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<4000005> b;

int S,N;

int main() {

cin.tie(0);
ios::sync_with_stdio(false);

cin>>N;

b=1;

for(int i=0; i<N; i++){
  int a;
  cin>>a;
  S+=a;
  b|=b<<a;
}

if(S%2) S++;

for(int i=S/2; i<=4000000; i++){
  if(b[i]){
    cout<<i<<endl;
    return 0;
  }
}

}