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.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] sa = br.readLine().split(" ");
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sa[i]);
		}
		br.close();

		int m = 2000;
		BigInteger dp = BigInteger.ONE;
		for (int i = 0; i < n; i++) {
			dp = dp.or(dp.shiftLeft(a[i]));
		}

		int sum = 0;
		for (int i = 0; i < n; i++) {
			sum += a[i];
		}
		int start = (sum + 1) / 2;
		int end = m * m;
		for (int i = start; i <= end; i++) {
			if (dp.testBit(i)) {
				System.out.println(i);
				return;
			}
		}
	}
}