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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double llf;
#define ft first
#define sd second
const int N=2000+5;
int a[N];
bitset<2000005> f;
int main(){
	int n;
	scanf("%d",&n);
	f[0]=1;
	int s=0;
	for(int i=1,a;i<=n;++i){
		scanf("%d",&a);
		s+=a;
		f|=f<<a;
	}
	for(int i=s>>1;i>=0;--i)
		if(f[i]){
			printf("%d\n",s-i);
			return 0;
		}
}