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: Accepted)

#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define forn(i,a,b) for(int i =a;i<b;i++)
#define fi first
#define se second
#define fast ios_base::sync_with_stdio(false);
using namespace std;

typedef long long int ll;
typedef vector<ll> vi;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int modi = 1e9 + 7;

ll gcd(ll a,ll b){ return b?gcd(b,a%b):a ;}

ll binpow(ll a,ll b){
	ll res = 1;
	while(b>0){
		if(b&1)
			res = res*a%modi;
		a = a*a%modi;
		b>>=1;
	}
	return res;
}

void solve(){
	int n;
	cin >> n;
	ll a[n];
	for(int i =0;i<n;i++)
		cin >> a[i];
	// reduce all to its smaller form
	map<int,int> lcm_factors;
	for(int i =0;i<n;i++){
		ll val = a[i];
		for(int j = 2;j*j<=val;j++){
			if(val%j == 0){
				int cnt = 0;
				while(val%j==0){
					cnt++;
					val/=j;
				}
				if(lcm_factors.count(j))
					lcm_factors[j] = max(lcm_factors[j],cnt);
				else
					lcm_factors[j] = cnt;
			}
		}
		if(val>1){
			if(lcm_factors.count(val))
			lcm_factors[val] = max(lcm_factors[val],1);
 			else
 				lcm_factors[val] = 1;
 		}
	}
	ll lcm = 1;
	for(auto e:lcm_factors){
		lcm = lcm*binpow(e.first,e.second)%modi;
	}
	// for(auto e:lcm_factors){
	// 	cout << e.first <<  " " << e.second << endl;
	// }
	ll ans = 0;
	for(int i =0;i<n;i++){
		ans = (ans+(lcm*binpow(a[i],modi-2))%modi)%modi;
	}
	// ans = ans*lcm%modi;
	cout << ans << endl;
}

int main(){
	fast;
	// #ifndef ONLINE_JUDGE
	// 	freopen("input.txt","r",stdin);
	// 	freopen("output.txt","w",stdout);
	// #endif

	// int t;cin >> t;while(t--)
		solve();
}