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: Accepted)

loop{
	n = gets.to_i()
	if n == 0 then
		break
	end
	
	s,t,b = gets.split
	room_path = {	"A"=>["B","D"],		"B"=>["A","C","E"],		"C"=>["B","F"],
					"D"=>["A","E","G"],	"E"=>["D","B","F","H"],	"F"=>["E","C","I"],
					"G"=>["H","D"],		"H"=>["E","G","I"],		"I"=>["F","H"]}
					
	room_path[b].each{|r|
		room_path[r].select!{|item| item != b}
	}
	
	room = Hash.new(0.0)
	room[s] = 1.0
	
	
	n.times do
		troom = Hash.new(0.0)
		room_path.each_key{|key|
			troom[key] = room[key]
		}
		
		room_path.each{|key,path|
			room[key] = ((4.0-path.size())/4) * troom[key]
			path.each{|r|
				room[key] += troom[r]/4
			}
		}
	end
	p room[t]
	
}