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.Linq;
using System.Collections.Generic;

class P
{
    static void Main()
    {
        Console.ReadLine();
        int[] a = Console.ReadLine().Split().Select(int.Parse).OrderBy(x => x).ToArray();
        int asum = a.Sum();
        bool[] isMakable = new bool[(asum + 1) / 2];
        int max = -1;
        for (int i = 0; i < a.Length; i++)
        {
            if (a[i] - 1 < isMakable.Length)
            {
                for (int j = 0; j <= max; j++)
                {
                    if (isMakable[j])
                    {
                        if (j + a[i] < isMakable.Length)
                        {
                            isMakable[j + a[i]] = true;
                            max = Math.Max(j + a[i],max);
                        }
                    }
                }
                isMakable[a[i] - 1] = true;
                max = Math.Max(a[i] - 1, max);
            }
        }
        Console.WriteLine(asum - (max + 1));
    }
}