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)

N = gets.to_i
As = gets.split.map(&:to_i)
M = 10**9 + 7

require 'prime'
l = As.inject(&:lcm)

def mpow(x, n)
  ret = 1
  while n > 0
    if n.even?
      x = x * x % M
      n >>= 1
    else
      ret = ret * x % M
      n -= 1
    end
  end
  ret
end

inv = ->(x){mpow(x, M - 2)}
puts l*As.inject(0){|s, a| (s + inv[a]) % M} % M