Problem:
Score : 700 points

Problem Statement

We have N gemstones labeled 1 through N.

You can perform the following operation any number of times (possibly zero).

Select a positive integer x, and smash all the gems labeled with multiples of x.

Then, for each i, if the gem labeled i remains without getting smashed, you will receive a_i yen (the currency of Japan).
However, a_i may be negative, in which case you will be charged money.

By optimally performing the operation, how much yen can you earn?

Constraints

All input values are integers.

1 \leq N \leq 100

|a_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the maximum amount of money that can be earned.

Sample Input 1

6
1 2 -6 4 5 3

Sample Output 1

12

It is optimal to smash Gem 3 and 6.

Sample Input 2

6
100 -100 -100 -100 100 -100

Sample Output 2

200

Sample Input 3

5
-1 -2 -3 -4 -5

Sample Output 3

0

It is optimal to smash all the gems.

Sample Input 4

2
-1000 100000

Sample Output 4

99000

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let n = scan.read::<usize>();
    let mut a = scan.readn::<i64>(n);
    for i in (1..n + 1).rev() {
        let mut sum = 0;
        for j in 1..n + 1 {if j % i == 0 {sum += a[j-1]}}
        if sum < 0 {
            for j in 1..n + 1 {
                if j % i == 0 {a[j-1] = 0}
            }
        }
    }
    println!("{}", a.into_iter().sum::<i64>());
}

// region template
#[allow(dead_code)]
fn iu(i: isize) -> usize { i as usize }
#[allow(dead_code)]
fn ui(u: usize) -> isize { u as isize }

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut ret = vec![];
        for _ in 0..n { ret.push(self.read::<T>()) }
        ret
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion