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<bits/stdc++.h>
using namespace std;
#define FILEIN freopen("input.txt", "r", stdin)
#define endl "\n"
#define ll long long

const ll m = 1e9 + 7;

ll findLcm(vector<ll> v){
    ll ans = v[0];
    for(int i = 1; i<v.size(); i++){
        ans = (ans * v[i])/(__gcd(ans, v[i]));
    }
    return ans;
}

int main(){
    // FILEIN;
    int n; cin>>n;
    vector<ll> v(n);
    for(auto &i : v) cin>>i;
    ll lcm = findLcm(v), ans = 0;
    for(auto i : v){
        ans += lcm / i;
    }
    cout<<ans%m<<endl;
}