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
fscanf(STDIN, "%d", $n);
fscanf(STDIN, "%s", $s);
$n = (int) $n;
$A = explode(" ", $s);

# func
function gcd($a, $b) {
  if ($b === 0 || $a === $b)
    return $a;
  
  return gcd($b, $a % $b);
}
 
function lcm($a, $b){
  return $a * $b / gcd($a, $b);
}

# A's lcm
$c = (int) $A[0];
for($i = 1; $i < $n; $i++){
  $c = lcm($c, (int) $A[$i]);
}

# result
$sum = 0;
$break_num = pow(10, 9) + 7;
for($i = 0; $i < $n; $i++){
  $sum += ($c / $A[$i]) % $break_num;
}
echo $sum."\n";
?>