
"""simple docstring"""





from __future__ import annotations

from math import gcd



def 						_lowerCAmelCase				(				UpperCamelCase_  ,				UpperCamelCase_ = 2  ,				UpperCamelCase_ = 1  ,				UpperCamelCase_ = 3  ,				):
		# A value less than 2 can cause an infinite loop in the algorithm.
		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(UpperCamelCase_  ,				UpperCamelCase_  ,				UpperCamelCase_				) -> int:
				return (pow(UpperCamelCase_  ,				2				) + step) % modulus

		for _ in range(UpperCamelCase_				):
				# These track the position within the cycle detection logic.
				__SCREAMING_SNAKE_CASE            = seed
				__SCREAMING_SNAKE_CASE            = seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						__SCREAMING_SNAKE_CASE            = rand_fn(UpperCamelCase_  ,				UpperCamelCase_  ,				UpperCamelCase_				)
						__SCREAMING_SNAKE_CASE            = rand_fn(UpperCamelCase_  ,				UpperCamelCase_  ,				UpperCamelCase_				)
						__SCREAMING_SNAKE_CASE            = rand_fn(UpperCamelCase_  ,				UpperCamelCase_  ,				UpperCamelCase_				)

						# 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``.
						__SCREAMING_SNAKE_CASE            = gcd(hare - tortoise  ,				UpperCamelCase_				)

						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.
				__SCREAMING_SNAKE_CASE            = 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

							__magic_name__       =			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",
							)
							__magic_name__       =			parser.parse_args()

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










'''simple docstring'''

from typing import Optional, Tuple, Union

import flax
import flax.linen as nn
import jax
import jax.numpy as jnp
from flax.core.frozen_dict import FrozenDict

from ..configuration_utils import ConfigMixin, flax_register_to_config
from ..utils import BaseOutput
from .embeddings_flax import FlaxTimestepEmbedding, FlaxTimesteps
from .modeling_flax_utils import FlaxModelMixin
from .unet_ad_blocks_flax import (
    FlaxCrossAttnDownBlockaD,
    FlaxCrossAttnUpBlockaD,
    FlaxDownBlockaD,
    FlaxUNetMidBlockaDCrossAttn,
    FlaxUpBlockaD,
)






@flax.struct.dataclass
class 						a				(   _lowerCamelCase     ):
				snake_case_      =		42







@flax_register_to_config
class 						a				(   nn.Module   ,     _lowerCamelCase   ,     _lowerCamelCase     ):
				snake_case_      =		32
				snake_case_      =		4
				snake_case_      =		4
				snake_case_      =		(
				    "CrossAttnDownBlock2D",
				    "CrossAttnDownBlock2D",
				    "CrossAttnDownBlock2D",
				    "DownBlock2D",
				)
				snake_case_      =		("UpBlock2D", "CrossAttnUpBlock2D", "CrossAttnUpBlock2D", "CrossAttnUpBlock2D")
				snake_case_      =		False
				snake_case_      =		(320, 640, 1_280, 1_280)
				snake_case_      =		2
				snake_case_      =		8
				snake_case_      =		None
				snake_case_      =		1_280
				snake_case_      =		0.0
				snake_case_      =		False
				snake_case_      =		jnp.floataa
				snake_case_      =		True
				snake_case_      =		0
				snake_case_      =		False


				def   A_ (		self    :					Optional[int]       ,				lowercase_    :					jax.random.KeyArray					):
									# init input tensors
									snake_case_									=				(1, self.in_channels, self.sample_size, self.sample_size)
									snake_case_									=				jnp.zeros(lowercase_       ,				dtype=jnp.floataa					)
									snake_case_									=				jnp.ones((1,)       ,				dtype=jnp.intaa					)
									snake_case_									=				jnp.zeros((1, 1, self.cross_attention_dim)       ,				dtype=jnp.floataa					)

									snake_case_			,snake_case_									=				jax.random.split(lowercase_					)
									snake_case_									=				{'''params''': params_rng, '''dropout''': dropout_rng}

									return self.init(lowercase_       ,				lowercase_       ,				lowercase_       ,				lowercase_					)["params"]


				def   A_ (		self    :					List[str]					):
									snake_case_									=				self.block_out_channels
									snake_case_									=				block_out_channels[0] * 4

									if self.num_attention_heads is not None:
														raise ValueError(
														    '''At the moment it is not possible to define the number of attention heads via `num_attention_heads` because of a naming issue as described in https://github.com/huggingface/diffusers/issues/2011#issuecomment-1547958131. Passing `num_attention_heads` will only be supported in diffusers v0.19.'''					)

