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;
using System.Text;
using System.Threading.Tasks;
using System.Windows;

namespace AtCoder
{
    static class Program
    {
        static void Main()
        {
            Solve();

            Console.ReadKey();
        }

        static void Solve()
        {
            var N = IO.GetLong();
            var A = IO.GetLongList();
            decimal mod = 1000000007;
            decimal lcm = 1;
            for(int i = 0; i < N; i++)
            {
                lcm = LCM(lcm, A[i]);
            }
            decimal ans = 0;
            for(int i = 0; i < N; i++)
            {
                ans += (lcm / A[i]) % mod;
            }

            Console.WriteLine(ans);


        }

        ////最大公約数
        //static public long GCD(long a, long b) { return b != 0 ? GCD(b, a % b) : a; }

        ////最小公倍数
        //static public long LCM(long a, long b) { return (long)a * b / GCD(a, b); }

        //最大公約数
        static public decimal GCD(decimal a, decimal b) { return b != 0 ? GCD(b, a % b) : a; }

        //最小公倍数
        static public decimal LCM(decimal a, decimal b) { return (decimal)a * b / GCD(a, b); }
    }

    static class IO
    {
        static public string GetString() { return Console.ReadLine(); }
        static public int GetInt() { return int.Parse(Console.ReadLine()); }
        static public long GetLong() { return long.Parse(Console.ReadLine()); }
        static public List<string> GetStringList() { return Console.ReadLine().Split(' ').ToList(); }
        static public List<int> GetIntList() { return Console.ReadLine().Split(' ').Select(int.Parse).ToList(); }
        static public List<long> GetLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }
        static public List<double> GetDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }
        static public void WriteStrings(object[] strings) { foreach (var o in strings) { Console.Write(o + " "); } }
    }
}