Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.FileNotFoundException;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

class Main {
	public void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		int s = 0;
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
			s += a[i];
		}
		BigInteger can = BigInteger.ONE;
		for (int i = 0; i < n; ++i) {
			can = can.shiftLeft(a[i]).or(can);
		}
		for (int i = (s + 1) / 2; i <= s; ++i) {
			if (can.testBit(i)) {
				System.out.println(i);
				return;
			}
		}
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

	public static void main(String[] args) throws FileNotFoundException {
		new Main().run();
	}
}