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<4000000> bs;
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	bs[0] = 1;
	int n; cin >> n;
	int s = 0;
	while(n--){
		int x; cin >> x;
		s += x;
		bs |= (bs << x);
	}
	
	s = (s + 1)/2;
	while(!bs[s]) s++;
	cout << s;
}