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;
const int N=2e3+5;
int n,s,x;
int main(){
bitset<N*N> f;
f[0]=1;
scanf("%d",&n); 
	for (register int i=1; i<=n; ++i)
	{
	scanf("%d",&x);
	f|=f<<x;
	s+=x;
	}
for (register int i=(s+1)/2; i<=s; ++i)
if (f[i]) {printf("%d\n",i); return 0;}
}