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<iostream>
#include<bitset>
using namespace std;
int sum,n;
bitset<1<<22>b;
int main(){
    ios::sync_with_stdio(0);
    b[0]=1;
    cin>>n;
    for(int i=1,p;i<=n;++i){
        cin>>p;
        b|=b<<p;
        sum+=p;
    }
    for(sum=sum+1>>1;!b[sum];++sum);
    cout<<sum<<endl;
    return 0;
}