Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>

using namespace std;

#define MOD 1000000007
typedef long long int ll;

int main(){
    
    #ifndef ONLINE_JUDGE
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    #endif

    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin>>n;
    int a[n]={0};
    for(int i=0;i<n;i++){
    	cin>>a[i];
    }
    bitset<4000010>poss;
    poss[0]=1;
    for(int i=0;i<n;i++){
    	poss|=(poss<<a[i]);
    }
    int sum=0;
    for(int i=0;i<n;i++){
    	sum+=a[i];
    }
    //cout<<sum<<endl;
    for(int i=sum/2+(sum%2);i<=sum;i++){
    	//cout<<i<<endl;
    	if(poss[i]==1){
    		cout<<i<<endl;
    		return 0;
    	}
    }
    

	return 0;
}