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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

//최대공약수 함수 
long long int gcd(long long int x, long long int y){
	long long int tmp;
	while(1){
		if(x%y==0) return y;	
		tmp=y;	
		y=x%y;
		x=tmp;
	}
}

int main(){
	long long int n,a,lcm=1,sum=0, ans[10010]={};
	
	scanf("%lld",&n);
	
	for(int i=0;i<n;i++){
		scanf("%lld",&a);
		ans[i]=a;
		lcm*=(a/gcd(lcm,a));
	}
	
	for(int i=0;i<n;i++){
		sum+=(lcm/ans[i]);
		//sum%=1000000007;
	}
	
	printf("%lld",sum%1000000007);
	return 0;
}