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()
s1 = s[:n]
s2 = s[n:][::-1]
def makeDic(s):
    dic = defaultdict(int)
    for i in range(2 ** n):
        mask = 1
        c1 = ""
        c2 = ""
        for j in range(n):
            if i & mask:
                c1 += s[j]
            else:
                c2 += s[j]
            mask <<= 1
        dic[(c1, c2)] += 1
    return dic


dic1 = makeDic(s1)
dic2 = makeDic(s2)
ans = 0
for key in dic1:
    if key in dic2:
        ans += dic1[key] * dic2[key]
print(ans)