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 (2.7.1) (judge verdict: Time Limit Exceeded)

MOD = 10**9 + 7
def pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end
def divisors(n)
  b = Array.new
  for i in 2..((n**0.5))
    while n % i == 0
      b.push(i)
      n = n / i
    end
  end
  b.push(n) if n != 1
  b
end
n = gets.to_i
a = gets.chomp.split(" ").map(&:to_i)
lcm = Hash.new(0)
divisors(a[0]).each do |x|
  lcm[x] += 1
end
(n-1).times do |i|
  h = Hash.new(0)
  divisors(a[i+1]).each do |x|
    h[x] += 1
  end
  lcm.each_key do |j|
    lcm[j] = h[j] if lcm[j] < h[j]
  end
  h.each_key do |j|
    lcm[j] = h[j] if lcm[j] < h[j]
  end
end
lcmNum = 1
lcm.each_key do |i|
  lcmNum = lcmNum * pow(i,lcm[i]) % MOD
end
ans = 0
n.times do |i|
  ans += lcmNum * pow(a[i], MOD-2) % MOD
  ans %= MOD
end
puts ans