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()
S1, S2 = S[: N], S[2*N-1: N-1: -1]
hash_S1, hash_S2 = {}, {}

for i in range(1<<N): # 赤に塗られた箇所が1
    red = []
    blue = []
    for j in range(N):
        if i >> j & 1:
            red.append(S1[j])
        else:
            blue.append(S1[j])
    
    key = ''.join(red) + '+' + ''.join(blue)
    if key in hash_S1:
        hash_S1[key] += 1
    else:
        hash_S1[key] = 1

ans = 0
for i in range(1<<N): # 赤に塗られた箇所が1
    red = []
    blue = []
    for j in range(N):
        if i >> j & 1:
            red.append(S2[j])
        else:
            blue.append(S2[j])
    
    key = ''.join(blue) + '+' + ''.join(red)
    if key in hash_S1:
        ans += hash_S1[key]

print(ans)