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()
first = S[:N]
last = S[::-1][:N]

d = defaultdict(int)
ans = 0

def paint(str, ptn):
  p = ['', '']
  for i in range(N):
    p[int(2**i & ptn > 0)] += str[i]
  return tuple(p)

for i in range(2**N):
  d[paint(first, i)] += 1
  
for i in range(2**N):
  ans += d[paint(last, i)]
  
print(ans)