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 LuaJIT (2.0.4) (judge verdict: Runtime Error)

n = io.read('n')
a = {}
for i = 1, n do
  a[i] = io.read('n')
end

for i = n, 1, -1 do
  local sum = 0
  for j = i, n, i do
    sum = sum + a[j]
  end
  if sum < 0 then
    for j = i, n, i do
      a[j] = 0
    end
  end
end

total = 0
for i = 1, n do
  total = total + a[i]
end
io.write(total, '\n')