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: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var n=sc.I;
		var a=sc.Ia;
		var h=new int[1000001];
		for(int i = 0;i<n;i++) {
			var pf=new Pf(a[i]);
			pf.Get((k,v)=>{h[k]=Max(h[k],v);});
		}
		Mint p=1;
		for(int i = 2;i<h.Length;i++) {
			if(h[i]>0){p*=Fp(i,h[i]);}
		}
		Mint ans=0;
		for(int i = 0;i<n;i++) {ans+=p/a[i];}
		Console.WriteLine("{0}",ans);
	}
	static long Fp(long x,long e){
		long r=1;
		while(e>0){
			if((e&1)>0){r*=x;r%=mod;}
			x=(x*x)%mod;
			e>>=1;
		}
		return r;
	}
}
public class Pf{
	public Dictionary<long,int> hs=new Dictionary<long,int>();
	public Pf(long n){
		if(n%2==0){
			int p=0;
			while((n&1)==0){n>>=1;p++;}
			hs.Add(2,p);
		}
		var q=(int)Sqrt(n)+1;
		for(int i=3;n!=1&&i<q;i+=2){
			if(n%i==0){
				int p=0;
				while(n%i==0){n/=i;p++;}
				q=(int)Sqrt(n)+1;
				hs.Add(i,p);
			}
		}
		if(n!=1){hs.Add(n,1);}
	}
	public void Get(Action<long,int> f){
		foreach(var e in hs){f(e.Key,e.Value);}
	}
}
public struct Mint{
	const int mod=(int)1e9+7;
	private long d;
	public Mint(long d){this.d=d;}
	public static implicit operator Mint(long d){return new Mint(d%mod);}
	public static explicit operator long(Mint d){return d.d;}
	public override string ToString(){return d.ToString();}
	public static Mint operator+(Mint a,long b){a.d=(a.d+b)%mod;return a;}
	public static Mint operator+(Mint a,Mint b){a.d=(a.d+b.d)%mod;return a;}
	public static Mint operator-(Mint a,long b){a.d=(mod+a.d-b)%mod;return a;}
	public static Mint operator-(Mint a,Mint b){a.d=(mod+a.d-b.d)%mod;return a;}
	public static Mint operator*(Mint a,long b){a.d=(a.d*b)%mod;return a;}
	public static Mint operator*(Mint a,Mint b){a.d=(a.d*b.d)%mod;return a;}
	public static Mint operator/(Mint a,long b){a.d=(a.d*Mi(b))%mod;return a;}
	public static Mint operator/(Mint a,Mint b){a.d=(a.d*Mi(b.d))%mod;return a;}
	private static long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}