





'''simple docstring'''






def       lowercase_      (		lowercase__						)   ->int:
						_snake_case:   Optional[Any]  					=		len(lowercase__						)
						_snake_case:   Optional[Any]  					=		len(matrix[0]						)
						_snake_case:   Union[str, Any]  					=		min(lowercase__				,  lowercase__						)

						for row in range(lowercase__						):
												# Check if diagonal element is not zero
												if matrix[row][row] != 0:
																		# Eliminate all the elements below the diagonal
																		for col in range(row + 1				,  lowercase__						):
																								_snake_case:   Dict  					=		matrix[col][row] / matrix[row][row]
																								for i in range(lowercase__				,  lowercase__						):
																														matrix[col][i] -= multiplier * matrix[row][i]
												else:
																		# Find a non-zero diagonal element to swap rows
																		_snake_case:   Optional[Any]  					=		True
																		for i in range(row + 1				,  lowercase__						):
																								if matrix[i][row] != 0:
																														_snake_case					,						_snake_case:   Any  					=		matrix[i], matrix[row]
																														_snake_case:   Optional[int]  					=		False
																														break
																		if reduce:
																								rank -= 1
																								for i in range(lowercase__						):
																														_snake_case:   Optional[int]  					=		matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
																		row -= 1

						return rank


if __name__ == "__main__":
		import doctest

		doctest.testmod()












'''simple docstring'''






def       lowercase_      (		lowercase__ = 1				,  lowercase__ = 1000						)   ->int:
						_snake_case:   int  					=		1
						_snake_case:   Union[str, Any]  					=		0

						for divide_by_number in range(lowercase__				,  digit + 1						):
												_snake_case:   list[int]  					=		[]
												_snake_case:   int  					=		numerator
												for _ in range(1				,  digit + 1						):
																		if now_divide in has_been_divided:
																								if longest_list_length < len(lowercase__						):
																														_snake_case:   Union[str, Any]  					=		len(lowercase__						)
																														_snake_case:   Tuple  					=		divide_by_number
																		else:
																								has_been_divided.append(lowercase__						)
																								_snake_case:   Union[str, Any]  					=		now_divide * 10 % divide_by_number

						return the_digit


# Tests
if __name__ == "__main__":
		import doctest

		doctest.testmod()





