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
input = sys.stdin.readline
from collections import defaultdict

def main():
  n = int(input())
  s = input().strip()
  pc = defaultdict(lambda: 0)
  for i in range(pow(2, n)):
    rd = ""
    bl = ""
    for b in range(n):
      if (i // pow(2, b))%2 == 1:
        rd += s[b]
      else:
        bl += s[b]
    pc[(rd, bl)] += 1

  ans = 0
  s = s[::-1]
  for i in range(pow(2, n)):
    rd = ""
    bl = ""
    for b in range(n):
      if (i // pow(2, b)) % 2 == 1:
        bl += s[b]
      else:
        rd += s[b]
    ans += pc[(rd, bl)]

  print(ans)


if __name__ == '__main__':
  main()