

from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

a		=TypeVar("""T""")






class        A_		(       Generic[T]				):
							def __init__(		self		:			List[str]   ,SCREAMING_SNAKE_CASE__		:			T):
								__lowerCamelCase				:				List[Any]					       = data
								__lowerCamelCase				:				Node[T] | None					       = None


							def __str__(		self		:			Any):
								return F"{self.data}"






class        A_		(       Generic[T]				):
							def __init__(		self		:			Optional[Any]):
								__lowerCamelCase				:				Node[T] | None					       = None
							def __iter__(		self		:			int):
								__lowerCamelCase				:				List[str]					       = self.top
								while node:
									yield node.data
									__lowerCamelCase				:				Optional[int]					       = node.next
							def __str__(		self		:			List[Any]):
								return "->".join([str(SCREAMING_SNAKE_CASE__) for item in self])
							def __len__(		self		:			List[str]):
								return len(tuple(iter(self)))
							def     lowerCAmelCase     (		self		:			int):
								return self.top is None
							def     lowerCAmelCase     (		self		:			Optional[int]   ,SCREAMING_SNAKE_CASE__		:			T):
								__lowerCamelCase				:				Dict					       = Node(SCREAMING_SNAKE_CASE__)
								if not self.is_empty():
									__lowerCamelCase				:				int					       = self.top
								__lowerCamelCase				:				Union[str, Any]					       = node
							def     lowerCAmelCase     (		self		:			Tuple):
								if self.is_empty():
									raise IndexError('pop from empty stack')
								assert isinstance(self.top   ,SCREAMING_SNAKE_CASE__)
								__lowerCamelCase				:				List[str]					       = self.top
								__lowerCamelCase				:				List[str]					       = self.top.next
								return pop_node.data
							def     lowerCAmelCase     (		self		:			Union[str, Any]):
								if self.is_empty():
									raise IndexError('peek from empty stack')

								assert self.top is not None
								return self.top.data


							def     lowerCAmelCase     (		self		:			int):
								__lowerCamelCase				:				Optional[int]					       = None


if __name__ == "__main__":
					from doctest import testmod

					testmod()







from __future__ import annotations

import numpy as np





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_				,    snake_case_							=    np.shape(UpperCamelCase__      )
							if rows != columns:
														snake_case_							=    (
														    '\'table\' has to be of square shaped array but got a '
														    F'''{rows}x{columns} array:\n{table}'''
														)
														raise ValueError(UpperCamelCase__      )

							snake_case_							=    np.zeros((rows, columns)      )
							snake_case_							=    np.zeros((rows, columns)      )
							for i in range(UpperCamelCase__      ):
														for j in range(UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					if upper[j][j] == 0:
																												raise ArithmeticError('No LU decomposition exists'      )
																					snake_case_							=    (table[i][j] - total) / upper[j][j]
														snake_case_							=    1
														for j in range(UpperCamelCase__   ,							UpperCamelCase__      ):
																					snake_case_							=    sum(lower[i][k] * upper[k][j] for k in range(UpperCamelCase__      )      )
																					snake_case_							=    table[i][j] - total
							return lower, upper


if __name__ == "__main__":
					import doctest

					doctest.testmod()




