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.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static int[] mods;
	static int[] muls;
	
	static void solve()
	{
		mods = new int[2];
		muls = new int[2];
		Random gen = new Random();
		for(int i = 0;i < 2;i++){
			mods[i] = BigInteger.probablePrime(30, gen).intValue();
			muls[i] = BigInteger.probablePrime(29, gen).intValue();
		}
		
		int n = ni();
		char[] s = ns(2*n);
		
		char[] t = Arrays.copyOf(s, n);
		long[][] l = en(t);

		char[] u = Arrays.copyOfRange(s, n, 2*n);
		for(int i = 0, j = n-1;i < j;i++,j--){
			char c = u[i]; u[i] = u[j]; u[j] = c;
		}
		long[][] r = en(u);
//		tr(t, u, muls, mods);
//		tr(l);
//		tr(r);
		
		long ans = 0;
		for(int i = 0;i < l.length;i++){
			long[] ll = l[i], lr = r[i];//l.length-1-i];
			for(long v : ll){
				ans += lowerBound(lr, v+1) - lowerBound(lr, v);
			}
		}
		out.println(ans);
	}
	
	static long[][] en(char[] s)
	{
		int n = s.length;
		int[] nums = new int[n+1];
		for(int i = 0;i < 1<<n;i++){
			nums[Integer.bitCount(i)]++;
		}
		long[][] ret = new long[n+1][];
		for(int i = 0;i <= n;i++){
			ret[i] = new long[nums[i]];
		}
		
		for(int i = 0;i < 1<<n;i++){
			long gh = 0;
			for(int k = 0;k < 2;k++){
				long h = 0;
				for(int j = 0;j < n;j++){
					if(i<<~j>=0){
						h = (h * muls[k] + s[j]) % mods[k];
					}
				}
				for(int j = n-1;j >= 0;j--){
					if(i<<~j<0){
						h = (h * muls[k] + s[j]) % mods[k];
					}
				}
				gh = gh<<32|h;
			}
			int bc = Integer.bitCount(i);
			ret[bc][--nums[bc]] = gh;
		}
		for(int i = 0;i <= n;i++)Arrays.sort(ret[i]);
		return ret;
	}
	
	public static int lowerBound(long[] a, long v)
	{
		int low = -1, high = a.length;
		while(high-low > 1){
			int h = high+low>>>1;
			if(a[h] >= v){
				high = h;
			}else{
				low = h;
			}
		}
		return high;
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}