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:
# encoding:utf-8

import itertools
from collections import defaultdict


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

	left = s[:n]
	right = s[n:]
	right = right[::-1]

	ans = 0
	#print(left, right)
	for n_r in range(n+1):
		d_left = defaultdict(lambda: 0)
		d_right = defaultdict(lambda: 0)
		#print([1 if x >= n_r else 0 for x in range(n)])
		pts = itertools.combinations(list(range(n)), r = n_r)
		
		for pt in pts:
			#print(pt)
			b_l = ""
			r_l = ""
			b_r = ""
			r_r = ""
			for i in range(n):
				if i in pt:
					b_l += left[i]
					b_r += right[i]
				else:
					r_l += left[i]
					r_r += right[i]

			d_left[(b_l, r_l)] += 1
			d_right[(b_r, r_r)] += 1

		for key in d_left:
#			print(n_r, key, d_left[key], d_right[key])
			ans += d_left[key] * d_right[key]

	print(ans)

	

if __name__ == '__main__':
	main()