <ctime>
#include <cassert>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <complex>
#include <string>
#include <vector>
#include <list>
#include <deque>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <iterator>
#include <functional>
#include <utility>
#include <algorithm>
#include <numeric>
#include <typeinfo>

using namespace std;

#define dump(n) cout<<"# "<<#n<<"="<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,n) repi(i,0,n)
#define iter(c) __typeof((c).begin())
#define foreach(i,c) for(iter(c) i=(c).begin();i!=(c).end();++i)
#define allof(c) (c).begin(),(c).end()
#define mp make_pair

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;
typedef pair<int,int> pii;

int main()
{
	for(int n;cin>>n,n;){
		vvd cur(3,vd(3));
		pii barn;
		char s,t,b; cin>>s>>t>>b;
		cur[(s-'A')/3][(s-'A')%3]=1;
		barn=mp((b-'A')/3,(b-'A')%3);
		while(n--){
			vvd next(3,vd(3));
			rep(i,3) rep(j,3){
				int di[]={-1,1,0,0};
				int dj[]={0,0,-1,1};
				int stop=0;
				rep(k,4){
					int ni=i+di[k],nj=j+dj[k];
					if(ni<0 || 3<=ni || nj<0 || 3<=nj || mp(ni,nj)==barn)
						stop++;
					else
						next[ni][nj]+=cur[i][j]/4;
				}
				next[i][j]+=cur[i][j]*stop/4;
			}
			cur=next;
		}
		printf("%f\n",cur[(t-'A')/3][(t-'A')%3]);
	}
	
	return 0;
}