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 = 2048;
int s = 0, n, a[N];
bitset<N*N> dp;

signed main(){
	cin >> n;
	for(int i=0;i<n;++i) cin >> a[i], s += a[i];
	dp[0] = 1;
	for(int i=0;i<n;++i)
		dp = dp | (dp << a[i]);
	for(int i=(s+1)/2;i<=s;++i) if(dp[i]) return cout << i, 0;
	
}