Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

input_lines = gets.chop.split.map(&:to_i)
input_lines2 = gets.chop.split.map(&:to_i)

answerArray = [1]
for i in 1...input_lines[0]
    for iA in 0...answerArray.count
        puts input_lines2[(answerArray[answerArray.count - 1 -  iA] - 1)]
        if  input_lines2[i] > input_lines2[(answerArray[answerArray.count - 1 -  iA] - 1)]
            answerArray.insert((answerArray.count -  iA), i + 1)
            break
        end
    end
    if  answerArray.count < i + 1 
        answerArray.insert(0, i + 1)
    end

end

answerString = ""
for test in answerArray
    if answerString == ""
        answerString = String(test)
    else
        answerString = answerString + " " + String(test)
    end
end
puts answerString