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, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, tan, asin, acos, atan, radians, degrees, log2, gcd
from itertools import accumulate, permutations, combinations, combinations_with_replacement, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left, insort, insort_left
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def TUPLE(): return tuple(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7 
#mod = 998244353
from decimal import *
#import numpy as np
#decimal.getcontext().prec = 10


def main():
	N = INT()
	S = input()

	s1 = []
	dic_s2 = defaultdict(int)

	for x in product([0, 1], repeat=N):
		s1_red = ""
		s1_blue = ""
		s2_red = ""
		s2_blue = ""
		for i in range(N):
			if x[i]:
				s1_red += S[i]
				s2_red += S[N+i]
			else:
				s1_blue += S[i]
				s2_blue += S[N+i]

		s1.append((s1_red, s1_blue))
		dic_s2[(s2_blue[::-1], s2_red[::-1])] += 1

	ans = 0
	for x in s1:
		ans += dic_s2[x]

	print(ans)

if __name__ == '__main__':
	main()