





'''simple docstring'''



from __future__ import annotations

from typing import Any




def       _lowerCAmelCase  ( *lowerCamelCase_	:     list[list[int]] ):
			if all(_check_not_integer(lowerCamelCase_ ) for m in matrix_s ):
						for i in matrix_s[1:]:
									_verify_matrix_sizes(matrix_s[0]						,				lowerCamelCase_ )
						return [[sum(lowerCamelCase_ ) for t in zip(*lowerCamelCase_ )] for m in zip(*lowerCamelCase_ )]
			raise TypeError('''Expected a matrix, got int/list instead''' )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     list[list[int]] ):
			if (
			    _check_not_integer(lowerCamelCase_ )
			    and _check_not_integer(lowerCamelCase_ )
			    and _verify_matrix_sizes(lowerCamelCase_						,				lowerCamelCase_ )
			):
						return [[i - j for i, j in zip(*lowerCamelCase_ )] for m in zip(lowerCamelCase_						,				lowerCamelCase_ )]
			raise TypeError('''Expected a matrix, got int/list instead''' )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     int | float ):
			return [[x * n for x in row] for row in matrix]




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     list[list[int]] ):
			if _check_not_integer(lowerCamelCase_ ) and _check_not_integer(lowerCamelCase_ ):
						__lowercase  ,						__lowercase   =							_verify_matrix_sizes(lowerCamelCase_						,				lowerCamelCase_ )

			if cols[0] != rows[1]:
						__lowercase   =							(
						    '''Cannot multiply matrix of dimensions '''
						    f"({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"
						)
						raise ValueError(lowerCamelCase_ )
			return [
			    [sum(m * n for m, n in zip(lowerCamelCase_						,				lowerCamelCase_ ) ) for j in zip(*lowerCamelCase_ )] for i in matrix_a
			]




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):
			__lowercase   =							int(lowerCamelCase_ )
			return [[int(row == column ) for column in range(lowerCamelCase_ )] for row in range(lowerCamelCase_ )]




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     bool = True ):
			if _check_not_integer(lowerCamelCase_ ):
						if return_map:
									return map(lowerCamelCase_						,				zip(*lowerCamelCase_ ) )
						else:
									return list(map(lowerCamelCase_						,				zip(*lowerCamelCase_ ) ) )
			raise TypeError('''Expected a matrix, got int/list instead''' )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     int						,				lowerCamelCase_	:     int ):
			__lowercase   =							matrix[:row] + matrix[row + 1 :]
			return [row[:column] + row[column + 1 :] for row in minor]




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]] ):
			if len(lowerCamelCase_ ) == 1:
						return matrix[0][0]

			return sum(
			    x * determinant(minor(lowerCamelCase_						,				0						,				lowerCamelCase_ ) ) * (-1) ** i
			    for i, x in enumerate(matrix[0] ) )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]] ):
			__lowercase   =							determinant(lowerCamelCase_ )
			if det == 0:
						return None

			__lowercase   =							[
			    [determinant(minor(lowerCamelCase_						,				lowerCamelCase_						,				lowerCamelCase_ ) ) for j in range(len(lowerCamelCase_ ) )]
			    for i in range(len(lowerCamelCase_ ) )
			]

			__lowercase   =							[
			    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row] )]
			    for row in range(len(lowerCamelCase_ ) )
			]
			__lowercase   =							list(transpose(lowerCamelCase_ ) )
			return scalar_multiply(lowerCamelCase_						,				1 / det )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]] ):
			return not isinstance(lowerCamelCase_						,				lowerCamelCase_ ) and not isinstance(matrix[0]						,				lowerCamelCase_ )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]] ):
			return len(lowerCamelCase_ ), len(matrix[0] )




def       _lowerCAmelCase  ( lowerCamelCase_	:     list[list[int]]						,				lowerCamelCase_	:     list[list[int]] ):
			__lowercase   =							_shape(lowerCamelCase_ ) + _shape(lowerCamelCase_ )
			if shape[0] != shape[3] or shape[1] != shape[2]:
						__lowercase   =							(
						    '''operands could not be broadcast together with shape '''
						    f"({shape[0], shape[1]}), ({shape[2], shape[3]})"
						)
						raise ValueError(lowerCamelCase_ )
			return (shape[0], shape[2]), (shape[1], shape[3])




def       _lowerCAmelCase  ( ):
			__lowercase   =							[[1_2, 1_0], [3, 9]]
			__lowercase   =							[[3, 4], [7, 4]]
			__lowercase   =							[[1_1, 1_2, 1_3, 1_4], [2_1, 2_2, 2_3, 2_4], [3_1, 3_2, 3_3, 3_4], [4_1, 4_2, 4_3, 4_4]]
			__lowercase   =							[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
			print(f"Add Operation, {add(lowerCamelCase_						,				lowerCamelCase_ ) = } \n" )
			print(
			    f"Multiply Operation, {multiply(lowerCamelCase_						,				lowerCamelCase_ ) = } \n"						,				)
			print(f"Identity: {identity(5 )}\n" )
			print(f"Minor of {matrix_c} = {minor(lowerCamelCase_						,				1						,				2 )} \n" )
			print(f"Determinant of {matrix_b} = {determinant(lowerCamelCase_ )} \n" )
			print(f"Inverse of {matrix_d} = {inverse(lowerCamelCase_ )}\n" )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()












'''simple docstring'''



import math




def       _lowerCAmelCase  ( lowerCamelCase_	:     int ):

			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5						,				int(math.sqrt(lowerCamelCase_ ) + 1 )						,				6 ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True




def       _lowerCAmelCase  ( lowerCamelCase_	:     int = 6_0_0_8_5_1_4_7_5_1_4_3 ):

			try:
						__lowercase   =							int(lowerCamelCase_ )
			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.''' )
			__lowercase   =							0
			if is_prime(lowerCamelCase_ ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(lowerCamelCase_ ):
						return n
			for i in range(3						,				int(math.sqrt(lowerCamelCase_ ) ) + 1						,				2 ):
						if n % i == 0:
									if is_prime(n // i ):
												__lowercase   =							n // i
												break
									elif is_prime(lowerCamelCase_ ):
												__lowercase   =							i
			return max_number


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





