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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
constexpr int M = 1e9 + 7;
constexpr int INF = 1e9;

int main() {
    int N;
    cin >> N;
    vector<int> a(N);
    for(int i = 0; i < N; ++i) {
        cin >> a[i];
    }
    vector<bool> deleted(N);
    for(int i = N; i >= 1; --i) {
        ll sum = 0;
        for(int j = i; j <= N; j += i) {
            if(deleted[j - 1]) {
                continue;
            }
            sum += a[j - 1];
        }
        if(sum < 0) {
            for(int j = i; j <= N; j += i) {
                deleted[j - 1] = true;
            }
        }
    }
    ll res = 0;
    for(int i = 0; i < N; ++i) {
        if(deleted[i]) {
            continue;
        }
        res += a[i];
    }
    cout << res << endl;
}