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
import sys
input = sys.stdin.readline

n = int(input())
S = input().rstrip()
L = S[:n]
R = S[n:][::-1]
C = defaultdict(int)
ans = 0
for i in range(1<<n):
  l = ""
  r = ""
  for j, s in enumerate(L):
    if i>>j & 1:
      l += s
    else:
      r += s
  C[l+"."+r] += 1
for i in range(1<<n):
  l = ""
  r = ""
  for j, s in enumerate(R):
    if i>>j & 1:
      l += s
    else:
      r += s
  ans += C[l+"."+r]
print(ans)