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.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class E
{
	public static void Main() => (new Solver()).Solve();
}

public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		var A = GetLongs(N);

		var cnt = Enumerable.Range(0, N).Select(x => factorization(A[x])).ToArray();
		var max = new Dictionary<long, long>();
		for(int i = 0; i < N; i++)
		{
			foreach(long p in cnt[i].Keys)
			{
				long c = 0;
				max.TryGetValue(p, out c);
				max[p] = Max(c, cnt[i][p]);
			}
		}

		var ans = new ModInt(0);
		for(int i = 0; i < N; i++)
		{
			var B = new ModInt(1);
			foreach(long p in max.Keys)
			{
				long c = 0;
				cnt[i].TryGetValue(p, out c);
				B *= ModInt.Pow(new ModInt(p), new ModInt(max[p] - c));
			}
			ans += B;
		}
		WriteLine(ans.Val);
	}

	private Dictionary<long, long> factorization(long x)
	{
		var cnt = new Dictionary<long, long>();
		long rest = x;
		for(long i = 2; i * i <= x; i++)
		{
			while(rest % i == 0)
			{
				rest /= i;
				long c = 0;
				cnt.TryGetValue(i, out c);
				cnt[i] = c + 1;
			}
		}
		if(rest > 1)
		{
			long c = 0;
			cnt.TryGetValue(rest, out c);
			cnt[rest] = c + 1;
		}
		return cnt;
	}
}

public struct ModInt
{
	public long Mod { get; private set; }
	public long Val { get; private set; }

	public ModInt(long v)
	{
		// must initialize (default: Mod = 0)
		Mod = 1000000007;
		Val = (v + Mod) % Mod;
	}

	public static ModInt operator+(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val + y.Val;
		if(tmp >= mod)
			tmp -= mod;
		return new ModInt(tmp);
	}

	public static ModInt operator-(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long tmp = x.Val;
		if(tmp < y.Val)
			tmp += mod;
		tmp -= y.Val;
		return new ModInt(tmp);
	}

	public static ModInt operator*(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		return new ModInt((x.Val * y.Val) % mod);
	}

	public static ModInt operator/(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long pow = mod - 2;
		long yy = y.Val;
		long inv = 1;
		while(pow > 0)
		{
			if((pow & 1) == 1)
				inv = (inv * yy) % mod;
			yy = (yy * yy) % mod;
			pow >>= 1;
		}
		return new ModInt((x.Val * inv) % mod);
	}

	public static ModInt Pow(ModInt x, ModInt y)
	{
		long mod = x.Mod;
		long pow = y.Val;
		long xx = x.Val;
		long v = 1;
		while(pow > 0)
		{
			if((pow & 1) == 1)
				v = (v * xx) % mod;

			xx = (xx * xx) % mod;
			pow >>= 1;
		}
		return new ModInt(v);
	}

	public static ModInt operator+(ModInt x, long y) => x + new ModInt(y);
	public static ModInt operator-(ModInt x, long y) => x - new ModInt(y);
	public static ModInt operator*(ModInt x, long y) => x * new ModInt(y);
	public static ModInt operator/(ModInt x, long y) => x / new ModInt(y);
	public static ModInt operator++(ModInt x) => x + new ModInt(1);
	public static ModInt operator--(ModInt x) => x - new ModInt(1);
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => Enumerable.Range(0, (int)N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(long N) => Enumerable.Range(0, (int)N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDouble()).ToArray();
	public static decimal[] GetDecimals(long N) => Enumerable.Range(0, (int)N).Select(_ => GetDecimal()).ToArray();
	public static string[] GetStrings(long N) => Enumerable.Range(0, (int)N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}