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: Wrong Answer)

import java.util.Scanner;

/**
 * Created by hkoba on 2018/01/08.
 */
public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        // スペース区切りの整数の入力
        int k = sc.nextInt();
        int total = 0;
        int max = 0;
        for (int i = 0; i < k; i++) {
            int v = sc.nextInt();
            total += v;
            if (v > max) {
                max = v;
            }
        }
        if (k == 1) {
            max = 0;
        }
        System.out.println(total - max);
    }
}