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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.BitSet;
import java.util.Scanner;
import java.util.stream.IntStream;

class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int[] A  =IntStream.range(0,N).map(i->scan.nextInt()).toArray();
        BitSet bs = new BitSet(2000*N+1);
        bs.set(N*2000);
        int sum=0;
        for(int i=0;i<N;++i){
            bs.or(bs.get(A[i],2000*N+1));
            sum+=A[i];
        }
        int k = (sum+1)/2;
        int d = bs.previousSetBit(2000*N-k);
        System.out.println(2000*N-d);
    }
}