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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        String str = scan.nextLine();

        int n = Integer.parseInt(str);

        str = scan.nextLine();
        String[] substr = str.split(" ", 0);

        int[] array = new int[200000];
        for (int i=0; i<n; i++) {
        	array[i] = Integer.parseInt(substr[i]);
        }

        int l = lcm(array[0], array[1]);
        for (int i=2; i<n; i++) {
        	l = lcm(array[i],l);
        }
        int ans = 0;
        for (int i=0; i<n; i++) {
        	ans += l/array[i];
        }
        System.out.println(ans);

    }

    //最小公倍数lcm
    static int lcm (int a, int b) {
    	int temp;
    	long c = a;
    	c *= b;
        while((temp = a%b)!=0) {
        	a = b;
        	b = temp;
        }
        return (int)(c/b);
    }
}