Problem: 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.

Examples

Input

3
1 2 1


Output

2


Input

1
58


Output

58

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

bitset<4000002>s;
int n, x, sum;

int main()
{
  cin >> n;
  s[0] = 1;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    s = s | (s << x);
    sum += x;
  }
  int t  = (sum + 1) / 2;
  for (int i = t; i <= sum; i++)
    if (s[i]) {
      cout << i;
      return 0;
    }
  return 0;
}