

import contextlib
import copy
import random
from typing import Any, Dict, Iterable, Optional, Union

import numpy as np
import torch

from .utils import deprecate, is_transformers_available


if is_transformers_available():
			import transformers

def 			lowerCamelCase__			(       _a):
	random.seed(_a)
	np.random.seed(_a)
	torch.manual_seed(_a)
	torch.cuda.manual_seed_all(_a)
	# ^^ safe to call this function even if cuda is not available






class _UpperCamelCase				:
			'''simple docstring'''







			def __init__(      self				:			List[str]   ,   a				:			Iterable[torch.nn.Parameter]   ,   a				:			float = 0.9999   ,   a				:			float = 0.0   ,   a				:			int = 0   ,   a				:			bool = False   ,   a				:			Union[float, int] = 1.0   ,   a				:			Union[float, int] = 2 / 3   ,   a				:			Optional[Any] = None   ,   a				:			Dict[str, Any] = None   ,   **a				:			Dict   ,   )				->							Tuple:

				"""simple docstring"""

				if isinstance(a   ,   torch.nn.Module						):
					SCREAMING_SNAKE_CASE :   Optional[Any]					  =							(
					    "Passing a `torch.nn.Module` to `ExponentialMovingAverage` is deprecated. "
					    "Please pass the parameters of the module instead."
					)
					deprecate(
					    "passing a `torch.nn.Module` to `ExponentialMovingAverage`"   ,   "1.0.0"   ,   a   ,   standard_warn=a   ,   )
					SCREAMING_SNAKE_CASE :   Optional[Any]					  =							parameters.parameters()

					# set use_ema_warmup to True if a torch.nn.Module is passed for backwards compatibility
					SCREAMING_SNAKE_CASE :   Tuple					  =							True

				if kwargs.get("max_value"   ,   a						) is not None:
					SCREAMING_SNAKE_CASE :   List[Any]					  =							"The `max_value` argument is deprecated. Please use `decay` instead."
					deprecate("max_value"   ,   "1.0.0"   ,   a   ,   standard_warn=a						)
					SCREAMING_SNAKE_CASE :   str					  =							kwargs["max_value"]

				if kwargs.get("min_value"   ,   a						) is not None:
					SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							"The `min_value` argument is deprecated. Please use `min_decay` instead."
					deprecate("min_value"   ,   "1.0.0"   ,   a   ,   standard_warn=a						)
					SCREAMING_SNAKE_CASE :   List[Any]					  =							kwargs["min_value"]

				SCREAMING_SNAKE_CASE :   Optional[int]					  =							list(a						)
				SCREAMING_SNAKE_CASE :   str					  =							[p.clone().detach() for p in parameters]

				if kwargs.get("device"   ,   a						) is not None:
					SCREAMING_SNAKE_CASE :   int					  =							"The `device` argument is deprecated. Please use `to` instead."
					deprecate("device"   ,   "1.0.0"   ,   a   ,   standard_warn=a						)
					self.to(device=kwargs["device"]						)

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							None

				SCREAMING_SNAKE_CASE :   Optional[int]					  =							decay
				SCREAMING_SNAKE_CASE :   Tuple					  =							min_decay
				SCREAMING_SNAKE_CASE :   Tuple					  =							update_after_step
				SCREAMING_SNAKE_CASE :   Tuple					  =							use_ema_warmup
				SCREAMING_SNAKE_CASE :   List[Any]					  =							inv_gamma
				SCREAMING_SNAKE_CASE :   int					  =							power
				SCREAMING_SNAKE_CASE :   Optional[int]					  =							0
				SCREAMING_SNAKE_CASE :   List[Any]					  =							None  # set in `step()`

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							model_cls
				SCREAMING_SNAKE_CASE :   Dict					  =							model_config
			@classmethod
			def 				__UpperCamelCase			(      cls				:			Optional[Any]   ,   a				:			Optional[int]   ,   a				:			Tuple						)				->							"EMAModel":

				"""simple docstring"""

				SCREAMING_SNAKE_CASE  ,SCREAMING_SNAKE_CASE :   Tuple					  =							model_cls.load_config(a   ,   return_unused_kwargs=a						)
				SCREAMING_SNAKE_CASE :   Any					  =							model_cls.from_pretrained(a						)

