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,S = open(0).read().split()
N = int(N)
ldic = defaultdict(int)
rdic = defaultdict(int)
L = S[:N]
R = S[N:][::-1]
for i in range(2**N):
  la = ''
  lb = ''
  ra = ''
  rb = ''
  for j in range(N):
    if i%2==1:
      la += L[j]
      ra += R[j]
    else:
      lb += L[j]
      rb += R[j]
    i >>= 1
  ldic[(la,lb)] += 1
  rdic[(ra,rb)] += 1
ans = sum(rdic[k]*ldic[k] for k in ldic.keys())
print(ans)