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:
N = int(input())
S = input()


def count(s):
    res = {}
    for i in range(2**N):
        t1 = ''
        t2 = ''
        for j in range(N):
            if i & 1 << j:
                t1 += s[j]
            else:
                t2 += s[j]
        k = t1 + t2[::-1] + str(bin(i).count('1'))
        res[k] = res.get(k, 0) + 1
    return res


h1 = count(S[:N])
h2 = count(S[N:][::-1])
ans = 0
for k, v in h1.items():
    if k in h2:
        ans += v * h2[k]
print(ans)

# https://www.youtube.com/watch?v=eB0eT-948Vw