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:
from collections import Counter

def main():
  n = int(input())
  S = input()
  A = S[:n]
  B = S[n:][::-1]
  ans = 0
  La = []
  for i in range(2**n):
    a1, a2 = "", ""
    for j in range(n):
      if i>>j & 1:
        a1 += A[j]
      else:
        a2 += A[j]
    La.append(a1+"#"+a2)

  Da = Counter(La)

  for i in range(2**n):
    b1, b2 = "", ""
    for j in range(n):
      if i>>j & 1:
        b1 += B[j]
      else:
        b2 += B[j]
    ans += Da[b1+"#"+b2]

  print(ans)
  
if __name__ == "__main__":
  main()