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: Accepted)

MOD = 1000000007

def prime_fact(n)
  #素因数分解
  i = 2
  while i ** 2 <= n do
    cnt = 0
    while n % i == 0
      cnt += 1
      n /= i
    end

    @map[i] = cnt if cnt > 0 && (@map[i] == nil || @map[i] < cnt)
    i += 1
  end

  @map[n] = 1 if n != 1 && @map[n] == nil
end

def power(n, a, m)
  res = 1

  if a > 0
    res = power(n, a / 2, m)
    if a % 2 == 0
      res = (res * res) % m
    else
      res = ((res * res) % m * n) % m
    end
  end
  
  return res
end

def main
  n = gets.chomp.to_i
  a = gets.chomp.split.map(&:to_i)

  @map = {}

  a.each do |v|
    prime_fact(v)
  end

  gcd = 1
  @map.map { |v, k|
    gcd *= power(v, k, MOD)
  }

  ans = 0
  a.each do |v|
    ans += (gcd / v) 
  end

  puts ans % MOD
end

main