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 <cstdio>
#include <bitset>
using namespace std;

int n, s, a;
bitset<1 << 22> d;
int main()
{
	int i;
	cin >> n;
	d[0] = 1;
	while (n--) {
		scanf("%d", &a);
		d |= d << a;
		s += a;
	}
	for (i = (s + 1) / 2; ; i++) {
		if (d[i]) {cout << i; return 0;}
	}
    return 0;
}