Problem: You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

* The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

* 1 \leq N \leq 18
* The length of S is 2N.
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the number of ways to paint the string that satisfy the condition.

Examples

Input

4
cabaacba


Output

4


Input

11
mippiisssisssiipsspiim


Output

504


Input

4
abcdefgh


Output

0


Input

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


Output

9075135300

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(10**6)

def main():
	n = int(input())
	s = input()

	dic = {}
	for i in range(0,2**n):
		temp = bin(i)[2:].zfill(n)
		ts1 = ""
		ts2 = ""
		for j in range(n):
			if temp[j] == "1":
				ts1 += s[j]
			else:
				ts2 += s[j]
		if (ts1, ts2) in dic.keys():
			dic[(ts1,ts2)] += 1
		else:
			dic.update({(ts1,ts2):1})
			
	ans = 0
	s = s[::-1]
	for i in range(0,2**n):
		temp = bin(i)[2:].zfill(n)
		ts1  =""
		ts2 = ""
		for j in range(n):
			if temp[j] == "1":
				ts1 += s[j]
			else:
				ts2 += s[j]
		if (ts1, ts2) in dic.keys():
			ans += dic[(ts1,ts2)]
	print(ans)

main()