Problem: You are given N integers A_1, A_2, ..., A_N.

Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.

Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.

Find the median of this list, S_{2^{N-1}}.

Constraints

* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the median of the sorted list of the sums of all non-empty subsequences of A.

Examples

Input

3
1 2 1


Output

2


Input

1
58


Output

58

Solution (in JAVA):

Solution:

import java.math.BigInteger;
import java.util.Arrays;

public class Main {
	private static void solve() {

		int n = ni();
		int[] a = na(n);

		BigInteger one = BigInteger.ONE;
		for (int v : a) {
			one = one.or(one.shiftLeft(v));
		}

		for (int i = (Arrays.stream(a).sum() + 1) / 2;; i ++) {
			if (one.testBit(i)) {
				System.out.println(i);
				return;
			}
		}
	}

	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			@Override
			public void run() {
				long start = System.currentTimeMillis();
				String debug = args.length > 0 ? args[0] : null;
				if (debug != null) {
					try {
						is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
					} catch (Exception e) {
						throw new RuntimeException(e);
					}
				}
				reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
				solve();
				out.flush();
				tr((System.currentTimeMillis() - start) + "ms");
			}
		}, "", 64000000).start();
	}

	private static java.io.InputStream is = System.in;
	private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
	private static java.util.StringTokenizer tokenizer = null;
	private static java.io.BufferedReader reader;

	public static String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new java.util.StringTokenizer(reader.readLine());
			} catch (Exception e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	private static double nd() {
		return Double.parseDouble(next());
	}

	private static long nl() {
		return Long.parseLong(next());
	}

	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 char[] ns() {
		return next().toCharArray();
	}

	private static long[] nal(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private static int[][] ntable(int n, int m) {
		int[][] table = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[i][j] = ni();
			}
		}
		return table;
	}

	private static int[][] nlist(int n, int m) {
		int[][] table = new int[m][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				table[j][i] = ni();
			}
		}
		return table;
	}

	private static int ni() {
		return Integer.parseInt(next());
	}

	private static void tr(Object... o) {
		if (is != System.in)
			System.out.println(java.util.Arrays.deepToString(o));
	}
}