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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;
import java.util.stream.Stream;

class Main{
	static class System{
		private static final InputStream in=java.lang.System.in;
		private static final PrintWriter out=new PrintWriter(java.lang.System.out,false);
	}
	public static void main(String[]$){
		new Main().solve();
		System.out.flush();
	}
	static Scanner s=new Scanner(System.in);
	static IntStream REPS(int v){return IntStream.range(0,v);}
	static IntStream REPS(int l,int r){return IntStream.rangeClosed(l,r);}
	static int gInt(){return s.nextInt();}
	static long gLong(){return s.nextLong();}
	static long gDouble(){return s.nextLong();}

	static IntStream ints(int n){return REPS(n).map(i->gInt());}
	static Stream<String> strs(int n){return REPS(n).mapToObj(i->s.next());}

	private void solve(){
		int n=gInt(),a[]=ints(n).toArray();
		for(int p=0;p<100;++p) {
			for(int d=n;d>=1;--d) {
				int cdsum=0;
				for(int i=d-1;i<n;i+=d)
					cdsum+=a[i];
				if(cdsum<0) {
					for(int i=d-1;i<n;i+=d)
						a[i]=0;
				}
			}
		}
		System.out.println(Arrays.stream(a).sum());
	}
}