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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io;

fn main() {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    let iter = buf.trim().split_whitespace();
    let mut nums: Vec<i32> = Vec::new();
    for i in iter {
        nums.push(i.parse::<i32>().unwrap());
    }
    nums.sort_by(|a, b| b.cmp(a));
    println!("{}", nums[0]);
}