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;
#define all(a) (a).begin(),(a).end()
typedef long long ll;

using P = pair<string,string>;

void rec(string &s, map<P,ll> &mp, int i, string s1, string s2){
    if(i == (int)s.size()){
        mp[P(s1,s2)]++;
        return;
    }
    rec(s,mp,i+1,s1+s[i],s2);
    rec(s,mp,i+1,s1,s2+s[i]);
}

int main(void){
    int n;
    string s;
    cin>>n>>s;
    string s1 = s.substr(0,n);
    string s2 = s.substr(n,n);
    reverse(all(s2));
    map<P,ll> mp1,mp2;
    rec(s1,mp1,0,"","");
    rec(s2,mp2,0,"","");
    ll res = 0;
    for(auto itr : mp1){
        P p = itr.first;
        res += mp1[p]*mp2[p];
    }
    cout<<res<<endl;
    return 0;
}