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 = 2005;
typedef long long ll;

int n, a[N], tot, ans;
bitset <N*N> f;

int main() {
	cin>>n;
	f[0] = 1;
	for(int i = 1; i <= n; i++) {
		cin>>a[i];
		f |= f<<a[i];
		tot += a[i];
	}
	ans = (tot + 1)/2;
	while(!f[ans]) ans++;
	cout<<ans<<endl;
}