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 A[2010];
bitset<2000010> bs;

int main() {
	int N;
	cin >> N;
	int sum=0;
	for(int i=0; i<N; ++i){
		cin >> A[i];
		sum += A[i];
	}
	bs[0]=1;
	for(int i=0; i<N; ++i){
		bs |= (bs<<(A[i]));
	}
	int ans=sum/2;
	while(!bs[ans]) --ans;
	cout << sum-ans << endl;
	return 0;
}