

'''simple docstring'''
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 					_snake_case		(__SCREAMING_SNAKE_CASE):
			__A  :	torch.FloatTensor
			__A  :	Optional[torch.FloatTensor]        =None




def  a__       (    _SCREAMING_SNAKE_CASE   :       int	,				_SCREAMING_SNAKE_CASE   :       Optional[int]=0.999	,				_SCREAMING_SNAKE_CASE   :       List[Any]="cosine"	,				)     ->					Union[str, Any]:


	"""simple docstring"""





	if alpha_transform_type == "cosine":

		def alpha_bar_fn(_SCREAMING_SNAKE_CASE   :       Union[str, Any]				):
			return math.cos((t + 0.008) / 1.008 * math.pi / 2				) ** 2

	elif alpha_transform_type == "exp":

		def alpha_bar_fn(_SCREAMING_SNAKE_CASE   :       Optional[Any]				):
			return math.exp(t * -12.0				)

	else:
		raise ValueError(F'''Unsupported alpha_tranform_type: {alpha_transform_type}'''				)

	UpperCAmelCase_     :      List[str]						=  []
	for i in range(_SCREAMING_SNAKE_CASE				):
		UpperCAmelCase_     :      Tuple						=  i / num_diffusion_timesteps
		UpperCAmelCase_     :      int						=  (i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(_SCREAMING_SNAKE_CASE				) / alpha_bar_fn(_SCREAMING_SNAKE_CASE				)	,				_SCREAMING_SNAKE_CASE				)				)
	return torch.tensor(_SCREAMING_SNAKE_CASE	,				dtype=torch.floataa				)





class 					_snake_case		(__SCREAMING_SNAKE_CASE			,			__SCREAMING_SNAKE_CASE):






			@register_to_config
			def __init__(  self			,_snake_case = 10_00			,_snake_case = "fixed_small_log"			,_snake_case = True			,_snake_case = 1.0			,_snake_case = "epsilon"			,_snake_case = "squaredcos_cap_v2"			,):
				if beta_schedule != "squaredcos_cap_v2":
					raise ValueError("UnCLIPScheduler only supports `beta_schedule`: 'squaredcos_cap_v2'"     )

				UpperCAmelCase_     :      Optional[Any]						=  betas_for_alpha_bar(_snake_case     )

				UpperCAmelCase_     :      Union[str, Any]						=  1.0 - self.betas
				UpperCAmelCase_     :      int						=  torch.cumprod(self.alphas			,dim=0     )
				UpperCAmelCase_     :      List[str]						=  torch.tensor(1.0     )

				# standard deviation of the initial noise distribution
				UpperCAmelCase_     :      int						=  1.0

				# setable values
				UpperCAmelCase_     :      Any						=  None
				UpperCAmelCase_     :      Union[str, Any]						=  torch.from_numpy(np.arange(0			,_snake_case     )[::-1].copy()     )

				UpperCAmelCase_     :      Optional[Any]						=  variance_type






			def 		UpperCamelCase__							(  self			,_snake_case			,_snake_case = None     ):
				return sample






			def 		UpperCamelCase__							(  self			,_snake_case			,_snake_case = None     ):
				UpperCAmelCase_     :      Optional[Any]						=  num_inference_steps
				UpperCAmelCase_     :      Optional[Any]						=  (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
				UpperCAmelCase_     :      Tuple						=  (np.arange(0			,_snake_case     ) * step_ratio).round()[::-1].copy().astype(np.intaa     )
				UpperCAmelCase_     :      Tuple						=  torch.from_numpy(_snake_case     ).to(_snake_case     )






			def 		UpperCamelCase__							(  self			,_snake_case			,_snake_case=None			,_snake_case=None			,_snake_case=None     ):
				if prev_timestep is None:
					UpperCAmelCase_     :      Any						=  t - 1

