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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

function isPrime($n)
{
    if ($n < 2) {
        return false;
    } elseif ($n === 2) {
        return true;
    } elseif ($n % 2 === 0) {
        return false;
    }

    $limit = floor(sqrt($n));

    for ($i = 3; $i <= $limit; $i += 2) {
        if ($n % $i === 0) {
            return false;
        }
    }

    return true;
}

list($a, $b) = explode(' ', trim(fgets(STDIN)));

$limit = min(floor(sqrt($a)), floor(sqrt($b)));

$div = [];
for ($i = 2; $i <= $limit; $i++) {
    if ($a % $i === 0 && $b % $i === 0) {
        $div[] = $i;
    }
}

$count = 1;
for ($i = 0; $i < count($div); $i++) {
    if (isPrime($div[$i])) {
        $count++;
    }
}

echo $count . PHP_EOL;