import bisect
import copy
from collections import defaultdict

import numpy as np
from torch.utils.data import BatchSampler, Sampler

from utils import logger

def        SCREAMING_SNAKE_CASE_					(						snake_case__       ,  snake_case__							)					->     Any:
							lowerCAmelCase     		=		copy.deepcopy(snake_case__							)
							lowerCAmelCase     		=		sorted(snake_case__							)
							lowerCAmelCase     		=		[bisect.bisect_right(snake_case__       ,  snake_case__							) for y in x]
							return quantized

def        SCREAMING_SNAKE_CASE_					(						snake_case__       ,  snake_case__=0							)					->     Any:
							lowerCAmelCase     		=		np.arange(start=3       ,  stop=snake_case__       ,  step=4							).tolist() if k > 0 else [1_0]
							lowerCAmelCase     		=		_quantize(snake_case__       ,  snake_case__							)
							# count number of elements per group
							lowerCAmelCase     		=		np.unique(snake_case__       ,  return_counts=snake_case__							)[1]
							lowerCAmelCase     		=		[0] + bins + [np.inf]
							logger.info('''Using {} as bins for aspect lengths quantization'''.format(snake_case__							)							)
							logger.info('''Count of instances per bin: {}'''.format(snake_case__							)							)
							return groups






class        lowercase_  (  UpperCamelCase_						):



	"""simple docstring"""





	def __init__(							self		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->Optional[int]:
								if not isinstance(__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    ):
															raise ValueError(
															    '''sampler should be an instance of torch.utils.data.Sampler, but got sampler={}'''.format(__SCREAMING_SNAKE_CASE    )    )
								lowerCAmelCase     		=		sampler
								lowerCAmelCase     		=		group_ids
								lowerCAmelCase     		=		batch_size


	def __iter__(							self    )						->List[str]:
								lowerCAmelCase     		=		defaultdict(__SCREAMING_SNAKE_CASE    )
								lowerCAmelCase     		=		defaultdict(__SCREAMING_SNAKE_CASE    )

								lowerCAmelCase     		=		0
								for idx in self.sampler:
															lowerCAmelCase     		=		self.group_ids[idx]
															buffer_per_group[group_id].append(__SCREAMING_SNAKE_CASE    )
															samples_per_group[group_id].append(__SCREAMING_SNAKE_CASE    )
															if len(buffer_per_group[group_id]    ) == self.batch_size:
																						yield buffer_per_group[group_id]  # TODO
																						num_batches += 1
																						del buffer_per_group[group_id]
															assert len(buffer_per_group[group_id]    ) < self.batch_size

								# now we have run out of elements that satisfy
								# the group criteria, let's return the remaining
								# elements so that the size of the sampler is
								# deterministic
								lowerCAmelCase     		=		len(self    )
								lowerCAmelCase     		=		expected_num_batches - num_batches
								if num_remaining > 0:
															# for the remaining batches, group the batches by similar lengths
															lowerCAmelCase     		=		[]
															for group_id, idxs in sorted(buffer_per_group.items()		,      key=lambda __SCREAMING_SNAKE_CASE    : x[0]    ):
																						batch_idx.extend(__SCREAMING_SNAKE_CASE    )
																						if len(__SCREAMING_SNAKE_CASE    ) >= self.batch_size:
																													yield batch_idx[: self.batch_size]
																													lowerCAmelCase     		=		batch_idx[self.batch_size :]
																													num_remaining -= 1
															if len(__SCREAMING_SNAKE_CASE    ) > 0:
																						yield batch_idx
																						num_remaining -= 1
								assert num_remaining == 0




	def __len__(							self    )						->str:
								return (len(self.sampler    ) + self.batch_size - 1) // self.batch_size




import random




class        lowercase_  :



	"""simple docstring"""





	def __init__(							self		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->None:
								lowerCAmelCase     		=		x
								lowerCAmelCase     		=		y


	def       SCREAMING_SNAKE_CASE_    (							self    )						->bool:
								return (self.x**2 + self.y**2) <= 1




	@classmethod
	def       SCREAMING_SNAKE_CASE_    (							cls    )						->Tuple:
								return cls(x=random.random()		,      y=random.random()    )

def        SCREAMING_SNAKE_CASE_					(						snake_case__							)					->     float:
							if number_of_simulations < 1:
														raise ValueError('''At least one simulation is necessary to estimate PI.'''							)

							lowerCAmelCase     		=		0
							for _ in range(snake_case__							):
														lowerCAmelCase     		=		Point.random_unit_square()

														if random_point.is_in_unit_circle():
																					number_in_unit_circle += 1

							return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
	# import doctest

	# doctest.testmod()
	from math import pi

	lowercase__      :    int          =     '''Please enter the desired number of Monte Carlo simulations: '''
	lowercase__      :    Dict          =     estimate_pi(int(input(prompt).strip()))
	print(f'An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}')



