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<2000002> b;
int sum,k;
int main() {
	int n,V;
	scanf("%d",&n);
	b[0]=1;
	while(n--) { 
		int v;
		scanf("%d",&v);
		b|=b<<v;
		sum+=v;
	}
	int i=(sum)/2+1;
	while(i--)  if(b[i]) {k=sum-i;break;}
	printf("%lld",k);
}