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 = str(input())

dic = defaultdict(int)

for i in range(2 ** N):
    a = str()
    b = str()
    for j in range(N):
        if (i >> j) & 1:
            a += S[j + N]
        else:
            b += S[j + N]
    
    dic[(a, b)] += 1

count = 0
for i in range(2 ** N):
    a = str()
    b = str()
    for j in range(N):
        if (i >> j) & 1:
            a += S[j]
        else:
            b += S[j]
    count += dic[b[::-1], a[::-1]]

print (count)