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: Accepted)

/**
 *    author:  tourist
 *    created: 09.01.2018 10:40:48       
**/
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 2018;
const int MAX_A = 2018;

int main() {
  int n;
  cin >> n;
  bitset<MAX_N * MAX_A> b;
  b[0] = 1;
  int sum = 0;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    b |= (b << a);
    sum += a;
  }
  for (int j = (sum + 1) / 2; j <= sum; j++) {
    if (b[j] == 1) {
      cout << j << endl;
      break;
    }
  }
  return 0;
}