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;

namespace py
{
    class Program
    {
        static void Main(string[] args)
        {
            Int64 N = Int64.Parse(Console.ReadLine());
            Int64[] A = CovSI(Console.ReadLine().Split(' '),N);
            /*-*/
            Int64 gbsA = GetZXGBS(A);
            Int64 sum = 0;
            foreach(Int64 x in A)
            {
                sum += (gbsA / x);
            }
            double xr = sum % (Math.Pow(10, 9)+7);
            Console.WriteLine(xr);
        }
        static Int64[] CovSI(string[] Ab,Int64 N)
        {
            Int64[] A = new Int64[N];
            for (Int64 i = 0; i < N; i++)
            {
                A[i] = Int64.Parse(Ab[i]);
            }
            return A;
        }
        static Int64 GetZXGBS(Int64[] P)
        {
            if (P.Length == 1)
                return P[0];
            List<Int64> resultList = new List<Int64>();
            if (P.Length % 2 == 0)
            {
                for (Int64 i = 0; i < P.Length-1; i = i + 2)
                {
                    Int64 result = GetMod(P[i], P[i + 1]);
                    resultList.Add(result);
                }
            }
            else
            {
                for (Int64 i = 0; i < P.Length-1; i = i + 2)
                {
                    Int64 result = GetMod(P[i], P[i + 1]);
                    resultList.Add(result);
                }
                resultList.Add(P[P.Length - 1]);
            }
            return GetZXGBS(resultList.ToArray());
        }
        static Int64 GetMod(Int64 na, Int64 nb)
        {
            Int64 n1 = Math.Max(na, nb);
            Int64 n2 = Math.Min(na, nb);
            Int64 product = n1 * n2;
            while (n2 != 0)
            {
                n1 = n1 > n2 ? n1 : n2;
                Int64 m = n1 % n2;
                n1 = n2;
                n2 = m;
            }
            return (product / n1);
        }
    }
}