				SCREAMING_SNAKE_CASE :   Tuple					  =							cls(model.parameters()   ,   model_cls=a   ,   model_config=model.config						)

				ema_model.load_state_dict(a						)
				return ema_model
			def 				__UpperCamelCase			(      self				:			List[str]   ,   a				:			Any						)				->							List[Any]:

				"""simple docstring"""

				if self.model_cls is None:
					raise ValueError("`save_pretrained` can only be used if `model_cls` was defined at __init__."						)

				if self.model_config is None:
					raise ValueError("`save_pretrained` can only be used if `model_config` was defined at __init__."						)

				SCREAMING_SNAKE_CASE :   List[Any]					  =							self.model_cls.from_config(self.model_config						)
				SCREAMING_SNAKE_CASE :   List[str]					  =							self.state_dict()
				state_dict.pop("shadow_params"   ,   a						)

				model.register_to_config(**a						)
				self.copy_to(model.parameters()						)
				model.save_pretrained(a						)
			def 				__UpperCamelCase			(      self				:			List[str]   ,   a				:			int						)				->							float:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   int					  =							max(0   ,   optimization_step - self.update_after_step - 1						)

				if step <= 0:
					return 0.0

				if self.use_ema_warmup:
					SCREAMING_SNAKE_CASE :   Any					  =							1 - (1 + step / self.inv_gamma) ** -self.power
				else:
					SCREAMING_SNAKE_CASE :   List[str]					  =							(1 + step) / (10 + step)

				SCREAMING_SNAKE_CASE :   Optional[Any]					  =							min(a   ,   self.decay						)
				# make sure decay is not smaller than min_decay
				SCREAMING_SNAKE_CASE :   str					  =							max(a   ,   self.min_decay						)
				return cur_decay_value
			@torch.no_grad()
			def 				__UpperCamelCase			(      self				:			Optional[int]   ,   a				:			Iterable[torch.nn.Parameter]						)				->							int:

				"""simple docstring"""

				if isinstance(a   ,   torch.nn.Module						):
					SCREAMING_SNAKE_CASE :   Tuple					  =							(
					    "Passing a `torch.nn.Module` to `ExponentialMovingAverage.step` is deprecated. "
					    "Please pass the parameters of the module instead."
					)
					deprecate(
					    "passing a `torch.nn.Module` to `ExponentialMovingAverage.step`"   ,   "1.0.0"   ,   a   ,   standard_warn=a   ,   )
					SCREAMING_SNAKE_CASE :   List[Any]					  =							parameters.parameters()

				SCREAMING_SNAKE_CASE :   List[str]					  =							list(a						)

				self.optimization_step += 1

				# Compute the decay factor for the exponential moving average.
				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							self.get_decay(self.optimization_step						)
				SCREAMING_SNAKE_CASE :   Any					  =							decay
				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							1 - decay

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							contextlib.nullcontext
				if is_transformers_available() and transformers.deepspeed.is_deepspeed_zeroa_enabled():
					import deepspeed

				for s_param, param in zip(self.shadow_params   ,   a						):
					if is_transformers_available() and transformers.deepspeed.is_deepspeed_zeroa_enabled():
						SCREAMING_SNAKE_CASE :   List[str]					  =							deepspeed.zero.GatheredParameters(a   ,   modifier_rank=a						)

					with context_manager():
						if param.requires_grad:
							s_param.sub_(one_minus_decay * (s_param - param)						)
						else:
							s_param.copy_(a						)
			def 				__UpperCamelCase			(      self				:			Optional[Any]   ,   a				:			Iterable[torch.nn.Parameter]						)				->							None:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Any					  =							list(a						)
				for s_param, param in zip(self.shadow_params   ,   a						):
					param.data.copy_(s_param.to(param.device						).data						)
			def 				__UpperCamelCase			(      self				:			List[str]   ,   a				:			int=None   ,   a				:			Union[str, Any]=None						)				->							None:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   int					  =							[
				    p.to(device=a   ,   dtype=a						) if p.is_floating_point() else p.to(device=a						)
				    for p in self.shadow_params
				]
			def 				__UpperCamelCase			(      self				:			Dict						)				->							dict:

