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<algorithm>
#include<bitset>
#define ll long long
using namespace std;
int n,m,cnt,ans,sum;
bitset<2000010> f;
int main()
{
	int i,s,a,b,j,k;
	scanf("%d",&n);f[0]=1;
	for(i=1;i<=n;i++)scanf("%d",&a),f|=(f<<a),sum+=a;
	for(i=sum/2;i>=0 && !f[i];i--);
	printf("%d",sum-i);
	return 0;
}