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 as dd

n = int(input())
_s = list(map(ord, list(input())))
s,t = _s[:n], _s[:n-1:-1]
d = dict()
mod = 10**9 + 9

def get(st):
  for bit in range(1<<n):
    u = v = 0
    for j,e in enumerate(st):
      if bit & (1<<j):
        u = (u*100 + e)%mod
      else:
        v = (v*100 + e)%mod
    yield (u,v)

ans = 0
d = dd(int)
for x in get(s): d[x] += 1
for x in get(t): ans += d[x]
print(ans)