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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
  $mod = pow(10, 9) + 7;
  function gcd($a, $b) {
    if ($b > $a) list($a, $b) = [$b, $a];
      
      while($b > 0) {
        $tb = $b;
          $b = $a % $b;
          $a = $tb;
      }
      return $a;
  } 

function lcm($a, $b) {
    return $a * $b / gcd($a, $b);
}
  
  $n = fgets(STDIN);
  $ne = preg_split("/\s/", fgets(STDIN));

  $gcd = 1;
  for ($i = 0; $i < $n; $i++) {
    $gcd = lcm($gcd, (int)$ne[$i]);
  }
  $sum = 0;
  for ($i = 0; $i < $n; $i++) {
    $sum += ($gcd / $ne[$i]);
      $sum %= $mod;
  }
echo $sum;