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:
from collections import defaultdict
con = 10 ** 9 + 7; INF = float("inf")

def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	N = int(input())
	S = input()
	D1 = defaultdict(int)
	D2 = defaultdict(int)
	for i in range(1 << N):
		R = ""
		B = ""
		for j in range(N):
			if ((i >> j) & 1) == 1:
				R += S[j]
			else:
				B += S[j]

		RB = R + "," + B
		D1[RB] += 1

	for i in range(1 << N):
		R = ""
		B = ""
		for j in range(N):
			if ((i >> j) & 1) == 1:
				R += S[-1 - j]
			else:
				B += S[-1 - j]

		RB = R + "," + B
		D2[RB] += 1

	ans = 0
	for i in D1:
		ans += D1[i] * D2[i]

	print(ans)


if __name__ == '__main__':
	main()