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 sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

N = read()
S = input()

ans = 0

for bits in range(2**N):
  bs = []; rs = []
  for i in range(N):
    if ((1 << i) & bits) == 0:
      rs.append(S[i])
    else:
      bs.append(S[i])
  rs.reverse(); bs.reverse()

  lenr = len(rs); lenb = len(bs)
  dp = [[0] * (lenb + 1) for _ in range(lenr + 1)]
  dp[0][0] = 1
  for i in range(lenr + 1):
    for j in range(lenb + 1):
      if i < lenr and rs[i] == S[N+i+j]:
        dp[i+1][j] += dp[i][j]
      if j < lenb and bs[j] == S[N+i+j]:
        dp[i][j+1] += dp[i][j]
  ans += dp[-1][-1]

print(ans)