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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

require 'prime'

MOD = 10 ** 9 + 7
N = gets.to_i
A = gets.split.map(&:to_i)
B = []

primes = Hash.new(0)

A.each do |a|
  a.prime_division.each do |n, e|
    if primes[n] < e
      primes[n] = e
    end
  end
end

cache = Hash.new(0)

primes.each do |n, e|
  v = 1

  e.times do
    v *= n
    v %= MOD
  end

  cache[n] = v
end

ans = 0

A.each do |a|
  b = 1

  divs = a.prime_division.to_h

  primes.each do |n, e|
    if divs[n]
      (e - divs[n]).times do
        b *= n
        b %= MOD
      end
    else
      b *= cache[n]
      b %= MOD
    end
  end

  ans += b
  ans %= MOD
end

puts ans