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 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>

 
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a%b);
}
int lcm(int a[], int n) {
  int res = 1, i;
  for (i = 0; i < n; i++) {
    res = res*a[i]/gcd(res, a[i]);
  }
  return res;
}
 


int main(){
  int n;
  scanf("%d",&n);
  int arr[n];
  for(int i=0;i<n;i++){
    scanf("%d",&arr[i]);
  }
  int a;
  a= lcm(arr,n);
  int sum1=0;
  for(int i=0;i<n;i++){
   sum1+=a/arr[i]; 
  }
  printf("%d\n",sum1);
}