				UpperCAmelCase_     :      Tuple						=  self.alphas_cumprod[t]
				UpperCAmelCase_     :      List[str]						=  self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
				UpperCAmelCase_     :      Tuple						=  1 - alpha_prod_t
				UpperCAmelCase_     :      Optional[Any]						=  1 - alpha_prod_t_prev

				if prev_timestep == t - 1:
					UpperCAmelCase_     :      Any						=  self.betas[t]
				else:
					UpperCAmelCase_     :      Optional[int]						=  1 - alpha_prod_t / alpha_prod_t_prev

				# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
				# and sample from it to get previous sample
				# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
				UpperCAmelCase_     :      List[str]						=  beta_prod_t_prev / beta_prod_t * beta

				if variance_type is None:
					UpperCAmelCase_     :      Dict						=  self.config.variance_type

				# hacks - were probably added for training stability
				if variance_type == "fixed_small_log":
					UpperCAmelCase_     :      int						=  torch.log(torch.clamp(_snake_case			,min=1E-20     )     )
					UpperCAmelCase_     :      List[str]						=  torch.exp(0.5 * variance     )
				elif variance_type == "learned_range":
					# NOTE difference with DDPM scheduler
					UpperCAmelCase_     :      Optional[Any]						=  variance.log()
					UpperCAmelCase_     :      Union[str, Any]						=  beta.log()

					UpperCAmelCase_     :      Dict						=  (predicted_variance + 1) / 2
					UpperCAmelCase_     :      List[str]						=  frac * max_log + (1 - frac) * min_log

				return variance






			def 		UpperCamelCase__							(  self			,_snake_case			,_snake_case			,_snake_case			,_snake_case = None			,_snake_case=None			,_snake_case = True			,):
				UpperCAmelCase_     :      int						=  timestep

				if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
					UpperCAmelCase_					,					UpperCAmelCase_     :      Any						=  torch.split(_snake_case			,sample.shape[1]			,dim=1     )
				else:
					UpperCAmelCase_     :      List[Any]						=  None

				# 1. compute alphas, betas
				if prev_timestep is None:
					UpperCAmelCase_     :      Optional[int]						=  t - 1

				UpperCAmelCase_     :      int						=  self.alphas_cumprod[t]
				UpperCAmelCase_     :      Optional[int]						=  self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
				UpperCAmelCase_     :      Dict						=  1 - alpha_prod_t
				UpperCAmelCase_     :      Dict						=  1 - alpha_prod_t_prev

				if prev_timestep == t - 1:
					UpperCAmelCase_     :      List[str]						=  self.betas[t]
					UpperCAmelCase_     :      int						=  self.alphas[t]
				else:
					UpperCAmelCase_     :      Optional[int]						=  1 - alpha_prod_t / alpha_prod_t_prev
					UpperCAmelCase_     :      List[str]						=  1 - beta

				# 2. compute predicted original sample from predicted noise also called
				# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
				if self.config.prediction_type == "epsilon":
					UpperCAmelCase_     :      Tuple						=  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
				elif self.config.prediction_type == "sample":
					UpperCAmelCase_     :      Optional[int]						=  model_output
				else:
					raise ValueError(
					    f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`'''
					    " for the UnCLIPScheduler."     )

				# 3. Clip "predicted x_0"
				if self.config.clip_sample:
					UpperCAmelCase_     :      Dict						=  torch.clamp(
					    _snake_case			,-self.config.clip_sample_range			,self.config.clip_sample_range     )

				# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
				# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
				UpperCAmelCase_     :      int						=  (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
				UpperCAmelCase_     :      List[str]						=  alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

				# 5. Compute predicted previous sample µ_t
				# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
				UpperCAmelCase_     :      List[str]						=  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

				# 6. Add noise
				UpperCAmelCase_     :      Union[str, Any]						=  0
				if t > 0:
					UpperCAmelCase_     :      Optional[Any]						=  randn_tensor(
					    model_output.shape			,dtype=model_output.dtype			,generator=_snake_case			,device=model_output.device     )

					UpperCAmelCase_     :      Any						=  self._get_variance(
					    _snake_case			,predicted_variance=_snake_case			,prev_timestep=_snake_case			,)

					if self.variance_type == "fixed_small_log":
						UpperCAmelCase_     :      Union[str, Any]						=  variance
					elif self.variance_type == "learned_range":
						UpperCAmelCase_     :      List[str]						=  (0.5 * variance).exp()
					else:
						raise ValueError(
						    f'''variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`'''
						    " for the UnCLIPScheduler."     )

