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: Accepted)

import java.io.InputStream;
import java.math.BigInteger;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        List<BigInteger> A = new LinkedList<>();
        for (int i = 0; i < n; i++) A.add(BigInteger.valueOf(input .nextInt()));
        input .close();

        BigInteger lcm = A.stream().parallel()
                .reduce(BigInteger.ONE, (a, b) -> a.divide(a.gcd(b)).multiply(b));

        BigInteger ans = A.stream().parallel()
                .map(lcm::divide)
                .reduce(BigInteger::add)
                .get();

        BigInteger mod = BigInteger.valueOf(1000000007);
        System.out.println(ans.mod(mod));
    }


}