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<stdlib.h>
#include<string.h>
#define NUM 1000000007

long int calkoyaku(long int a,long int b){
  //printf("%ld %ld\n",a,b);
  if(a%b==0){
    return b;}
  if(b%a==0){
    return a;}
  //printf("koyaku\n");
  return calkoyaku(b,labs(a%b));
}

long int calkobai(long int a,int b){
  long int koyaku=calkoyaku(a,(long int)b)%NUM;
  //printf("kobai\n");
  return a*b/koyaku;
}

int main(){
  int n;
  scanf("%d\n",&n);
  long int kobai=1;
  int a[n];
  for(int i=0;i<n;i++){
    scanf("%d",&a[i]);
    //printf("came1\n");
    kobai=calkobai(kobai,a[i]);
    //printf("came2\n");
  }
  long int count=0;
  //printf("came3\n");
  for(int i=0;i<n;i++){
    count+=kobai/a[i];
    count%=NUM;}

  printf("%ld\n",count);

  return 0;
}