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.Dynamic;
using System.Linq;

namespace AtCoderBeginnerContest152
{
	class Program
	{
		private const int ModNum = 1000000007;

		static void Main(string[] args)
		{
			var number = int.Parse(Console.ReadLine());
			var numbers = Console.ReadLine().Split().Select(x => uint.Parse(x)).ToArray();

			var lcm = (ulong)numbers[0];
			for (var i = 1; i < number; i++)
			{
				lcm = Euclid(lcm, numbers[i]);
			}

			ulong result = 0;
			for (var i = 0; i < number; i++)
			{
				result += lcm / numbers[i];
				result %= ModNum;
			}

			Console.WriteLine(result);
		}

		static ulong Euclid(ulong a, ulong b)
		{
			var big = a;
			var small = b;
			if (b > a)
			{
				small = a;
				big = b;
			}
			while (true)
			{
				var div = big / small;
				var sub = big - small * div;
				if (sub == 0)
				{
					break;
				}

				big = small;
				small = sub;
			}

			return a * b / small;
		}
	}
}