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.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Console;

namespace AtCoder_1
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = CinT();
            var a = CinTAr();
            long gcdp = a[0];
            for(int i = 1;i < n; i++)
            {
                gcdp = LCM(gcdp, a[i]);
            }
            long res = 0;
            for (int i = 0; i < n; i++)
            {
                res += gcdp / a[i];
            }
            Cout(res % MOD10E9);

            Cin();
        }



        static Random Rand = new Random();
        static string[] AlphabetTable = new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
        static int GetDigits(long num)
        {
            return (int)Math.Floor(Math.Log10(num)) + 1;
        }
        static int GetNumByDigit(long num, int digit)
        {
            return (int)((num / ((int)Math.Pow(10, digit - 1))) % 10);
        }
        static int loop(int num, int max)
        {
            if (num > max)
            {
                return num % max;
            }
            else if (num < 0)
            {
                return max - (-num) % max;
            }
            else
            {
                return num;
            }
        }
        static long GCD(long a, long b)
        {
            if (a < b) { swap(ref a, ref b); }
            if (a % b == 0) { return b; }
            else { return GCD(b, a % b); }
        }

        static long LCM(long a, long b)
        {
            return a * b / GCD(a, b);
        }

        static void swap<T>(ref T a, ref T b)
        {
            T t = a;
            a = b;
            b = t;
        }

        static readonly int MOD10E9 = (1000000000 + 7);
        static bool isInt(double d) { return (int)d == d; }
        static string Cin() { return ReadLine(); }
        static string[] CinAr() { return ReadLine().Split(' '); }
        static int CinT() { return S2i(Cin()); }
        static int[] CinTAr() { return CinAr().Select((x, i) => { return S2i(x); }).ToArray(); }
        static long CinL() { return S2L(Cin()); }
        static long[] CinLAr() { return CinAr().Select((x, i) => { return S2L(x); }).ToArray(); }
        static double CinD() { return S2D(Cin()); }
        static double[] CinDAr() { return CinAr().Select((x, i) => { return S2D(x); }).ToArray(); }
        static int S2i(string s) { return int.Parse(s); }
        static long S2L(string s) { return long.Parse(s); }
        static double S2D(string s) { return double.Parse(s); }
        static void Cout(object s) { WriteLine(s); }
        static long[] yakusuu(long n)
        {
            if (n == 1) { return new long[] { 1 }; }
            List<long> res = new List<long>();
            res.Add(1);
            for (long i = 2; i <= n / 2 + 1; i++)
            {
                if (n % i == 0)
                {
                    res.Add(i);
                }
            }
            res.Add(n);
            return res.ToArray();
        }
        static bool isPrime(long num)
        {
            if (num == 1) { return false; }
            for (long i = 2; i <= Math.Sqrt(num) + 1; i++)
            {
                if (num % i == 0) { return false; }
            }
            return true;
        }

        static void CoutAr<Type>(IEnumerable<Type> types)
        {
            WriteLine(string.Join(" ", types));
        }

        public static long nCr(int n, int r)
        {
            // naive: return Factorial(n) / (Factorial(r) * Factorial(n - r));
            return nPr(n, r) / Factorial(r);
        }

        public static long nPr(int n, int r)
        {
            // naive: return Factorial(n) / Factorial(n - r);
            return FactorialDivision(n, n - r);
        }

        private static long FactorialDivision(int topFactorial, int divisorFactorial)
        {
            long result = 1;
            for (int i = topFactorial; i > divisorFactorial; i--)
                result *= i;
            return result;
        }

        private static long Factorial(int i)
        {
            if (i <= 1)
                return 1;
            return i * Factorial(i - 1);
        }
    }

    public struct Pair<T>
    {
        public T a;
        public T b;
        public T c;
        public Pair(T _a, T _b) { a = _a; b = _b; c = default(T); }
        public Pair(T _a, T _b, T _c) { a = _a; b = _b; c = _c; }
    }
}