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> f;
int n, s, a[2005];

int main() {
	cin >> n;
	f.set(0);
	for(int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
		f |= (f << a[i]);
		s += a[i];
	}
	for(int i = (s+1)/2; i <= s; i++){
		if(f[i]){
			cout << i << endl;
			break;
		}
	}

	return 0;
}