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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
#include <cmath>
#include <iostream>
#include <vector>
#include <string>
#include <utility>
#include <algorithm>
#include <queue>
#include <map>
using namespace std;
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define REP(i,n) for(ll i=0;i<n;i++)
#define REPR(i,n) for(ll i=n-1;i>=0;i--)

typedef long long ll;
#define INF 1e18

#define MOD (ll)(1e9+7);
//ll cnt1=0,cnt2=0,cnt3=0,cnt4=0;

map<ll,ll> fact(ll a){
	map<ll,ll> ans;
	ll end=sqrt(a);
	FOR(i,2,end+1){
		while(a%i==0){
			a/=i;
			ans[i]++;
			//cnt1++;
		}
	}
	if(a!=1){
		ans[a]++;
	}
	return ans;
}

map<ll,ll> calcLcm(map<ll,ll> a,map<ll,ll> b){
	for(auto it:a){
		b[it.first]=max(b[it.first],it.second);
		//cnt2++;
	}
	return b;
}
ll power(ll a,ll b){
	static map<ll,vector<ll>> list;
	if(list[a].size()>b){
		//cout<<a<<"^"<<b<<"="<<list[a][b]<<endl;
		return list[a][b];
	}
	if(list[a].size()==0){
		list[a].reserve(b+1);
		list[a].push_back(1);
	}
	while(list[a].size()<=b){
		list[a].push_back(list[a].back()*a);
		list[a].back()%=MOD;
	}
	//cout<<a<<"^"<<b<<"="<<list[a].back()<<endl;
	return list[a].back();
}
ll factToInt(map<ll,ll> a){
	ll ans=1;
	for(auto it:a){
		ans*=power(it.first,it.second);
	}
	return ans;
}

int main(){
	ll n; cin>>n;
	vector<ll> a(n);
	REP(i,n) cin>>a[i];
	vector<map<ll,ll>> aFact;
	map<ll,ll> lcmFact;
	for(auto it:a){
		aFact.push_back(fact(it));
		lcmFact=calcLcm(aFact.back(),lcmFact);
	}
	ll ans=0;
	REP(i,n){
		map<ll,ll> tmpLcm=lcmFact;
		map<ll,ll> i_fact=aFact[i];
		for(auto it:i_fact){
			tmpLcm[it.first]-=it.second;
			//cnt4++;
		}
		ans+=factToInt(tmpLcm);
		ans%=MOD;
	}
	//cout<<cnt1<<" "<<cnt2<<" "<<cnt3<<" "<<cnt4<<endl;
	cout<<ans<<endl;
	return 0;
}