#include <iostream>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>
#include <sstream>
using namespace std;

long cnt,as;
char s,t,b;
const int dy[]={-1,0,1,0};
const int dx[]={0,1,0,-1};
int main(){
  int n,tx,ty;
  long field[2][5][5];
  for(;cin>>n,n;){
    cin.ignore();
    cnt=as=0;
    scanf(" %c %c %c ",&s,&t,&b);
    memset(field,0,sizeof(field));
    int x= s=='A'||s=='D'||s=='G'?1:s=='B'||s=='E'||s=='H'?2:3;
    int y= s=='A'||s=='B'||s=='C'?1:s=='D'||s=='E'||s=='F'?2:3;
    
    int p= t=='A'||t=='D'||t=='G'?1:t=='B'||t=='E'||t=='H'?2:3;
    int q= t=='A'||t=='B'||t=='C'?1:t=='D'||t=='E'||t=='F'?2:3;

    int u= b=='A'||b=='D'||b=='G'?1:b=='B'||b=='E'||b=='H'?2:3;
    int t= b=='A'||b=='B'||b=='C'?1:b=='D'||b=='E'||b=='F'?2:3;

    field[0][y][x]=1;
    field[0][0][0]=field[0][0][1]=field[0][0][2]=field[0][0][3]=field[0][0][4]=1;
    field[0][4][0]=field[0][4][1]=field[0][4][2]=field[0][4][3]=field[0][4][4]=1;
    field[0][1][0]=field[0][2][0]=field[0][3][0]=1;
    field[0][1][4]=field[0][2][4]=field[0][3][4]=1;
    for(int k=0;k<n;k++){
      for(int i=1;i<4;i++){
        for(int j=1;j<4;j++){
          if(i==t && j==u)continue;

          for(int g=0;g<4;g++){
            tx=j+dx[g];
            ty=i+dy[g];
            if(tx<1 || ty<1 || tx>=4 || ty>=4)continue;
            field[1][i][j]+=field[0][ty][tx];
          }
          /*
          if(field[0][i][j]!=0 && (i-1==t&&j==u || i+1==t&&j==u ||
                                   i==t&&j-1==u || i==t&&j+1==u) ){
            field[1][i][j]++;
          }*/
          int uguu=0;
          if(field[0][i][j]>0){
            for(int g=0;g<4;g++){
              tx=j+dx[g];
              ty=i+dy[g];
              if((tx<1 || ty<1 || tx>=4 || ty>=4) || ty==t&&tx==u){
                uguu++;
              }
            }
            
            field[1][i][j]+=field[0][i][j]*uguu;
          }
        }
      }
      /*
      for(int ii=1;ii<4;ii++){
        for(int jj=1;jj<4;jj++){
          printf("%7ld ",field[1][ii][jj]);
        }
        puts("");
      }
      puts("");*/
      for(int i=1;i<4;i++)for(int j=1;j<4;j++)field[0][i][j]=field[1][i][j],field[1][i][j]=0;
    }

    printf("%.8lf\n",(double)field[0][q][p]/pow(4.0,(double)n));
  }
  return 0;
}