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:
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n = int(input())
S = input()
s1 = S[:n];s2 = S[n:][::-1]
C1 = collections.Counter()
C2 = collections.Counter()
for bit in range(2**n):
  tmp10 = ""
  tmp11 = ""
  tmp20 = ""
  tmp21 = ""
  for i in range(n):
    if bit >> i & 1:
      tmp10 += s1[i]
      tmp20 += s2[i]
    else:
      tmp11 += s1[i]
      tmp21 += s2[i]
  C1[(tmp10,tmp11)] += 1
  C2[(tmp21,tmp20)] += 1
for key,item in C1.items():
  ans += C2[key] * item 
print(ans)