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 <iostream>
#include <bitset>
using namespace std;
int main(){
	int i;
	int N;
	int A;
	int S = 0;
	bitset<2000 * 2000> bs;
	bs[0] = 1;
	cin >> N;
	while (N--){
		cin >> A;
		bs |= (bs << A);
		//bs |= A;
		S += A;
	}	
	S = (S >> 1) + (S & 1);
	while (!bs[S]) S++;
	cout << S;

	return 0;
}