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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
int main() {
    int n,i,nr,sum=0;
    bitset<400001> bit;
    bit = 1;
    cin>>n;
    for(i=1; i<=n; i++) {
        cin>>nr;
        bit|=bit<<nr;
        sum+=nr;
    }
    if(n==1) {
        cout<<sum<<'\n';
        return 0;
    }
    for(i=sum/2+sum%2; i<=sum; i++)
        if(bit[i]==1) {
            cout<<i<<'\n';
            break;
        }
    return 0;
}