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 combinations
from collections import defaultdict
n = int(input())
s = input()

d = defaultdict(int)
left = set()
for r in range(n+1):
    for cl in combinations(range(n),r):
        sl = ""
        sr = ""
        for i in range(n):
            if i in cl:
                sl += s[i]
            else:
                sr += s[i]
        left.add(sl+","+sr)
        d[sl+","+sr] += 1

res = 0
for r in range(n+1):
    for cl in combinations(range(n,2*n),r):
        sl = ""
        sr = ""
        for i in range(n,2*n):
            if i in cl:
                sl = s[i] + sl
            else:
                sr = s[i] + sr
        if sr+","+sl in left:
            res += d[sr+","+sl]

print(res)