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 <iostream>
#include <map>
#include <algorithm>
using namespace std;
typedef long long ll;
ll M = 1000000007;
ll A[10005];
map<ll,int> p[10005];
int main() {
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  map<ll,int> m;
  ll A;
  for (int i=0; i<N; i++) {
    cin >> A;
    for (ll j=2; j*j <= A; j++) {
      while (A % j == 0) {
        p[i][j]++;
        A /= j;
      }
    }
    p[i][A]++;
    for (auto& it : p[i]) {
      m[it.first] = max(m[it.first], it.second);
    }
  }
  ll ret = 0;
  for (int i=0; i<N; i++) {
    ll d = 1;
    for (auto& it : m) {
      for (int j=0; j < it.second - p[i][it.first]; j++) {
        d = (d * it.first) % M;
      }
    }
    ret = (ret + d) % M;
  }
  cout << ret << endl;
}