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;

int main() {
  int N;
  cin >> N;
  vector<int> A(N);
  for(auto& i: A) cin >> i;

  auto S = accumulate(begin(A), end(A), 0);
  auto dp = bitset<4000001>().set(0);
  for(auto i: A) dp |= dp << i;
  for(auto i = (S+1)/2; i <= S; ++i) if(dp.test(i)) {cout << i << endl; break;}
}