#include "bits/stdc++.h"
using namespace std;
typedef unsigned long long ull;
char s[40];
int n;
map<pair<ull, ull>, int> cnt[20][20];
ull ans;
void dfs(int i, int len, ull s1, ull s2, int ty) {
    if(i == n + 1)
        ans += ty * (cnt[len][2 * n - len][make_pair(s1, s2)] += !ty);
    else
        dfs(i + 1, len + 1, s1 * 131 + s[i], s2, ty),
        dfs(i + 1, len, s1, s2 * 131 + s[i], ty);
}
int main() {
    cin >> n >> (s + 1);
    dfs(1, 0, 0, 0, 0);
    reverse(s + 1, s + 1 + 2 * n);
    dfs(1, 0, 0, 0, 1);
    cout << ans << endl;
}
### Prompt

Create a solution in Cpp for the following 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

### Response

```cpp
#include "bits/stdc++.h"
using namespace std;
typedef unsigned long long ull;
char s[40];
int n;
map<pair<ull, ull>, int> cnt[20][20];
ull ans;
void dfs(int i, int len, ull s1, ull s2, int ty) {
    if(i == n + 1)
        ans += ty * (cnt[len][2 * n - len][make_pair(s1, s2)] += !ty);
    else
        dfs(i + 1, len + 1, s1 * 131 + s[i], s2, ty),
        dfs(i + 1, len, s1, s2 * 131 + s[i], ty);
}
int main() {
    cin >> n >> (s + 1);
    dfs(1, 0, 0, 0, 0);
    reverse(s + 1, s + 1 + 2 * n);
    dfs(1, 0, 0, 0, 1);
    cout << ans << endl;
}
```