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: Time Limit Exceeded)

using System;

namespace E
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var MOD = 1000000007;

            long lcm = A[0];
            for (int i = 1; i < N; i++) lcm = LCM(lcm, A[i]);

            var result = 0L;
            for (int i = 0; i < N; i++)
            {
                result += lcm / A[i];
                result %= MOD;
            }
            Console.WriteLine(result);
        }

        static long LCM(long A, long B)
        {
            return A / GCD(A, B) * B;
        }

        static long GCD(long A, long B)
        {
            if (B > A) return GCD(B, A);
            if (A % B == 0)
            {
                return B;
            }
            else
            {
                return GCD(B, A % B);
            }
        }
    }
}