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: Runtime Error)

def exgcd(a, b)
  if b == 0
    return [1, 0]
  end

  y, x = exgcd(b, a % b)
  y -= a / b * x
  return [x, y]
end

MOD = 1_000_000_007

def inv(a)
  x, y = exgcd(a, MOD)
  return x
end

def modpow(b, i)
  t = 1
  i.times do
    t = t * b % MOD
  end
  return t
end

n = gets.to_i
as = gets.split.map(&:to_i)


lcm = 1


facts = {}

as.each do |a|
  x = a
  fs = []
  2.upto(Math.sqrt(a).ceil) do |k|
    cnt = 0
    while x % k == 0
      x /= k
      cnt += 1
    end

    if cnt > 0
      facts[k] = [facts[k] || 0, cnt].max
    end
  end

  # prime number
  if x > 1
    facts[x] = [facts[x] || 0, 1].max
  end
end

lcm = facts.map { |k, v|
  modpow(k, v)
}.reduce(&:*) % MOD

sum = 0
as.each do |a|
  iv = inv(a)
  sum += lcm * iv % MOD
end

p sum % MOD

# bs = as.map {|a| lcm / a }

# p bs.reduce(&:+) % MOD