#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;


int main(){
	int n;
	int dx[]={1,0,-1,0};
	int dy[]={0,1,0,-1};
	double nxt[3][3],cur[3][3];
	while(cin>>n,n){
		memset(cur,0,sizeof(cur));
		int xs[3],ys[3];
		for(int i=0;i<3;i++){
			char c;
			int a;
			cin>>c;
			a=c-'A';
			xs[i]=a%3;
			ys[i]=a/3;
		}
		cur[xs[0]][ys[0]]=1;
		for(int i=0;i<n;i++){
			memset(nxt,0,sizeof(nxt));
			for(int x=0;x<3;x++){
				for(int y=0;y<3;y++){
					for(int i=0;i<4;i++){
						if(x+dx[i]==xs[2]&&y+dy[i]==ys[2]||x+dx[i]<0||2<x+dx[i]||y+dy[i]<0||2<y+dy[i])
							nxt[x][y]+=cur[x][y]/4;
						else
							nxt[x+dx[i]][y+dy[i]]+=cur[x][y]/4;
					}
				}
			}
			memcpy(cur,nxt,sizeof(cur));
		}
		printf("%.8f\n",cur[xs[1]][ys[1]]);
	}
	return 0;
}