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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

factors n =
  let loop_j n i j =
        if n `mod` i == 0 then
          loop_j (n `div` i) i (j + 1)
        else
          (n, j)
  in
    let loop_i n i =
          if i * i > n then
            if n == 1 then [] else [(n, 1)]
          else if n `mod` i == 0 then
            let (n', c) = loop_j (n `div` i) i 1
            in
              (i, c) : loop_i n' (i + 1)
          else
            loop_i n (i + 1)
    in
      loop_i n 2
  
merge [] _ = []
merge _ [] = []
merge (x:xs) (y:ys) =
  if fst x == fst y then
    x : merge xs ys
  else if x < y then
         merge xs (y:ys)
       else
         merge (x:xs) ys

main = do
  [a,b] <- map read . words <$> getLine
  let facta = factors a
  let factb = factors b 
  let ans = 1 + length (merge facta factb )
  putStrLn $ show ans