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.Linq;

class E
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Console.ReadLine().Split().Select(int.Parse).ToArray();

		var aM = a.Max();
		if (aM == 1) { Console.WriteLine(n); return; }

		var ps = PrimesF(2, aM);
		var cs = new int[aM + 1];
		var a2 = (int[])a.Clone();

		for (int i = 0; i < n; i++)
			foreach (var p in ps)
			{
				if (a2[i] == 1) break;
				var c = 0;
				for (; a2[i] % p == 0; c++) a2[i] /= p;
				if (c > cs[p]) cs[p] = c;
			}

		var lcm = ps.Where(p => cs[p] > 0).Select(p => ((MInt)p).Pow(cs[p])).Aggregate((x, y) => x * y);
		Console.WriteLine(a.Select(x => lcm / x).Aggregate((x, y) => x + y).V);
	}

	static int[] PrimesF(int m, int M)
	{
		var b = PrimeFlags(M);
		return Enumerable.Range(m, M - m + 1).Where(i => b[i]).ToArray();
	}
	static bool[] PrimeFlags(int M)
	{
		var rM = (int)Math.Sqrt(M);
		var b = new bool[M + 1]; b[2] = true;
		for (int i = 3; i <= M; i += 2) b[i] = true;
		for (int p = 3; p <= rM; p++) if (b[p]) for (var i = p * p; i <= M; i += 2 * p) b[i] = false;
		return b;
	}
}

struct MInt
{
	const int M = 1000000007;
	public long V;
	public MInt(long v) { V = (v %= M) < 0 ? v + M : v; }

	public static implicit operator MInt(long v) => new MInt(v);
	public static MInt operator +(MInt x, MInt y) => x.V + y.V;
	public static MInt operator -(MInt x, MInt y) => x.V - y.V;
	public static MInt operator *(MInt x, MInt y) => x.V * y.V;
	public static MInt operator /(MInt x, MInt y) => x * y.Inv();

	public MInt Pow(int i) => MPow(V, i);
	public MInt Inv() => MPow(V, M - 2);

	static long MPow(long b, int i)
	{
		for (var r = 1L; ; b = b * b % M)
		{
			if (i % 2 > 0) r = r * b % M;
			if ((i /= 2) < 1) return r;
		}
	}
}