				"""simple docstring"""

				return {
				    "decay": self.decay,
				    "min_decay": self.min_decay,
				    "optimization_step": self.optimization_step,
				    "update_after_step": self.update_after_step,
				    "use_ema_warmup": self.use_ema_warmup,
				    "inv_gamma": self.inv_gamma,
				    "power": self.power,
				    "shadow_params": self.shadow_params,
				}
			def 				__UpperCamelCase			(      self				:			Tuple   ,   a				:			Iterable[torch.nn.Parameter]						)				->							None:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Optional[int]					  =							[param.detach().cpu().clone() for param in parameters]
			def 				__UpperCamelCase			(      self				:			Tuple   ,   a				:			Iterable[torch.nn.Parameter]						)				->							None:

				"""simple docstring"""

				if self.temp_stored_params is None:
					raise RuntimeError("This ExponentialMovingAverage has no `store()`ed weights " "to `restore()`"						)
				for c_param, param in zip(self.temp_stored_params   ,   a						):
					param.data.copy_(c_param.data						)

				# Better memory-wise.
				SCREAMING_SNAKE_CASE :   Tuple					  =							None






			def 				__UpperCamelCase			(      self				:			Optional[int]   ,   a				:			dict						)				->							None:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   int					  =							copy.deepcopy(a						)

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							state_dict.get("decay"   ,   self.decay						)
				if self.decay < 0.0 or self.decay > 1.0:
					raise ValueError("Decay must be between 0 and 1"						)

				SCREAMING_SNAKE_CASE :   Optional[int]					  =							state_dict.get("min_decay"   ,   self.min_decay						)
				if not isinstance(self.min_decay   ,   a						):
					raise ValueError("Invalid min_decay"						)

				SCREAMING_SNAKE_CASE :   List[str]					  =							state_dict.get("optimization_step"   ,   self.optimization_step						)
				if not isinstance(self.optimization_step   ,   a						):
					raise ValueError("Invalid optimization_step"						)

				SCREAMING_SNAKE_CASE :   Dict					  =							state_dict.get("update_after_step"   ,   self.update_after_step						)
				if not isinstance(self.update_after_step   ,   a						):
					raise ValueError("Invalid update_after_step"						)

				SCREAMING_SNAKE_CASE :   List[Any]					  =							state_dict.get("use_ema_warmup"   ,   self.use_ema_warmup						)
				if not isinstance(self.use_ema_warmup   ,   a						):
					raise ValueError("Invalid use_ema_warmup"						)

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							state_dict.get("inv_gamma"   ,   self.inv_gamma						)
				if not isinstance(self.inv_gamma   ,   (float, int)						):
					raise ValueError("Invalid inv_gamma"						)

				SCREAMING_SNAKE_CASE :   List[Any]					  =							state_dict.get("power"   ,   self.power						)
				if not isinstance(self.power   ,   (float, int)						):
					raise ValueError("Invalid power"						)

				SCREAMING_SNAKE_CASE :   Tuple					  =							state_dict.get("shadow_params"   ,   a						)
				if shadow_params is not None:
					SCREAMING_SNAKE_CASE :   List[Any]					  =							shadow_params
					if not isinstance(self.shadow_params   ,   a						):
						raise ValueError("shadow_params must be a list"						)
					if not all(isinstance(a   ,   torch.Tensor						) for p in self.shadow_params						):
						raise ValueError("shadow_params must all be Tensors"						)
'''simple docstring'''


import math
import sys

def   A_      (       SCREAMING_SNAKE_CASE_						)			->int:
  if number != int(SCREAMING_SNAKE_CASE_						):
    raise ValueError("""the value of input must be a natural number"""						)
  if number < 0:
    raise ValueError("""the value of input must not be a negative number"""						)
  if number == 0:
    return 1
  lowercase_     =       [-1] * (number + 1)
  lowercase_     =       0
  for i in range(1 ,	number + 1						):
    lowercase_     =       sys.maxsize
    lowercase_     =       int(math.sqrt(SCREAMING_SNAKE_CASE_						)						)
    for j in range(1 ,	root + 1						):
      lowercase_     =       1 + answers[i - (j**2)]
      lowercase_     =       min(SCREAMING_SNAKE_CASE_ ,	SCREAMING_SNAKE_CASE_						)
    lowercase_     =       answer
  return answers[number]


if __name__ == "__main__":
       import doctest

       doctest.testmod()

