#include <stdio.h>
#include <cmath>
#include <algorithm>
#include <stack>

using namespace std;

int b_row,b_col,memo[16][3][3];

char b[2];

bool rangeCheck(int row,int col){
	if(row >= 0 && row <= 2 && col >= 0 && col <= 2)return true;
	else{
		return false;
	}
}

int translate(char ch){
	switch(ch){
	case 'A':return 0;
	case 'B':return 1;
	case 'C':return 2;
	case 'D':return 10;
	case 'E':return 11;
	case 'F':return 12;
	case 'G':return 20;
	case 'H':return 21;
	case 'I':return 22;
	}

	return -1; //must not reach here.
}

int main(){

	int n,tmp,energy_row,energy_col,row,col,div_row[4] = {-1,0,0,1},div_col[4] = {0,-1,1,0};
	char start[2],energy[2];

	while(true){
		scanf("%d",&n);
		if(n == 0)break;

		for(int i = 0; i < 16; i++){
			for(int p = 0; p < 3; p++){
				for(int k = 0; k < 3; k++)memo[i][p][k] = 0;
			}

		}

		scanf("%s %s %s",start,energy,b);

		tmp = translate(b[0]);
		b_row = tmp/10;
		b_col = tmp%10;

		tmp = translate(energy[0]);
		energy_row = tmp/10;
		energy_col = tmp%10;

		tmp = translate(start[0]);

		row = tmp/10,col = tmp%10;

		memo[0][row][col] = 1;

		for(int loop = 0; loop <= n-1; loop++){
			for(int i = 0; i < 3; i++){
				for(int k = 0; k < 3; k++){
					if(i != b_row || k != b_col){ //????????§????????´???
						for(int p = 0; p < 4; p++){
							if(rangeCheck(i+div_row[p],k+div_col[p]) == true && (i+div_row[p] != b_row || k + div_col[p] != b_col)){ //?§????????????§??????????????????????????§??????
								memo[loop+1][i+div_row[p]][k+div_col[p]] += memo[loop][i][k];
							}else{ //?°?????????¨???1????????????????????????????????´?????????????????´??????????????¨????????´????????°???????????????
								memo[loop+1][i][k] += memo[loop][i][k];
							}
						}
					}
				}
			}
		}

		printf("%.8lf\n",((double)memo[n][energy_row][energy_col])/((double)pow(4,n)));
	}

	return 0;
}