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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

int main(){
	int n;
	cin >> n;
	string str;
	cin >> str;
	string s[2];
	s[0] = str.substr(0, n);
	s[1] = str.substr(n, n);
	reverse(s[1].begin(), s[1].end());
	map<pair<string,string>, LL> freq[2];
	for(int j = 0; j < 2; j++){
		for(int r = 0; r < (1<<n); r++){
			string cur[2];
			for(int z = 0; z < n; z++){
				cur[(r >> z) & 1] += s[j][z];
			}
			freq[j][{cur[0], cur[1]}]++;
		}
	}
	LL ans = 0;
	for(auto x : freq[0]){
		ans += freq[0][x.first] * freq[1][x.first];
	}
	cout << ans << '\n';
}