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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;
using System.Linq;

class Program
{
    void solve()
    {
        int n = int.Parse(Console.ReadLine());
        int[] a = new int[n];
        int max = 0;
        string[] buff = Console.ReadLine().Split(' ');
        while (n-- > 0)
        {
            a[n] = int.Parse(buff[n]);
            if (a[n] > max) max = a[n];
        }
        Console.WriteLine(max);
    }

    public static int Main()
    {
        bool loop = false;
#if ES_DEBUG
        loop = true;
#endif
        do
        {
            new Program().solve();
        } while (loop);
        return 0;
    }
}