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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        long[] array = new long[n];

        for (int i = 0; i < n; i++) {
            array[i] = sc.nextLong();
        }

        long num = 1;

        for (int i = 0; i < n; i++) {
            num = lcm(num, array[i]);
        }

        long ans = 0;

        for (int i = 0; i < n; i++) {
            ans += num / array[i];

            if (ans > 1000000007) {
                ans = ans % 1000000007;
            }
        }

        System.out.println(ans);

    }

    private static long lcm(long m, long n) {
        return m * n / gcd(m, n);
    }

    private static long gcd(long m, long n) {
        if (m < n)
            return gcd(n, m);
        if (n == 0)
            return m;
        return gcd(n, m % n);
    }

}