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.Numerics;

namespace py
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            BigInteger[] A = CovSI(Console.ReadLine().Split(' '),N);
            /*-*/
            BigInteger gbsA = GetZXGBS(A);
            BigInteger sum = 0;
            foreach(BigInteger x in A)
            {
                sum += (gbsA / x);
            }
            BigInteger xr;
            string ax = (Math.Pow(10, 9) + 7).ToString();
            BigInteger.DivRem(sum, BigInteger.Parse(ax), out xr);
            Console.WriteLine(xr);
        }
        static BigInteger[] CovSI(string[] Ab,int N)
        {
            BigInteger[] A = new BigInteger[N];
            for (int i = 0; i < N; i++)
            {
                A[i] = BigInteger.Parse(Ab[i]);
            }
            return A;
        }
        static BigInteger GetZXGBS(BigInteger[] P)
        {
            if (P.Length == 1)
                return P[0];
            List<BigInteger> resultList = new List<BigInteger>();
            if (P.Length % 2 == 0)
            {
                for (int i = 0; i < P.Length-1; i = i + 2)
                {
                    BigInteger result = GetMod(P[i], P[i + 1]);
                    resultList.Add(result);
                }
            }
            else
            {
                for (int i = 0; i < P.Length-1; i = i + 2)
                {
                    BigInteger result = GetMod(P[i], P[i + 1]);
                    resultList.Add(result);
                }
                resultList.Add(P[P.Length - 1]);
            }
            return GetZXGBS(resultList.ToArray());
        }
        static BigInteger GetMod(BigInteger na, BigInteger nb)
        {
            BigInteger n1;
            BigInteger n2;
            findMaxMin(na, nb, out n1, out n2);
            BigInteger product = n1 * n2;
            while (n2 != 0)
            {
                n1 = n1 > n2 ? n1 : n2;
                BigInteger m = n1 % n2;
                n1 = n2;
                n2 = m;
            }
            return (product / n1);
        }
        static int findMaxMin(BigInteger n1, BigInteger n2,out BigInteger nx,out BigInteger nm)
        {
            if (BigInteger.Subtract(n1, n2) > 0)
            {
                nx = n1;
                nm = n2;
                return 0;
            }
            else
            {
                nm = n1;
                nx = n2;
                return 0;
            }
        }
    }
}