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.*;import java.util.stream.*;public class Main{public static void main(String[] g){Scanner c=new Scanner(System.in);int n=c.nextInt();int[] a=IntStream.range(0,n).map(i->c.nextInt()).toArray();int s=Arrays.stream(a).sum();BitSet b=new BitSet();b.set(s);IntStream.range(0,n).forEach(i->b.or(b.get(a[i],s+1)));System.out.println(b.nextSetBit((s+1)/2));}}