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>

using namespace std;

long long mod = 1e9 + 7;

long long inv(long long a){
  long long m = mod, u = 1, v = 0;
  while(m){
    long long t = a / m;
    a -= t * m;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if(u < 0) u += mod;
  return u;
}

long long gcd(long long a, long long b){
  if(a < b) swap(a, b);
  if(b == 0) return a;
  else return gcd(b, a % b);
}

int main(){
  int N;
  cin >> N;
  
  vector<long long> A(N);
  for(int i = 0; i < N; i++) cin >> A[i];
  
  long long l = A[0];
  for(int i = 1; i < N; i++){
    l = l / gcd(l, A[i]) * A[i];
  }
  
  long long sum = 0;
  for(int i = 0; i < N; i++){
    sum += l / A[i];
    sum %= mod;
  }
  
  cout << sum << endl;
  
  return 0;
}