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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define r(i,n) for(int i = 0; i<n; i++)
typedef long long ll;
using namespace std;

ll gcd(ll a, ll b){
  if(b==0)return a;
  else return gcd(b,a%b);
}

ll lcm(ll a, ll b){
  return a / gcd(a, b) * b;
}

int main(){
  ll n;
  cin >> n;
  queue<int> q[n];
  vector<int> v(n);
  r(i,n)cin >> v[i];
  ll count=0,g=v[0];
  r(i,n-1)g=gcd(g,v[i+1]);
  r(i,n)v[i]/=g;
  r(i,n){
    r(k,n){
      if(k!=i)q[k].push(lcm(v[i],v[k])/v[k]);
    }
    r(j,n){
      if(i!=j){
        ll gc=gcd(v[i],v[j]);
      v[j]/=gc;
      }
    }
    v[i]=1;
  }
  r(i,n){
    ll a=1;
    while(!q[i].empty()){
      a=(a*(q[i].front()))%1000000007;
      q[i].pop();
    }
    count+=a;
    count%=1000000007;
  }
  cout<<count<<endl;
}