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.math.BigInteger;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner scan=new Scanner(System.in);
        int n=0;
        if(scan.hasNext())
            n=scan.nextInt();
        BigInteger[] arr=new BigInteger[n];
        for(int i=0;i<n;i++){
            String str="";
            if(scan.hasNext())
                str=scan.next();
            arr[i]=new BigInteger(str);
        }
        BigInteger lcm=lcm(arr);
        long l=Long.parseLong(String.valueOf(lcm));
        /*BigInteger p=new BigInteger("0");
        for(int i=0;i<n;i++){
            p= p.add((lcm.divide(arr[i])).mod(new BigInteger("1000000007")));
            p=p.mod(new BigInteger("1000000007"));
        }*/
        long p=0;
        for(int i=0;i<n;i++){
            int k=Integer.parseInt(String.valueOf(arr[i]));
            p+=((l/k)%1000000007);
            p=p%1000000007;
        }
        System.out.println(p);
    }
    static BigInteger gcd(BigInteger a, BigInteger b)
    {
        if (b.equals(new BigInteger("0")))
            return a;
        return gcd(b, a.mod(b));
    }

    static BigInteger lcm(BigInteger arr[])
    {
        BigInteger ans = arr[0];
        for (int i = 1; i < arr.length; i++)
            ans = (((arr[i].multiply(ans))).divide(
                    (gcd(arr[i], ans))));

        return ans;
    }
}