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 PYTHON):

Solution:
#!/usr/bin/env python

import sys
import math
import itertools as it
from collections import deque

sys.setrecursionlimit(10000000)

def func():
    N = input()
    S = raw_input()

    S1 = S[:N]
    S2 = S[N:]

    m = {}

    for i in range((1 << N)):
        s1 = s2 = ''
        for j in range(N):
            if(i & (1 << j)):
                s1 = s1 + S1[j]
            else:
                s2 = S1[j] + s2
        if (s1, s2) in m:
            m[(s1, s2)] += 1
        else:
            m[(s1, s2)] = 1

    ans = 0

    for i in range((1 << N)):
        s1 = s2 = ''
        for j in range(N):
            if(i & (1 << j)):
                s1 = S2[j] + s1
            else:
                s2 = s2 + S2[j]
        if (s1, s2) in m:
            ans += m[(s1, s2)]

    print ans

func()