
'''simple docstring'''







from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       torch.Tensor:
				# The first operation in a checkpoint can't be in-place, but it's
				# nice to have in-place addition during inference. Thus...
				if not inplace:
								__a       :     Dict								=	ma + ma
				else:
								ma += ma

				return ma

def 				_snake_case (		lowercase			,    lowercase						)       ->       torch.Tensor:
				__a       :     Dict								=	-1 * len(lowercase						)
				__a       :     str								=	list(range(len(tensor.shape[:zero_index]						)						)						)
				return tensor.permute(first_inds + [zero_index + i for i in inds]						)

def 				_snake_case (		lowercase			,    lowercase						)       ->       torch.Tensor:
				return t.reshape(t.shape[:-no_dims] + (-1,)						)

def 				_snake_case (		lowercase			,    lowercase			,    lowercase			,    lowercase = 1E-4						)       ->       torch.Tensor:
				__a       :     int								=	mask.expand(*value.shape						)
				return torch.sum(mask * value			,    dim=lowercase						) / (eps + torch.sum(lowercase			,    dim=lowercase						))

def 				_snake_case (		lowercase			,    lowercase = 2.3_1_2_5			,    lowercase = 2_1.6_8_7_5			,    lowercase = 6_4						)       ->       torch.Tensor:
				__a       :     List[Any]								=	torch.linspace(lowercase			,    lowercase			,    no_bins - 1			,    device=pts.device						)
				__a       :     int								=	torch.sqrt(torch.sum((pts.unsqueeze(-2						) - pts.unsqueeze(-3						)) ** 2			,    dim=-1						)						)
				return torch.bucketize(lowercase			,    lowercase						)

def 				_snake_case (		lowercase			,    lowercase						)       ->       dict:
				__a       :     Optional[Any]								=	dicts[0]
				__a       :     List[str]								=	{}
				for k, v in first.items():
								__a       :     Tuple								=	[d[k] for d in dicts]
								if isinstance(lowercase			,    lowercase						):
												__a       :     Union[str, Any]								=	dict_multimap(lowercase			,    lowercase						)
								else:
												__a       :     int								=	fn(lowercase						)

				return new_dict

def 				_snake_case (		lowercase			,    lowercase						)       ->       torch.Tensor:
				__a       :     int								=	v_bins.view(((1,) * len(x.shape						)) + (len(lowercase						),)						)
				__a       :     Optional[Any]								=	x[..., None] - reshaped_bins
				__a       :     List[str]								=	torch.argmin(torch.abs(lowercase						)			,    dim=-1						)
				return nn.functional.one_hot(lowercase			,    num_classes=len(lowercase						)						).float()

def 				_snake_case (		lowercase			,    lowercase			,    lowercase = 0			,    lowercase = 0						)       ->       torch.Tensor:
				__a       :     List[Union[slice, torch.Tensor]]								=	[]
				for i, s in enumerate(data.shape[:no_batch_dims]						):
								__a       :     Tuple								=	torch.arange(lowercase						)
								__a       :     Dict								=	r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape						) - i - 1)))						)
								ranges.append(lowercase						)

				__a       :     List[Union[slice, torch.Tensor]]								=	[slice(lowercase						) for _ in range(len(data.shape						) - no_batch_dims						)]
				__a       :     List[Any]								=	inds
				ranges.extend(lowercase						)
				# Matt note: Editing this to get around the behaviour of using a list as an array index changing
				# in recent Numpy versions
				return data[tuple(lowercase						)]


__SCREAMING_SNAKE_CASE		:  Dict        =      TypeVar('T')

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       Dict[Any, Union[dict, list, tuple, Any]]:
				__a       :     Dict[Any, Union[dict, list, tuple, Any]]								=	{}
				for k, v in dic.items():
								if isinstance(lowercase			,    lowercase						):
												__a       :     Dict								=	dict_map(lowercase			,    lowercase			,    lowercase						)
								else:
												__a       :     int								=	tree_map(lowercase			,    lowercase			,    lowercase						)

				return new_dict

@overload
def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       Any:
				...

@overload
def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       dict:
				...

@overload
def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       list:
				...

@overload
def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       tuple:
				...

def 				_snake_case (		lowercase			,    lowercase			,    lowercase						)       ->       Optional[Any]:
				if isinstance(lowercase			,    lowercase						):
								return dict_map(lowercase			,    lowercase			,    lowercase						)
				elif isinstance(lowercase			,    lowercase						):
								return [tree_map(lowercase			,    lowercase			,    lowercase						) for x in tree]
				elif isinstance(lowercase			,    lowercase						):
								return tuple(tree_map(lowercase			,    lowercase			,    lowercase						) for x in tree						)
				elif isinstance(lowercase			,    lowercase						):
								return fn(lowercase						)
				else:
								print(type(lowercase						)						)
								raise ValueError("""Not supported"""						)
__SCREAMING_SNAKE_CASE		:  Optional[int]        =      partial(tree_map, leaf_type=torch.Tensor)

'''simple docstring'''







def 				_snake_case (		lowercase = 2_0						)       ->       int:

				try:
								__a       :     Optional[Any]								=	int(lowercase						)
				except (TypeError, ValueError):
								raise TypeError("""Parameter n must be int or castable to int."""						)
				if n <= 0:
								raise ValueError("""Parameter n must be greater than or equal to one."""						)
				__a       :     List[Any]								=	0
				while 1:
								i += n * (n - 1)
								__a       :     Union[str, Any]								=	0
								for j in range(2			,    lowercase						):
												if i % j != 0:
																__a       :     Any								=	1
																break
								if nfound == 0:
												if i == 0:
																__a       :     List[str]								=	1
												return i
				return None


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