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 <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int n;
ll a[200];
ll Max=INT_MIN;

void dfs(int p,bitset<105>&d,ll c){
	if(p==n+1){
		Max=max(Max,c);
		return;
	}
	if(d[p]==1)dfs(p+1,d,c);
	else{
		auto e=d;
		ll cnt=0;
		for(int j=p;j<=n;j+=p){
			if(e[j]==0)cnt-=a[j],e[j]=1;
		}
		//if(cnt>0){
			dfs(p+1,e,c);
		//}
		dfs(p+1,d,c+a[p]);
	}
}
int main(){
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i];
	auto b=bitset<105>(0);
	dfs(1,b,0);
	cout<<Max<<endl;
}