									# If `num_attention_heads` is not defined (which is the case for most models)
									# it will default to `attention_head_dim`. This looks weird upon first reading it and it is.
									# The reason for this behavior is to correct for incorrectly named variables that were introduced
									# when this library was created. The incorrect naming was only discovered much later in https://github.com/huggingface/diffusers/issues/2011#issuecomment-1547958131
									# Changing `attention_head_dim` to `num_attention_heads` for 40,000+ configurations is too backwards breaking
									# which is why we correct for the naming here.
									snake_case_									=				self.num_attention_heads or self.attention_head_dim

									# input
									snake_case_									=				nn.Conv(
									    block_out_channels[0]       ,				kernel_size=(3, 3)       ,				strides=(1, 1)       ,				padding=((1, 1), (1, 1))       ,				dtype=self.dtype       ,				)

									# time
									snake_case_									=				FlaxTimesteps(
									    block_out_channels[0]       ,				flip_sin_to_cos=self.flip_sin_to_cos       ,				freq_shift=self.config.freq_shift					)
									snake_case_									=				FlaxTimestepEmbedding(lowercase_       ,				dtype=self.dtype					)

									snake_case_									=				self.only_cross_attention
									if isinstance(lowercase_       ,				lowercase_					):
														snake_case_									=				(only_cross_attention,) * len(self.down_block_types					)

									if isinstance(lowercase_       ,				lowercase_					):
														snake_case_									=				(num_attention_heads,) * len(self.down_block_types					)

									# down
									snake_case_									=				[]
									snake_case_									=				block_out_channels[0]
									for i, down_block_type in enumerate(self.down_block_types					):
														snake_case_									=				output_channel
														snake_case_									=				block_out_channels[i]
														snake_case_									=				i == len(lowercase_					) - 1

														if down_block_type == "CrossAttnDownBlock2D":
																			snake_case_									=				FlaxCrossAttnDownBlockaD(
																			    in_channels=lowercase_       ,				out_channels=lowercase_       ,				dropout=self.dropout       ,				num_layers=self.layers_per_block       ,				num_attention_heads=num_attention_heads[i]       ,				add_downsample=not is_final_block       ,				use_linear_projection=self.use_linear_projection       ,				only_cross_attention=only_cross_attention[i]       ,				use_memory_efficient_attention=self.use_memory_efficient_attention       ,				dtype=self.dtype       ,				)
														else:
																			snake_case_									=				FlaxDownBlockaD(
																			    in_channels=lowercase_       ,				out_channels=lowercase_       ,				dropout=self.dropout       ,				num_layers=self.layers_per_block       ,				add_downsample=not is_final_block       ,				dtype=self.dtype       ,				)

														down_blocks.append(lowercase_					)
									snake_case_									=				down_blocks

									# mid
									snake_case_									=				FlaxUNetMidBlockaDCrossAttn(
									    in_channels=block_out_channels[-1]       ,				dropout=self.dropout       ,				num_attention_heads=num_attention_heads[-1]       ,				use_linear_projection=self.use_linear_projection       ,				use_memory_efficient_attention=self.use_memory_efficient_attention       ,				dtype=self.dtype       ,				)

									# up
									snake_case_									=				[]
									snake_case_									=				list(reversed(lowercase_					)					)
									snake_case_									=				list(reversed(lowercase_					)					)
									snake_case_									=				list(reversed(lowercase_					)					)
									snake_case_									=				reversed_block_out_channels[0]
									for i, up_block_type in enumerate(self.up_block_types					):
														snake_case_									=				output_channel
														snake_case_									=				reversed_block_out_channels[i]
														snake_case_									=				reversed_block_out_channels[min(i + 1       ,				len(lowercase_					) - 1					)]

