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.*;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		String S = sc.next();
		HashMap<String, Integer> map = new HashMap<String, Integer>();
		for (int i=0;i<(1<<N);i++) {
			int[] arr = new int[N];
			int tmp = i;
			String red = "";
			String blue = "";
			for (int j=0;j<N;j++) {
				arr[j] = tmp%2;
				tmp /= 2;
				if (arr[j]==1) red += S.charAt(j);
				else blue += S.charAt(j);
			}
			String key = red + " " + blue;
			if (map.containsKey(key)) {
				map.put(key, map.get(key)+1);
			} else {
				map.put(key, 1);
			}
		}

		long ans = 0L;

		for (int i=0;i<(1<<N);i++) {
			int[] arr = new int[N];
			int tmp = i;
			String red = "";
			String blue = "";
			for (int j=N-1;j>=0;j--) {
				arr[j] = tmp%2;
				tmp /= 2;
				if (arr[j]==1) red += S.charAt(N+j);
				else blue += S.charAt(N+j);
			}
			String key = red + " " + blue;
			if (map.containsKey(key)) {
				ans += map.get(key);
			} else {
			}
		}
		System.out.println(ans);
	}
}