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: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		long a[] = new long[N];
		StringTokenizer st = new StringTokenizer(br.readLine());
		for(int i=0;i<N;i++) {
			a[i] = Long.parseLong(st.nextToken());
		}
		Arrays.sort(a);
		if(N%2==0) {
			long total = 0;
			for(int i=N-1;i>=N/2;i--) {
				total += a[i];
			}
			System.out.println(total);
		}else {
			long total = 0;
			for(int i=0;i<=N/2-1;i++) {
				total += a[i];
			}
			System.out.println(total);
		}
	}
}