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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Console;

namespace CPLib
{
    class Atria
    {
        const long mod = 1000000000 + 7;
        static void Main(string[] args)
        {
            int n = int.Parse(ReadLine());
            int[] s = ReadLine().Split(' ').Select(int.Parse).ToArray();
            if (n == 1)
            {
                WriteLine(s[0]);
                return;
            }
            var lcm = Lcm(s[0],s[1]);
            for (int i = 2; i < n; i++)
            {
                lcm = Lcm(lcm, s[i]);
            }

            long ans = 0;
            for (int i = 0; i < n; i++)
            {
                ans += lcm / s[i];
                ans %= mod;
            }
            WriteLine(ans);
        }
        /// <summary>
        /// Gcd (Gross Common Dividing) 最大公約数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        static long Gcd(long a, long b)
        {
            var v = new[] { a, b };
            while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
            return v[0];
        }
        /// <summary>
        /// Lcm (Last Common Multiple) 最小公倍数 
        /// Gcdライブラリの仕様が前提
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        static long Lcm(long a, long b)
        {
            return a / Gcd(a, b) * b;
        }
    }
}