
#include <iostream>
#include <string.h>

using namespace std;

int n;
char room[10] = "ABCDEFGHI";
char s, t, b;
int off[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
int x, y;

double table[3][3];

double solve()
{
	memset(&table[0][0], 0, sizeof(double) * 9);
	table[y][x] = 1.0;
	for(int k=0; k<n; k++)
	{
		double temp[3][3];
		memset(&temp[0][0], 0, sizeof(double) * 9);
		for(int j=0; j<3; j++)
		{
			for(int i=0; i<3; i++)
			{
				if(table[j][i] != 0.0)
				{
					for(int m=0; m<4; m++)
					{
						int xx = i + off[m][0];
						int yy = j + off[m][1];
						int index = xx + yy * 3;
						xx = (xx>=0 && xx<3 && room[index] != b) ? xx : i;
						yy = (yy>=0 && yy<3 && room[index] != b) ? yy : j;
						temp[yy][xx] += table[j][i] / 4.0;
					}
				}
			}
		}

		memcpy(&table[0][0], &temp[0][0], sizeof(double) * 9);
	}

	for(int i=0; i<9; i++)
	{
		if(room[i]==t) return table[i/3][i%3];
	}

	return 0.0;
}

int main()
{
	while( 1 )
	{
		cin >> n;
		if(n==0) break;
		
		cin >> s >> t >> b;
		for(int i=0; i<9; i++)
		{
			if(room[i] == s)
			{
				x = i%3;
				y = i/3;
			}
		}

		printf("%.8f\n", solve());
	}

	return 0;
}