#include <bits/stdc++.h>
using namespace std;
int map[3][3], b_row, b_col;
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;
}
void func(int rest, int row, int col) {
  if (rest == 0) {
    map[row][col]++;
    return;
  }
  if (rangeCheck(row, col - 1) == true && (row != b_row || col - 1 != b_col)) {
    func(rest - 1, row, col - 1);
  } else {
    func(rest - 1, row, col);
  }
  if (rangeCheck(row, col + 1) == true && (row != b_row || col + 1 != b_col)) {
    func(rest - 1, row, col + 1);
  } else {
    func(rest - 1, row, col);
  }
  if (rangeCheck(row - 1, col) == true && (row - 1 != b_row || col != b_col)) {
    func(rest - 1, row - 1, col);
  } else {
    func(rest - 1, row, col);
  }
  if (rangeCheck(row + 1, col) == true && (row + 1 != b_row || col != b_col)) {
    func(rest - 1, row + 1, col);
  } else {
    func(rest - 1, row, col);
  }
}
int main() {
  int n, tmp, energy_row, energy_col;
  char start[2], energy[2];
  while (true) {
    scanf("%d", &n);
    if (n == 0) break;
    for (int i = 0; i < 3; i++) {
      for (int k = 0; k < 3; k++) map[i][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]);
    func(n, tmp / 10, tmp % 10);
    printf("%.8lf\n",
           ((double)map[energy_row][energy_col]) / ((double)pow(4, n)));
  }
  return 0;
}