					UpperCAmelCase_     :      List[Any]						=  variance * variance_noise

				UpperCAmelCase_     :      Tuple						=  pred_prev_sample + variance

				if not return_dict:
					return (pred_prev_sample,)

				return UnCLIPSchedulerOutput(prev_sample=_snake_case			,pred_original_sample=_snake_case     )






			def 		UpperCamelCase__							(  self			,_snake_case			,_snake_case			,_snake_case			,):
				# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
				UpperCAmelCase_     :      int						=  self.alphas_cumprod.to(device=original_samples.device			,dtype=original_samples.dtype     )
				UpperCAmelCase_     :      str						=  timesteps.to(original_samples.device     )

				UpperCAmelCase_     :      Dict						=  alphas_cumprod[timesteps] ** 0.5
				UpperCAmelCase_     :      str						=  sqrt_alpha_prod.flatten()
				while len(sqrt_alpha_prod.shape     ) < len(original_samples.shape     ):
					UpperCAmelCase_     :      Dict						=  sqrt_alpha_prod.unsqueeze(-1     )

				UpperCAmelCase_     :      List[str]						=  (1 - alphas_cumprod[timesteps]) ** 0.5
				UpperCAmelCase_     :      Optional[int]						=  sqrt_one_minus_alpha_prod.flatten()
				while len(sqrt_one_minus_alpha_prod.shape     ) < len(original_samples.shape     ):
					UpperCAmelCase_     :      Union[str, Any]						=  sqrt_one_minus_alpha_prod.unsqueeze(-1     )

				UpperCAmelCase_     :      Optional[Any]						=  sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
				return noisy_samples








from collections import Counter
from timeit import timeit


def 		lowercase_	(  _UpperCamelCase = ""							,      ):


			'''simple docstring'''







			return sum(c % 2 for c in Counter(input_str.replace(''' '''							,      ''''''	).lower()	).values()	) < 2


def 		lowercase_	(  _UpperCamelCase = ""	):


			'''simple docstring'''







			if len(_UpperCamelCase	) == 0:
						return True
			__lowercase			       = input_str.replace(''' '''							,      ''''''	).lower()
			# character_freq_dict: Stores the frequency of every character in the input string
			__lowercase			       = {}

			for character in lower_case_input_str:
						__lowercase			       = character_freq_dict.get(_UpperCamelCase							,      0	) + 1
			__lowercase			       = 0

			for character_count in character_freq_dict.values():
						if character_count % 2:
									odd_char += 1
			if odd_char > 1:
						return False
			return True


def 		lowercase_	(  _UpperCamelCase = ""	):


			'''simple docstring'''







			print('''\nFor string = '''							,      _UpperCamelCase							,      ''':'''	)
			print(
			    '''> can_string_be_rearranged_as_palindrome_counter()'''							,      '''\tans ='''							,      can_string_be_rearranged_as_palindrome_counter(_UpperCamelCase	)							,      '''\ttime ='''							,      timeit(
			        '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'''							,      setup='''import __main__ as z'''							,      )							,      '''seconds'''							,      )
			print(
			    '''> can_string_be_rearranged_as_palindrome()'''							,      '''\tans ='''							,      can_string_be_rearranged_as_palindrome(_UpperCamelCase	)							,      '''\ttime ='''							,      timeit(
			        '''z.can_string_be_rearranged_as_palindrome(z.check_str)'''							,      setup='''import __main__ as z'''							,      )							,      '''seconds'''							,      )


if __name__ == "__main__":
	a			:			int												=					input(
	    '''Enter string to determine if it can be rearranged as a palindrome or not: '''
	).strip()
	benchmark(check_str)
	a			:			Tuple												=					can_string_be_rearranged_as_palindrome_counter(check_str)
	print(f'''{check_str} can {'' if status else 'not '}be rearranged as a palindrome''')


