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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>
#include <numeric>

using namespace std;

template<class T>
T gcd(T a, T b) {
  if (b == 0) {
    return a;
  } else {
    return gcd(b, a % b);
  }
}

template<class T>
T lcm(T a, T b) {
  return a * b / gcd(a, b); 
}

const int mod = 1e9+7;
using ll = long long;

int main(int argc, const char *argv[])
{
  int n;
  cin >> n;

  vector<ll> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }

  ll a_lcm = accumulate(a.begin(), a.end(), 1ll,
      [](ll acc, ll cur) { return lcm(acc, cur); });

  ll ans = accumulate(a.begin(), a.end(), 0ll,
      [&](ll acc, ll cur) { return (acc + a_lcm / cur); });
  cout << ans % mod << "\n";
  return 0;
}