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 <4000010> bs;

int main() {
  int n;
  scanf("%d", &n);
  bs.reset();
  bs.set(0);
  int ans = 0;
  while (n--) {
    int foo;
    scanf("%d", &foo);
    bs |= bs << foo;
    ans += foo;
  }
  ++ans;
  ans /= 2;
  while (bs[ans] == 0) {
    ++ans;
  }
  printf("%d\n", ans);
}