														snake_case_									=				i == len(lowercase_					) - 1

														if up_block_type == "CrossAttnUpBlock2D":
																			snake_case_									=				FlaxCrossAttnUpBlockaD(
																			    in_channels=lowercase_       ,				out_channels=lowercase_       ,				prev_output_channel=lowercase_       ,				num_layers=self.layers_per_block + 1       ,				num_attention_heads=reversed_num_attention_heads[i]       ,				add_upsample=not is_final_block       ,				dropout=self.dropout       ,				use_linear_projection=self.use_linear_projection       ,				only_cross_attention=only_cross_attention[i]       ,				use_memory_efficient_attention=self.use_memory_efficient_attention       ,				dtype=self.dtype       ,				)
														else:
																			snake_case_									=				FlaxUpBlockaD(
																			    in_channels=lowercase_       ,				out_channels=lowercase_       ,				prev_output_channel=lowercase_       ,				num_layers=self.layers_per_block + 1       ,				add_upsample=not is_final_block       ,				dropout=self.dropout       ,				dtype=self.dtype       ,				)

														up_blocks.append(lowercase_					)
														snake_case_									=				output_channel
									snake_case_									=				up_blocks

									# out
									snake_case_									=				nn.GroupNorm(num_groups=32       ,				epsilon=1e-5					)
									snake_case_									=				nn.Conv(
									    self.out_channels       ,				kernel_size=(3, 3)       ,				strides=(1, 1)       ,				padding=((1, 1), (1, 1))       ,				dtype=self.dtype       ,				)


				def __call__(		self    :					Union[str, Any]       ,				lowercase_    :					Union[str, Any]       ,				lowercase_    :					int       ,				lowercase_    :					Any       ,				lowercase_    :					int=None       ,				lowercase_    :					Any=None       ,				lowercase_    :					bool = True       ,				lowercase_    :					bool = False       ,				):
									# 1. time
									if not isinstance(lowercase_       ,				jnp.ndarray					):
														snake_case_									=				jnp.array([timesteps]       ,				dtype=jnp.intaa					)
									elif isinstance(lowercase_       ,				jnp.ndarray					) and len(timesteps.shape					) == 0:
														snake_case_									=				timesteps.astype(dtype=jnp.floataa					)
														snake_case_									=				jnp.expand_dims(lowercase_       ,				0					)

									snake_case_									=				self.time_proj(lowercase_					)
									snake_case_									=				self.time_embedding(lowercase_					)

									# 2. pre-process
									snake_case_									=				jnp.transpose(lowercase_       ,				(0, 2, 3, 1)					)
									snake_case_									=				self.conv_in(lowercase_					)

									# 3. down
									snake_case_									=				(sample,)
									for down_block in self.down_blocks:
														if isinstance(lowercase_       ,				lowercase_					):
																			snake_case_			,snake_case_									=				down_block(lowercase_       ,				lowercase_       ,				lowercase_       ,				deterministic=not train					)
														else:
																			snake_case_			,snake_case_									=				down_block(lowercase_       ,				lowercase_       ,				deterministic=not train					)
														down_block_res_samples += res_samples

									if down_block_additional_residuals is not None:
														snake_case_									=				()

														for down_block_res_sample, down_block_additional_residual in zip(
														    lowercase_       ,				lowercase_					):
																			down_block_res_sample += down_block_additional_residual
																			new_down_block_res_samples += (down_block_res_sample,)

														snake_case_									=				new_down_block_res_samples

									# 4. mid
									snake_case_									=				self.mid_block(lowercase_       ,				lowercase_       ,				lowercase_       ,				deterministic=not train					)

									if mid_block_additional_residual is not None:
														sample += mid_block_additional_residual

									# 5. up
									for up_block in self.up_blocks:
														snake_case_									=				down_block_res_samples[-(self.layers_per_block + 1) :]
														snake_case_									=				down_block_res_samples[: -(self.layers_per_block + 1)]
														if isinstance(lowercase_       ,				lowercase_					):
																			snake_case_									=				up_block(
																			    lowercase_       ,				temb=lowercase_       ,				encoder_hidden_states=lowercase_       ,				res_hidden_states_tuple=lowercase_       ,				deterministic=not train       ,				)
														else:
																			snake_case_									=				up_block(lowercase_       ,				temb=lowercase_       ,				res_hidden_states_tuple=lowercase_       ,				deterministic=not train					)

        # 6. post-process
									snake_case_									=				self.conv_norm_out(lowercase_					)
									snake_case_									=				nn.silu(lowercase_					)
									snake_case_									=				self.conv_out(lowercase_					)
									snake_case_									=				jnp.transpose(lowercase_       ,				(0, 3, 1, 2)					)

									if not return_dict:
														return (sample,)

									return FlaxUNetaDConditionOutput(sample=lowercase_					)

