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.Numerics;

class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 29;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;

    myinout IO = new myinout();






    public void Solve()
    {

        var o = IO.intm;
        var n = o[0];
        var a = IO.longm;
        BigInteger l = a[0];
        for (int i = 0; i < n;++i){
            l = Math2.blcm(a[i], l);
        }

        BigInteger ans = 0;
        for (int i = 0; i < n;++i){
            ans += (l/a[i]);
            ans %= MOD;
        }
        IO.wri(ans);
    }




}






public static class Math2
{
    public static long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public static long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public static BigInteger bgcd(BigInteger i, BigInteger y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static BigInteger blcm(BigInteger i, BigInteger y)
    {
        return i * y / bgcd(i, y);
    }

    public static Dictionary<long, int> primefactorization(long N)
    {

        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public static List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

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

}

class myinout
{
    //in
    public string str => Console.ReadLine();

    public string[] strm => str.Split(' ');

    public long[] longm => strm.Select(long.Parse).ToArray();
    public int[] intm => strm.Select(int.Parse).ToArray();
    public char[] charm => str.ToArray();
    public double[] doublem => strm.Select(double.Parse).ToArray();
    public long long1 => longm[0];
    public int int1 => intm[0];
    public char char1 => charm[0];
    public double double1 => doublem[0];



    //out
    public void wri<T>(T i)
    {
        Console.WriteLine(i);
    }
    public void wri<T>(T[] i)
    {
        Console.WriteLine(string.Join(" ", i));
    }

    public void yn(bool i)
    {
        if (i) wri("Yes");
        else wri("No");
    }

}