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<iostream>
#include<bitset>

using namespace std;

bitset<2000000> Dp;
int A[2005];

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n;
    cin>>n;
    int sum=0;
    for(int i=1; i<=n; i++)
    {
        cin>>A[i];
        sum+=A[i];
    }

    //fiecare submult de suma<=sum/2 are coresp o subsecventa din restul el de suma>=sum/2
    Dp[0]=1;
    for(int i=1; i<=n; i++)
    {
        if(A[i]<=sum/2)
            Dp=Dp|(Dp<<(A[i]));
    }

    int val=sum/2;
    while(!Dp[val])
        val--;

    cout<<sum-val<<"\n";
    return 0;
}