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;

namespace AC
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt();
            var A = ReadArrayLong();
            var B = new long[N];
            var que = new Queue<long>();
            for (int i = 0; i < N-1; i++)
            {
                que.Enqueue(Lcm(A[i], A[i + 1]));
            }
            while (que.Count != 1)
            {
                var one = que.Dequeue();
                var two = que.Dequeue();
                var l = Lcm(one, two);
                que.Enqueue(l);
            }
            var chk = que.Dequeue();            
            for (int i = 0; i < N; i++)
            {
                B[i] = chk / A[i];
            }
            var ans = 0L;
            var mod = (long)Math.Pow(10, 9) + 7;
            for (int i = 0; i < N; i++)
            {
                ans += B[i];
                ans %= mod;
            }

            Console.WriteLine(ans);
            Console.ReadKey();
        }

        static long Gcd(long a, long b) { if (b == 0) return a; return Gcd(b, a % b); }
        static long Lcm(long a, long b) { return a / Gcd(a, b) * b; }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}