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<4000001>dp;
int n,a[2003],sum;
int main(){
	cin>>n;
	for(int i=0;i<n;i++)cin>>a[i],sum+=a[i];
	dp[0]=1;
	for(int i=0;i<n;i++)
		dp|=(dp<<a[i]);
	for(int i=0;i<=4000000;i++)
		if(dp[i]&&i*2>=sum){
			cout<<i;
			return 0;
		}
}