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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var n int
	fmt.Scan(&n)
	var a []int

	var tmp int
	a = append(a, 0)
	for i := 0; i < n; i++ {
		fmt.Scan(&tmp)
		a = append(a, tmp)
	}

	for i := n; i >= 1; i-- {
		if a[i] < 0 {
			if i > n / 2 {
				a[i] = 0
			} else {
				s := 0
				for j := i; j <= n; j += i {
					s += a[j]
				}
				if s < 0 {
					for j := i; j <= n; j += i {
						a[j] = 0
					}
				}
			}
		}
	}

	answer := 0
	for i := 0; i <= n; i++ {
		answer += a[i]
	}
	fmt.Println(answer)
}