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.

6
1 2 -6 4 5 3

12

It is optimal to smash Gem $3$ and $6$.

6
100 -100 -100 -100 100 -100

200

5
-1 -2 -3 -4 -5

0

It is optimal to smash all the gems.

2
-1000 100000

99000