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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let () = Scanf.scanf "%d\n" @@ fun n ->
  let as_ = Array.init (n + 1) @@ function
    | 0 -> 0
    | _ -> Scanf.scanf "%d " @@ fun a -> a in
  for i = n downto 1 do
    if
      ( > ) 0 @@
      Array.fold_left ( + ) 0 @@
      Array.init (n / i) (fun j -> as_.(i * (1 + j)))
    then
      for j = 1 to n / i do
        as_.(i * j) <- 0
      done
  done;
  Printf.printf "%d\n" @@ Array.fold_left ( + ) 0 as_