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<2000005>f;
int main()
{
    f[0]=1;
	int n,a,s=0;
	bool b=0;
    cin>>n;
    while(cin>>a)
    {
        f|=f<<a;
        s+=a;
    }
    for(register int i=int(ceil(s*1.0/2));i<=s;i++)
	{
        if(f[i])
		{
			cout<<i<<endl;
			b=1;
		}
		if(b==1)
			return 0;
    }
    return 0;
}