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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    // 最小公倍数
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    // ユークリッドの互除法 
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        string[] input = Console.ReadLine().Split();
        int[] A = new int[N];
        for(int i = 0; i < N; i++)
        {
            A[i] = int.Parse(input[i]);
        }
        long lcm = Lcm(A[0], A[1]);
        for (int i = 2; i < N; i++)
        {
            lcm=Lcm(lcm, A[i]);
        }
        long ans = 0;
        for(int i = 0; i < N; i++)
        {
            ans += lcm / A[i];
        }
        ans = ans % (1000000000 + 7);
        Console.WriteLine(ans);
    }
}