"""simple docstring"""






import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp



def 						a_		(      ):
				UpperCAmelCase__    =							ArgumentParser(
				    description=(
				        'PyTorch TPU distributed training launch '
				        'helper utility that will spawn up '
				        'multiple distributed processes'
				    ) )

				# Optional arguments for the launch helper
				parser.add_argument('--num_cores'      ,    type=lowerCamelCase      ,    default=1      ,    help='Number of TPU cores to use (1 or 8).' )

				# positional
				parser.add_argument(
				    'training_script'      ,    type=lowerCamelCase      ,    help=(
				        'The full path to the single TPU training '
				        'program/script to be launched in parallel, '
				        'followed by all the arguments for the '
				        'training script'
				    )      ,    )

				# rest from the training program
				parser.add_argument('training_script_args'      ,    nargs=lowerCamelCase )

				return parser.parse_args()



def 						a_		(      ):
				UpperCAmelCase__    =							parse_args()

				# Import training_script as a module.
				UpperCAmelCase__    =							Path(args.training_script )
				sys.path.append(str(script_fpath.parent.resolve() ) )
				UpperCAmelCase__    =							script_fpath.stem
				UpperCAmelCase__    =							importlib.import_module(lowerCamelCase )

				# Patch sys.argv
				UpperCAmelCase__    =							[args.training_script] + args.training_script_args + ['--tpu_num_cores', str(args.num_cores )]
				xmp.spawn(mod._mp_fn      ,    args=()      ,    nprocs=args.num_cores )


if __name__ == "__main__":
						main()




"""simple docstring"""






from __future__ import annotations
class        snake_case :




					"""simple docstring"""

					def __init__(       self     :			Dict					,lowerCamelCase__     :			list[list[int]]    ):
									UpperCAmelCase__    =							TypeError(
									    'Matrices must be formed from a list of zero or more lists containing at '
									    'least one and the same number of values, each of which must be of type '
									    'int or float.'    )
									if len(lowerCamelCase__    ) != 0:
													UpperCAmelCase__    =							len(rows[0]    )
													if cols == 0:
																	raise error
													for row in rows:
																	if len(lowerCamelCase__    ) != cols:
																					raise error
																	for value in row:
																					if not isinstance(lowerCamelCase__					,(int, float)    ):
																									raise error
													UpperCAmelCase__    =							rows
									else:
													UpperCAmelCase__    =							[]







					def 	__lowerCAmelCase		(       self     :			Union[str, Any]    ):
									return [[row[i] for row in self.rows] for i in range(len(self.rows[0]    )    )]







					@property
					def 	__lowerCAmelCase		(       self     :			str    ):
									return len(self.rows    )







					@property
					def 	__lowerCAmelCase		(       self     :			List[Any]    ):
									return len(self.rows[0]    )







					@property
					def 	__lowerCAmelCase		(       self     :			Any    ):
									return (self.num_rows, self.num_columns)







					@property
					def 	__lowerCAmelCase		(       self     :			Optional[int]    ):
									return self.order[0] == self.order[1]







					def 	__lowerCAmelCase		(       self     :			Optional[int]    ):
									UpperCAmelCase__    =							[
									    [0 if column_num != row_num else 1 for column_num in range(self.num_rows    )]
									    for row_num in range(self.num_rows    )
									]
									return Matrix(lowerCamelCase__    )







					def 	__lowerCAmelCase		(       self     :			str    ):
									if not self.is_square:
													return 0
									if self.order == (0, 0):
													return 1
									if self.order == (1, 1):
													return int(self.rows[0][0]    )
									if self.order == (2, 2):
													return int(
													    (self.rows[0][0] * self.rows[1][1])
													    - (self.rows[0][1] * self.rows[1][0])    )
									else:
													return sum(
													    self.rows[0][column] * self.cofactors().rows[0][column]
													    for column in range(self.num_columns    )    )







					def 	__lowerCAmelCase		(       self     :			List[str]    ):
									return bool(self.determinant()    )







					def 	__lowerCAmelCase		(       self     :			Any					,lowerCamelCase__     :			int					,lowerCamelCase__     :			int    ):
									UpperCAmelCase__    =							[
									    [
									        self.rows[other_row][other_column]
									        for other_column in range(self.num_columns    )
									        if other_column != column
									    ]
									    for other_row in range(self.num_rows    )
									    if other_row != row
									]
									return Matrix(lowerCamelCase__    ).determinant()







					def 	__lowerCAmelCase		(       self     :			Optional[Any]					,lowerCamelCase__     :			int					,lowerCamelCase__     :			int    ):
									if (row + column) % 2 == 0:
													return self.get_minor(lowerCamelCase__					,lowerCamelCase__    )
									return -1 * self.get_minor(lowerCamelCase__					,lowerCamelCase__    )







					def 	__lowerCAmelCase		(       self     :			Union[str, Any]    ):
									return Matrix(
									    [
									        [self.get_minor(lowerCamelCase__					,lowerCamelCase__    ) for column in range(self.num_columns    )]
									        for row in range(self.num_rows    )
									    ]    )







					def 	__lowerCAmelCase		(       self     :			int    ):
									return Matrix(
									    [
									        [
									            self.minors().rows[row][column]
									            if (row + column) % 2 == 0
									            else self.minors().rows[row][column] * -1
									            for column in range(self.minors().num_columns    )
									        ]
									        for row in range(self.minors().num_rows    )
									    ]    )







