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>
#define int long long
using namespace std;

const int maxn = 19;
int n;
string s;

map< pair<string, string>, int> mp;
int ans;
int32_t main() {
	cin >> n >> s;
	reverse(s.begin() + n, s.end());
	for(int mask = 0; mask < (1LL << n); mask++) {
		string s1 = "", t1 = "";
		for(int i = 0; i < n; i++) {
			int bit = (mask >> i) & 1;
			if(bit)
				s1 += s[n + i];
			else
				t1 += s[n + i]; 
		}
		mp[{s1, t1}]++;
	}
	
	for(int mask = 0; mask < (1LL << n); mask++) {
		string s1 = "", t1 = "";
		for(int i = 0; i < n; i++) {
			int bit = (mask >> i) & 1;
			if(bit)
				s1 += s[i];
			else
				t1 += s[i];
		}
		ans += mp[{s1, t1}];
	}
	cout << ans << '\n';
}