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 itertools import product
from collections import defaultdict
n = int(input())
s = input()
sa, sb = s[:n], s[n:][::-1]
a, b, ans = defaultdict(int), defaultdict(int), 0
for p in product(range(2), repeat=n):
    word_a_1, word_b_1, word_a_2, word_b_2 = "", "", "", ""
    for j in range(n):
        if p[j]:
            word_a_1 += sa[j]
            word_b_1 += sb[j]
        else:
            word_a_2 += sa[j]
            word_b_2 += sb[j]
    a[(word_a_1, word_a_2)] += 1
    b[(word_b_1, word_b_2)] += 1
while a:
    key, value = a.popitem()
    ans += value * b[key]
print(ans)