
from __future__ import annotations

from math import gcd






def   lowerCAmelCase_						(					_snake_case      :  int      ,   _snake_case      :  int = 2      ,   _snake_case      :  int = 1      ,   _snake_case      :  int = 3      ,   )				->		int | None:







	'''simple docstring'''


	if num < 2:
		raise ValueError("The input value cannot be less than 2"   )

	# Because of the relationship between ``f(f(x))`` and ``f(x)``, this
	# algorithm struggles to find factors that are divisible by two.
	# As a workaround, we specifically check for two and even inputs.
	#   See: https://math.stackexchange.com/a/2856214/165820
	if num > 2 and num % 2 == 0:
		return 2

	# Pollard's Rho algorithm requires a function that returns pseudorandom
	# values between 0 <= X < ``num``.  It doesn't need to be random in the
	# sense that the output value is cryptographically secure or difficult
	# to calculate, it only needs to be random in the sense that all output
	# values should be equally likely to appear.
	# For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
	# However, the success of Pollard's algorithm isn't guaranteed and is
	# determined in part by the initial seed and the chosen random function.
	# To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
	# where ``C`` is a value that we can modify between each attempt.
	def rand_fn(_snake_case      :  int      ,   _snake_case      :  int      ,   _snake_case      :  int   ) -> int:
		return (pow(_snake_case      ,   2   ) + step) % modulus

	for _ in range(_snake_case   ):
		# These track the position within the cycle detection logic.
		__magic_name__		:		str	   =     seed
		__magic_name__		:		int	   =     seed

		while True:
			# At each iteration, the tortoise moves one step and the hare moves two.
			__magic_name__		:		List[str]	   =     rand_fn(_snake_case      ,   _snake_case      ,   _snake_case   )
			__magic_name__		:		Dict	   =     rand_fn(_snake_case      ,   _snake_case      ,   _snake_case   )
			__magic_name__		:		int	   =     rand_fn(_snake_case      ,   _snake_case      ,   _snake_case   )

			# At some point both the tortoise and the hare will enter a cycle whose
			# length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
			# the tortoise and hare will end up on the same value modulo ``p``.
			# We can detect when this happens because the position difference between
			# the tortoise and the hare will share a common divisor with ``num``.
			__magic_name__		:		List[str]	   =     gcd(hare - tortoise      ,   _snake_case   )

			if divisor == 1:
				# No common divisor yet, just keep searching.
				continue
			else:
				# We found a common divisor!
				if divisor == num:
					# Unfortunately, the divisor is ``num`` itself and is useless.
					break
				else:
					# The divisor is a nontrivial factor of ``num``!
					return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
		__magic_name__		:		int	   =     hare

		# The new step value for the random function can just be incremented.
		# At first the results will be similar to what the old function would
		# have produced, but the value will quickly diverge after a bit.
		step += 1

	# We haven't found a divisor within the requested number of attempts.
	# We were unlucky or ``num`` itself is actually prime.
	return None


if __name__ == "__main__":
				import argparse

				snake_case :		List[str]							      =  argparse.ArgumentParser()
				parser.add_argument(
				    "num",
				    type=int,
				    help="The value to find a divisor of",
				)
				parser.add_argument(
				    "--attempts",
				    type=int,
				    default=3,
				    help="The number of attempts before giving up",
				)
				snake_case :		List[Any]							      =  parser.parse_args()

				snake_case :		Any							      =  pollard_rho(args.num, attempts=args.attempts)
				if divisor is None:
								print(F"{args.num} is probably prime")
				else:
								snake_case :		Tuple							      =  args.num // divisor
								print(F"{args.num} = {divisor} * {quotient}")


# This script creates a super tiny model that is useful inside tests, when we just want to test that
# the machinery works, without needing to the check the quality of the outcomes.
#
# This version creates a tiny model through reduction of a normal pre-trained model, but keeping the
# full vocab, merges file, and thus also resulting in a larger model due to a large vocab size.
# This gives ~3MB in total for all files.
#
# If you want a 50 times smaller than this see `fsmt-make-super-tiny-model.py`, which is slightly more complicated
#
#
# It will be used then as "stas/tiny-wmt19-en-de"

# Build
from transformers import FSMTTokenizer, FSMTConfig, FSMTForConditionalGeneration

snake_case :		List[str]							      =  "facebook/wmt19-en-de"
snake_case :		Dict							      =  FSMTTokenizer.from_pretrained(mname)
# get the correct vocab sizes, etc. from the master model
snake_case :		List[str]							      =  FSMTConfig.from_pretrained(mname)
config.update(
    dict(
        d_model=4,
        encoder_layers=1,
        decoder_layers=1,
        encoder_ffn_dim=4,
        decoder_ffn_dim=4,
        encoder_attention_heads=1,
        decoder_attention_heads=1,
    )
)

snake_case :		int							      =  FSMTForConditionalGeneration(config)
print(F"num of params {tiny_model.num_parameters()}")

# Test
snake_case :		Optional[Any]							      =  tokenizer(["Making tiny model"], return_tensors="pt")
snake_case :		List[str]							      =  tiny_model(**batch)

print("test output:", len(outputs.logits[0]))

# Save
snake_case :		Dict							      =  "tiny-wmt19-en-de"
tiny_model.half()  # makes it smaller
tiny_model.save_pretrained(mname_tiny)
tokenizer.save_pretrained(mname_tiny)

print(F"Generated {mname_tiny}")

# Upload
# transformers-cli upload tiny-wmt19-en-de
