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;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Numerics;

internal static class CR
{
    public static string Get() { return Console.ReadLine(); }
    public static IEnumerable<string> GetTexts() { return Console.ReadLine().Split(' '); }
    public static BigInteger GetInteger() { return BigInteger.Parse(Console.ReadLine()); }
    public static IEnumerable<BigInteger> GetIntegers() { return Console.ReadLine().Split(' ').Select(x => BigInteger.Parse(x)); }
}

namespace AtCoderBeginnerContest
{
    internal class Program
    {
        public static List<BigInteger> A { get; private set; }

        private static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.WriteLine(r); }

        private static object GetResult()
        {
            
            CR.Get();
            A = CR.GetIntegers().ToList();

            var lcm = A[0];
            for (int i = 0; i < A.Count; i++)
            {
                lcm = Lcm(lcm, A[i]);
            }

            BigInteger xxx = 0;
            foreach (var item in A)
            {
                xxx += lcm / item;
            }
            return xxx % 1000000007;
        }
        // 最小公倍数
        public static BigInteger Lcm(BigInteger a, BigInteger b)
        {
            return a * b / Gcd(a, b);
        }

        // ユークリッドの互除法 
        public static BigInteger Gcd(BigInteger a, BigInteger 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;
        }
    }
}