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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
using namespace std;
typedef long long ll;
ll n, mx, a[105];
 
void f(ll p) {
	ll i, s, b[105];
	if(p==n+1) {
		s = 0;
		for(i=1; i<=n; i++) s += a[i];
		mx = max(mx, s);
		return;
	}
	if(a[p]<0) {
		for(i=1; i<=n; i++) b[i] = a[i];
		for(i=p; i<=n; i+=p) a[i] = 0;
		f(p+1);
		for(i=1; i<=n; i++) a[i] = b[i];
	}
	f(p+1);
}
 
int main() {
	ll i, j, s;
	cin>>n;
	for(i=1; i<=n; i++) cin>>a[i];
	f(1);
	cout<<mx;
}