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()

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

S = S[::-1]
cnt_right = defaultdict(int)
for i in range(2 ** N):
    a, b = "", ""
    for j in range(N):
        if (i >> j) & 1:
            a += S[j]
        else:
            b += S[j]
    cnt_right[(a, b)] += 1
    
answer = 0
for k in cnt_left.keys():
    answer += cnt_left[k] * cnt_right[k]
print(answer)