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 static System.Console;
using static System.Int32;
using static System.Math;
using System.Linq;
using System.Collections.Generic;

class Solution
{
    static void Main()
    {
    lb:
        ReadLine();
        var ary = ReadLine().Split().Select(Parse).ToArray();
        //ary = Enumerable.Range(1, 1000).Select(n => 1000000 - n).ToArray();
        var ary2 = ary.ToArray();
        var bunkai = new Dictionary<int, int>();
        var sosu = new List<int>();
        for (int i = 2; i < 998; ++i)
        {
            if (sosu.Any(s => i % s == 0)) continue;
            sosu.Add(i);
            int count = 0;
            for (int j = 0; j < ary.Length; ++j)
            {
                int tmpC = 0;
                for (; ary[j] % i == 0; ++tmpC) ary[j] /= i;
                count = Max(tmpC, count);
            }
            if (0 < count) bunkai[i] = count;
        }
        foreach (var a in ary.Where(n => 1 < n)) bunkai[a] = 1;
        const int WARU = 1000000007;
        long result = 0;
        for (int i = 0; i < ary2.Length; ++i)
        {
            var a = ary2[i];
            long watta = 1;
            foreach (var pair in bunkai)
            {
                int count = pair.Value;
                while (a % pair.Key == 0)
                {
                    a /= pair.Key;
                    --count;
                }
                for (int j = 0; j < count; ++j)
                {
                    watta *= pair.Key;
                    watta %= WARU;
                }
            }
            result += watta;
            if (WARU <= result) result -= WARU;
        }

        WriteLine(result);
    }
}