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()

former = defaultdict(lambda: 0)
latter = defaultdict(lambda: 0)

def power(n):
  return chain(*(combinations(range(n), r) for r in range(n+1)))

def solve(N, S):
  for p in power(N):
    bs1 = []; rs1 = []; bs2 = []; rs2 = []
    for i in range(N):
      if i in p:
        rs1.append(S[i])
        rs2.append(S[-1-i])
      else:
        bs1.append(S[i])
        bs2.append(S[-1-i])
    former["".join(rs1), "".join(bs1)] += 1
    latter["".join(bs2), "".join(rs2)] += 1

  ans = 0
  for k, v in former.items():
    if k in latter:
      ans += v * latter[k]

  return ans

print(solve(N, S))