Problem:
Problem B: Cleaning Robot

Dr. Asimov, a robotics researcher, loves to research, but hates houseworks and his house were really dirty. So, he has developed a cleaning robot.

As shown in the following figure, his house has 9 rooms, where each room is identified by an alphabet:

The robot he developed operates as follows:

If the battery runs down, the robot stops.

If not so, the robot chooses a direction from four cardinal points with the equal probability, and moves to the room in that direction. Then, the robot clean the room and consumes 1 point of the battery.

However, if there is no room in that direction, the robot does not move and remains the same room. In addition, there is a junk room in the house where the robot can not enter, and the robot also remains when it tries to enter the junk room. The robot also consumes 1 point of the battery when it remains the same place.

A battery charger for the robot is in a room. It would be convenient for Dr. Asimov if the robot stops at the battery room when its battery run down.

Your task is to write a program which computes the probability of the robot stopping at the battery room.

Input

The input consists of several datasets. Each dataset consists of:

n
s t b

n is an integer that indicates the initial battery point. s, t, b are alphabets respectively represent the room where the robot is initially, the battery room, and the junk room.

The input ends with a dataset which consists of single 0 for n. Your program should not output for this dataset.

Output

For each dataset, print the probability as a floating point number in a line. The answer may not have an error greater than 0.000001.

Constraints

Judge data includes at most 100 data sets.

n ≤ 15

s, t, b are distinct.

Sample Input

1
E A C
1
E B C
2
E A B
0

Output for the Sample Input

0.00000000
0.25000000
0.06250000

Solution in Ruby (judge verdict: Wrong Answer)

# encoding: utf-8                                                            

$map = {
  :A => [1, 1], :B => [1, 2], :C => [1, 3],
  :D => [2, 1], :E => [2, 2], :F => [2, 3],
  :G => [3, 1], :H => [3, 2], :I => [3, 3]
}
 
def solve(n, s, b, j)
  s, b, j = s.to_sym, b.to_sym, j.to_sym
  dis = ($map[s][0] - $map[b][0]).abs + ($map[s][1] - $map[b][1]).abs
  if dis > n
    0.0
  else
    0.25 ** dis
  end
end

while n = gets
  n = n.to_i  
  break if n == 0
  s, b, j = gets.rstrip.split(/\s/)
  puts ("%.8f" % solve(n, s, b, j))
end