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 JAVA):

Solution:

import java.util.HashMap;
import java.util.Scanner;


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String s = sc.next();
		String first = s.substring(0,n);
		String second = s.substring(n,n*2);

		HashMap<String, Integer> map = new HashMap<String, Integer>();
		for (int i=0;i<1<<n;i++) {
			String tmp1 = "";
			String tmp2 = "";
			for (int j=0;j<n;j++) {
				if ((i>>j)%2!=0) {
					tmp1+=second.charAt(j);
				}
			}
			for (int j=n-1;j>=0;j--) {
				if ((i>>j)%2==0) {
					tmp2+=second.charAt(j);
				}
			}
			String tmp = tmp2+"_"+tmp1;
			if(map.containsKey(tmp)) {
				int x = map.get(tmp);
				map.put(tmp, x+1);
			} else {
				map.put(tmp, 1);
			}
		}
		long ans = 0;

		for (int i=0;i<1<<n;i++) {
			String tmp1 = "";
			String tmp2 = "";
			for (int j=0;j<n;j++) {
				if ((i>>j)%2!=0) {
					tmp1+=first.charAt(j);
				}
			}
			for (int j=n-1;j>=0;j--) {
				if ((i>>j)%2==0) {
					tmp2+=first.charAt(j);
				}
			}
			String tmp = tmp1+"_"+tmp2;
			if (map.containsKey(tmp)) {
//				System.out.println(tmp+" "+map.get(tmp));
				ans+=map.get(tmp);
			}
		}
		System.out.println(ans);
	}
}