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 defaultdict
N = int(input())
S = input()
S = S[:N]+S[2*N-1:N-1:-1]
ldic = defaultdict(int)
rdic = defaultdict(int)
for i in range(2**N):
  lred = ""
  lblue = ""
  rred = ""
  rblue = ""
  for j in range(N):
    if i%2==1:
      lred += S[j]
      rred += S[N+j]
    else:
      lblue += S[j]
      rblue += S[N+j]
    i >>= 1
  ldic[(lred,lblue)] += 1
  rdic[(rred,rblue)] += 1

ans = 0
for k in ldic.keys():
  ans += ldic[k]*rdic[k]
print(ans)