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>
const int N = 100005;
using namespace std;
typedef long long ll;
int a[N];
int n;
bitset<4000010> f;
int main()
{
	int i,j,k=0;
	scanf("%d",&n);
	f[0]=1;
	for(i=1;i<=n;i++)
	  {
       scanf("%d",&j);
       f|=f<<j;
       k+=j;
      }
    for(i=(k+1)/2;!f[i];i++);
    printf("%d\n",i);
	return 0;
}