#include<cstdio>
#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<string>
using namespace std;
char fie[4][4]={"ABC",
		"DEF",
		"GHI"};
int N;
char s,t,b;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};
double dp[16][4][4];
int used[16][4][4];
double solve(int no,int x,int y){
  if(no==N){
    if(fie[y][x]==t) return 1.0f;
    return 0.0f;
  }
  if(used[no][x][y]) return dp[no][x][y];
  double ret=0.0f;
  for(int i=0;i<4;i++){
    int nx = x+dx[i],ny = y+dy[i];
    if( nx < 0 || ny < 0 || nx>=3 || ny>=3 || fie[ny][nx]==b){
      ret += solve(no+1,x,y)/4.0f;
    } else{
      ret += solve(no+1,nx,ny)/4.0f;
    }
  }
  used[no][x][y]=1;
  return dp[no][x][y]=ret;
}
int main(){
  while(1){
    int x,y;
    cin >> N;
    if(!N) break;
    memset(used,0,sizeof(used));
    cin >> s >> t >> b;
    for(int i=0;i<3;i++)
      for(int j=0;j<3;j++)
	if(fie[i][j]==s){
	  x=j; y=i;
	}
    printf("%.9lf\n",solve(0,x,y));
  }
}