Home

Contest: Task: Related: TaskB TaskD

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

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

Sample Input 2

6
100 -100 -100 -100 100 -100

Sample Output 2

Sample Input 3

5
-1 -2 -3 -4 -5

Sample Output 3

It is optimal to smash all the gems.

Sample Input 4

2
-1000 100000