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 deque

def comb(s):
    p = deque([('','')])

    for i in range(len(s)):
        for j in range(2**i):
            e = p.pop()
            p.appendleft((e[0]+s[i],e[1]))
            p.appendleft((e[0],e[1]+s[i]))
    return p

n = int(input())
s = input()

sl = s[0:n]
sr = s[n:2*n][::-1]
keys1 = [c[0]+'-'+c[1] for c in comb(sl)]
keys2 = [c[0]+'-'+c[1] for c in comb(sr)]

dict = {}
for key1 in keys1:
    if key1 in dict:
        dict[key1] += 1
    else:
        dict[key1] = 1
cnt = 0
for key2 in keys2:
    if key2 in dict:
        cnt += dict[key2]

print(cnt)