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;
#define int long long
int32_t main() {
	int n, sum = 0;
	cin>>n;
	vector<int> v(n);
	for(auto &i:v){ cin>>i; sum += i;}
	bitset<4000010> dp(1);
	for(auto &i:v)
	    dp = dp | (dp<<i);
	for(int i=(sum+1)/2;i<=sum;i++)
	    if(dp[i])
	        return cout<<i,0;
	return 0;
}