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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt
  val seq = Seq.fill(n)(sc.nextLong).sorted.reverse
  
  def gcd(a: Long, b: Long): Long = {
    if (b == 0) a
    else gcd(b, a % b)
  }
  def lcm(a: Long, b: Long): Long = a * b / gcd(a, b)
  def multiLcm(seq: Seq[Long]): Long = seq.reduce(lcm)
  
  val LCM = multiLcm(seq)
  val sum = seq.map(LCM / _).sum
  println(sum % 1000000007)
}