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>
#define N 2005
#define M 4000005
using namespace std;
int n,a[N],S;
bitset<M> F;
int main()
{
	int i;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
		scanf("%d",&a[i]),S+=a[i];
	sort(a+1,a+n+1);
	F[0]=1;
	for(i=1;i<=n;i++)
		F|=(F<<a[i]);
	for(i=S/2;i>=0;i--)
		if(F[i]) break;
	cout<<S-i;
	return 0;
}