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>
	int a[10001];
int gcd(int a,int b){
	int r;
	int c,d;
	c=a;
	d=b;
	do{
		r=a%b;
		a=b;
		b=r;
	}while(r!=0);
	return c*d/a;
}
int main()
{
    int n;
    scanf("%d",&n);
    int i;
    for(i=0;i<n;i++) scanf("%d",&a[i]);
    long long int temp=a[0];
    for(i=1;i<n;i++){
    	temp=gcd(temp,a[i]);
	}
	int sum=0;
	for(i=0;i<n;i++){
		sum+=temp/a[i];
	}
	
	printf("%lld\n",sum%(1000000007));
    return 0;
}