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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>

typedef long long int int64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

int64 calc(int index,int n,int *a){
  if(3*index>n){
    int64 s=0;
    int i;
    for(i=1;i<=n;i++) s+=a[i];
    return s;
  }
  int64 res=calc(index+1,n,a);
  if(a[index]<0){
    int b[101];
    int i;
    for(i=index;i<=n;i+=index){
      b[i]=a[i];
      a[i]=0;
    }
    res=MAX(res,calc(index+1,n,a));
    for(i=index;i<=n;i+=index){
      a[i]=b[i];
    }
  }
  return res;
}

void run(void){
  int n;
  scanf("%d",&n);
  int a[101];
  int i;
  for(i=1;i<=n;i++) scanf("%d",a+i);
  for(i=n;3*i>n;i--){
    if(a[i]>=0) continue;
    int64 s=0;
    int j;
    for(j=i;j<=n;j+=i){
      s+=a[j];
    }
    if(s<=0){
      for(j=i;j<=n;j+=i){
	a[j]=0;
      }
    }
  }
  int64 ans=calc(1,n,a);
  printf("%lld\n",ans);
  return;
}


int main(void){
  run();
  return 0;
}