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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#define Nmax 2005

using namespace std;

ifstream fin("median.in");
ofstream fout("median.out");

int N;
int A[Nmax];
int S;
bitset <2000002> dp[Nmax];

int main()
{
    fin >> N;
    for(int i = 1; i <= N; i++)
        fin >> A[i], S += A[i];
    dp[0][0] = 1;
    for(int i = 1; i <= N; i++)
        dp[i] = dp[i - 1] | (dp[i - 1] << A[i]);
    for(int j = S / 2; j >= 0; j--)
        if(dp[N][j])
        {
            fout << S - j << "\n";
            return 0;
        }
    return 0;
}