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()
countp = defaultdict(int)
counts = defaultdict(int)
prefix = S[:N]
suffix = S[2*N-1:N-1:-1]
for i in range(1 << (N - 1)):
    p1 = ''
    s1 = ''
    p2 = ''
    s2 = ''
    for j in range(N):
        if (1 << j) & i:
            p1 += prefix[j]
            s1 += suffix[j]
        else:
            p2 += prefix[j]
            s2 += suffix[j]
    countp[(p1, p2)] += 1
    countp[(p2, p1)] += 1
    counts[(s1, s2)] += 1
    counts[(s2, s1)] += 1
    

# print(countp, counts)

ans = 0
for k, v in countp.items():
    ans += v * counts[k]

print(ans)