Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
int ketasu(long long int n){
  int ans=0;
  while(n!=0){
    n=n/10;
    ans++;
  }
  return ans;
}

long long int gcd(long long int a,long long int b)
{
    if (a < b) {
        a ^= b;
        b ^= a;
        a ^= b;
    }

    return b ? gcd(b, a % b) : a;
}

long long int lcm(long long int a,long long  int b)
{
    return a * b / gcd(a, b);
}

int main(void){
  int n;
  long long int tmp=1;
  long long int opi;
  long long ans=0;
  scanf("%d",&n);
  long long int a[n];
  int i;

  for(i=0;i<n;i++){
    scanf("%lld",&a[i]);
  }
  tmp=lcm(a[0],a[1]);
  for(i=2;i<n;i++){
    if(tmp%a[i]==0){
      continue;
    }
    opi=lcm(a[i],tmp);
    tmp=opi;
  }
  for(i=0;i<n;i++){
    ans=ans+tmp/a[i];
    ans=ans%(1000000000+7);
  }

  printf("%lld",ans);


  return 0;
}