






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
class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		_snake_case   :   torch.FloatTensor
		_snake_case   :   torch.FloatTensor
		_snake_case   :   Optional[torch.FloatTensor]							=  None





class   lowerCamelCase				(_snake_case			,  _snake_case      ):







		'''simple docstring'''



		_snake_case   :   str							=  2



		@register_to_config
		def __init__(							self    ,		_UpperCamelCase = 0.02    ,		_UpperCamelCase = 1_0_0    ,		_UpperCamelCase = 1.0_07    ,		_UpperCamelCase = 8_0    ,		_UpperCamelCase = 0.05    ,		_UpperCamelCase = 5_0    ,		)     ->							Dict:
							# standard deviation of the initial noise distribution
							UpperCAmelCase_   :				Optional[int]						=						sigma_max

							# setable values
							UpperCAmelCase_   :				int						=						None
							UpperCAmelCase_   :				np.IntTensor						=						None
							UpperCAmelCase_   :				torch.FloatTensor						=						None  # sigma(t_i)



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							torch.FloatTensor:
							return sample



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							str:
							UpperCAmelCase_   :				Tuple						=						num_inference_steps
							UpperCAmelCase_   :				Optional[int]						=						np.arange(0    ,		self.num_inference_steps       )[::-1].copy()
							UpperCAmelCase_   :				Union[str, Any]						=						torch.from_numpy(_UpperCamelCase       ).to(_UpperCamelCase       )
							UpperCAmelCase_   :				str						=						[
							    (
							        self.config.sigma_max**2
							        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
							    )
							    for i in self.timesteps
							]
							UpperCAmelCase_   :				Optional[Any]						=						torch.tensor(_UpperCamelCase    ,		dtype=torch.floataa    ,		device=_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							Tuple[torch.FloatTensor, float]:
							if self.config.s_min <= sigma <= self.config.s_max:
												UpperCAmelCase_   :				str						=						min(self.config.s_churn / self.num_inference_steps    ,		2**0.5 - 1       )
							else:
												UpperCAmelCase_   :				Any						=						0

							# sample eps ~ N(0, S_noise^2 * I)
							UpperCAmelCase_   :				int						=						self.config.s_noise * randn_tensor(sample.shape    ,		generator=_UpperCamelCase       ).to(sample.device       )
							UpperCAmelCase_   :				Optional[Any]						=						sigma + gamma * sigma
							UpperCAmelCase_   :				List[Any]						=						sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

							return sample_hat, sigma_hat



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = True    ,		)     ->							Union[KarrasVeOutput, Tuple]:
							UpperCAmelCase_   :				int						=						sample_hat + sigma_hat * model_output
							UpperCAmelCase_   :				Dict						=						(sample_hat - pred_original_sample) / sigma_hat
							UpperCAmelCase_   :				List[Any]						=						sample_hat + (sigma_prev - sigma_hat) * derivative

							if not return_dict:
												return (sample_prev, derivative)

							return KarrasVeOutput(
							    prev_sample=_UpperCamelCase    ,		derivative=_UpperCamelCase    ,		pred_original_sample=_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = True    ,		)     ->							Union[KarrasVeOutput, Tuple]:
							UpperCAmelCase_   :				int						=						sample_prev + sigma_prev * model_output
							UpperCAmelCase_   :				Union[str, Any]						=						(sample_prev - pred_original_sample) / sigma_prev
							UpperCAmelCase_   :				List[Any]						=						sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

							if not return_dict:
												return (sample_prev, derivative)

							return KarrasVeOutput(
							    prev_sample=_UpperCamelCase    ,		derivative=_UpperCamelCase    ,		pred_original_sample=_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase       )     ->							Optional[int]:
							raise NotImplementedError()














from collections import defaultdict
from math import ceil, sqrt




def 					lowercase__				(					__snake_case   :							int = 1_000_000					,	__snake_case   :							int = 10  ):


					'''simple docstring'''


					UpperCAmelCase_   :				defaultdict						=						defaultdict(__snake_case  )

					for outer_width in range(3					,	(t_limit // 4) + 2  ):
										if outer_width * outer_width > t_limit:
															UpperCAmelCase_   :				Union[str, Any]						=						max(
															    ceil(sqrt(outer_width * outer_width - t_limit  )  )					,	1  )
										else:
															UpperCAmelCase_   :				int						=						1

										hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

										for hole_width in range(__snake_case					,	outer_width - 1					,	2  ):
															count[outer_width * outer_width - hole_width * hole_width] += 1

					return sum(1 for n in count.values() if 1 <= n <= 10  )


if __name__ == "__main__":
		print(F'{solution() = }')






