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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	static PrintWriter out;
	static InputReader ir;
	static boolean debug = false;

	static void solve() {
		int n = ir.nextInt();
		char[] s = ir.next().toCharArray();
		int[] ct = new int[26];
		int[] ct2 = new int[26];
		for (int i = 0; i < 2 * n; i++) {
			if (i < n)
				ct2[s[i] - 'a']++;
			ct[s[i] - 'a']++;
		}
		for (int i = 0; i < 26; i++) {
			if (ct2[i] * 2 != ct[i]) {
				out.println(0);
				return;
			}
		}
		HashMap<String, Long> mp = new HashMap<>();
		HashMap<String, Long> mp2 = new HashMap<>();
		for (int i = 0; i < 1 << n; i++) {
			StringBuilder sb = new StringBuilder();
			for (int j = 0; j < n; j++) {
				if ((i & 1 << j) != 0)
					sb.append(s[j]);
			}
			StringBuilder sb2 = new StringBuilder();
			for (int j = n - 1; j >= 0; j--) {
				if ((i & 1 << j) == 0)
					sb2.append(s[j]);
			}
			if (mp.containsKey(sb.toString() + " " + sb2.toString())) {
				mp.put(sb.toString() + " " + sb2.toString(), mp.get(sb.toString() + " " + sb2.toString()) + 1);
			} else
				mp.put(sb.toString() + " " + sb2.toString(), 1L);
		}
		for (int i = 0; i < 1 << n; i++) {
			StringBuilder sb = new StringBuilder();
			for (int j = 0; j < n; j++) {
				if ((i & 1 << j) != 0)
					sb.append(s[2 * n - 1 - j]);
			}
			StringBuilder sb2 = new StringBuilder();
			for (int j = n - 1; j >= 0; j--) {
				if ((i & 1 << j) == 0)
					sb2.append(s[2 * n - 1 - j]);
			}
			if (mp2.containsKey(sb.toString() + " " + sb2.toString())) {
				mp2.put(sb.toString() + " " + sb2.toString(), mp2.get(sb.toString() + " " + sb2.toString()) + 1);
			} else
				mp2.put(sb.toString() + " " + sb2.toString(), 1L);
		}
		long res = 0;
		tr(mp);
		for (String k : mp.keySet()) {
			if (mp2.containsKey(k))
				res += mp2.get(k) * mp.get(k);
		}
		out.println(res);
	}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		if (debug)
			out.println(Arrays.deepToString(o));
	}
}