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:
N = int(input())
S = input()
S1 = S[:N]
S2 = S[N:][::-1]
from itertools import groupby, accumulate, product, permutations, combinations
from collections import defaultdict
def half(S):
  dic = defaultdict(lambda: 0)
  for pro in product([0,1],repeat=N):
    s1 = s2 = ''
    for i,p in enumerate(pro):
      s1 += S[i]*p
      s2 += S[i]*(1-p)
    dic[(s1,s2)] += 1
  return dic
dic1 = half(S1)
dic2 = half(S2)
ans = 0
for k,v in dic1.items():
  ans += v*dic2[k]
print(ans)