					def 	__lowerCAmelCase		(       self     :			Optional[Any]    ):
									UpperCAmelCase__    =							[
									    [self.cofactors().rows[column][row] for column in range(self.num_columns    )]
									    for row in range(self.num_rows    )
									]
									return Matrix(lowerCamelCase__    )







					def 	__lowerCAmelCase		(       self     :			List[Any]    ):
									UpperCAmelCase__    =							self.determinant()
									if not determinant:
													raise TypeError('Only matrices with a non-zero determinant have an inverse'    )
									return self.adjugate() * (1 / determinant)







					def __repr__(       self     :			Optional[Any]    ):
									return str(self.rows    )







					def __str__(       self     :			List[str]    ):
									if self.num_rows == 0:
													return "[]"
									if self.num_rows == 1:
													return "[[" + ". ".join(str(self.rows[0]    )    ) + "]]"
									return (
									    "["
									    + "\n ".join(
									        [
									            '[' + '. '.join([str(lowerCamelCase__    ) for value in row]    ) + '.]'
									            for row in self.rows
									        ]    )
									    + "]"
									)







					def 	__lowerCAmelCase		(       self     :			Tuple					,lowerCamelCase__     :			list[int]					,lowerCamelCase__     :			int | None = None    ):
									UpperCAmelCase__    =							TypeError('Row must be a list containing all ints and/or floats'    )
									if not isinstance(lowerCamelCase__					,lowerCamelCase__    ):
													raise type_error
									for value in row:
													if not isinstance(lowerCamelCase__					,(int, float)    ):
																	raise type_error
									if len(lowerCamelCase__    ) != self.num_columns:
													raise ValueError(
													    'Row must be equal in length to the other rows in the matrix'    )
									if position is None:
													self.rows.append(lowerCamelCase__    )
									else:
													UpperCAmelCase__    =							self.rows[0:position] + [row] + self.rows[position:]







					def 	__lowerCAmelCase		(       self     :			Dict					,lowerCamelCase__     :			list[int]					,lowerCamelCase__     :			int | None = None    ):
									UpperCAmelCase__    =							TypeError(
									    'Column must be a list containing all ints and/or floats'    )
									if not isinstance(lowerCamelCase__					,lowerCamelCase__    ):
													raise type_error
									for value in column:
													if not isinstance(lowerCamelCase__					,(int, float)    ):
																	raise type_error
									if len(lowerCamelCase__    ) != self.num_rows:
													raise ValueError(
													    'Column must be equal in length to the other columns in the matrix'    )
									if position is None:
													UpperCAmelCase__    =							[self.rows[i] + [column[i]] for i in range(self.num_rows    )]
									else:
													UpperCAmelCase__    =							[
													    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
													    for i in range(self.num_rows    )
													]







					def __eq__(       self     :			List[Any]					,lowerCamelCase__     :			object    ):
									if not isinstance(lowerCamelCase__					,lowerCamelCase__    ):
													return NotImplemented
									return self.rows == other.rows







					def __ne__(       self     :			Any					,lowerCamelCase__     :			object    ):
									return not self == other







					def __neg__(       self     :			Dict    ):
									return self * -1







					def __add__(       self     :			str					,lowerCamelCase__     :			Matrix    ):
									if self.order != other.order:
													raise ValueError('Addition requires matrices of the same order'    )
									return Matrix(
									    [
									        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns    )]
									        for i in range(self.num_rows    )
									    ]    )







					def __sub__(       self     :			List[str]					,lowerCamelCase__     :			Matrix    ):
									if self.order != other.order:
													raise ValueError('Subtraction requires matrices of the same order'    )
									return Matrix(
									    [
									        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns    )]
									        for i in range(self.num_rows    )
									    ]    )







					def __mul__(       self     :			List[str]					,lowerCamelCase__     :			Matrix | int | float    ):
									if isinstance(lowerCamelCase__					,(int, float)    ):
													return Matrix(
													    [[int(element * other    ) for element in row] for row in self.rows]    )
									elif isinstance(lowerCamelCase__					,lowerCamelCase__    ):
													if self.num_columns != other.num_rows:
																	raise ValueError(
																	    'The number of columns in the first matrix must '
																	    'be equal to the number of rows in the second'    )
													return Matrix(
													    [
													        [Matrix.dot_product(lowerCamelCase__					,lowerCamelCase__    ) for column in other.columns()]
													        for row in self.rows
													    ]    )
									else:
													raise TypeError(
													    'A Matrix can only be multiplied by an int, float, or another matrix'    )







					def __pow__(       self     :			Optional[int]					,lowerCamelCase__     :			int    ):
									if not isinstance(lowerCamelCase__					,lowerCamelCase__    ):
													raise TypeError('A Matrix can only be raised to the power of an int'    )
									if not self.is_square:
													raise ValueError('Only square matrices can be raised to a power'    )
									if other == 0:
													return self.identity()
									if other < 0:
													if self.is_invertable():
																	return self.inverse() ** (-other)
													raise ValueError(
													    'Only invertable matrices can be raised to a negative power'    )
									UpperCAmelCase__    =							self
									for _ in range(other - 1    ):
													result *= self
									return result







					@classmethod
					def 	__lowerCAmelCase		(       cls     :			Union[str, Any]					,lowerCamelCase__     :			list[int]					,lowerCamelCase__     :			list[int]    ):
									return sum(row[i] * column[i] for i in range(len(lowerCamelCase__    )    )    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



