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()

sl = s[:n]
sr = s[n:][::-1]

from collections import Counter
l = Counter()
r = Counter()

from itertools import product
for m in product([False, True], repeat=n):
  key = [sl[i] for i in range(n) if not m[i]]
  key += ['-']
  key += [sl[i] for i in range(n) if m[i]]
  l[''.join(key)] += 1
  
  key = [sr[i] for i in range(n) if not m[i]]
  key += ['-']
  key += [sr[i] for i in range(n) if m[i]]
  r[''.join(key)] += 1
  
ans = sum(l[lk] * r[lk] for lk in l.keys())

print(ans)