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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
as = [0] + gets.split.map(&:to_i)

((N/2+1)..N).each do |i|
    as[i] = 0 if as[i] < 0
end

loop do
    min_i = nil
    min = 0
    (2..(N/2)).each do |i|
        score = 0
        (1..(N/i)).each do |k|
            score += as[i*k]
        end
        if score < min
            min_i = i
            min = score
        end
    end
    if min == 0
        break
    else
        (1..(N/min_i)).each do |k|
            as[min_i*k] = 0
        end
    end
end
puts [as.inject(:+), 0].max