






"""simple docstring"""
from __future__ import annotations

from typing import Any







class     UpperCamelCase_ :





	def __init__(   self      :				Optional[Any]			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				int			,			lowerCAmelCase_      :				float = 0		)		->    None:
				UpperCAmelCase_  :				Any      =      row, column
				UpperCAmelCase_  :				int      =      [[default_value for c in range(lowerCAmelCase_		)] for r in range(lowerCAmelCase_		)]





	def __str__(   self      :				List[str]		)		->    str:
				UpperCAmelCase_  :				List[Any]      =      f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

				# Make string identifier
				UpperCAmelCase_  :				Optional[Any]      =      0
				for row_vector in self.array:
							for obj in row_vector:
										UpperCAmelCase_  :				Any      =      max(lowerCAmelCase_			,			len(str(lowerCAmelCase_		)		)		)
				UpperCAmelCase_  :				str      =      f"""%{max_element_length}s"""

				# Make string and return
				def single_line(lowerCAmelCase_      :				list[float]		) -> str:
							nonlocal string_format_identifier
							UpperCAmelCase_  :				List[str]      =      "["
							line += ", ".join(string_format_identifier % (obj,) for obj in row_vector		)
							line += "]"
							return line

				s += "\n".join(single_line(lowerCAmelCase_		) for row_vector in self.array		)
				return s





	def __repr__(   self      :				Dict		)		->    str:
				return str(self		)





	def   _SCREAMING_SNAKE_CASE   (   self      :				int			,			lowerCAmelCase_      :				tuple[int, int]		)		->    bool:
				if not (isinstance(lowerCAmelCase_			,			(list, tuple)		) and len(lowerCAmelCase_		) == 2):
							return False
				elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
							return False
				else:
							return True





	def __getitem__(   self      :				Tuple			,			lowerCAmelCase_      :				tuple[int, int]		)		->    Any:
				assert self.validate_indicies(lowerCAmelCase_		)
				return self.array[loc[0]][loc[1]]





	def __setitem__(   self      :				Union[str, Any]			,			lowerCAmelCase_      :				tuple[int, int]			,			lowerCAmelCase_      :				float		)		->    None:
				assert self.validate_indicies(lowerCAmelCase_		)
				UpperCAmelCase_  :				Optional[int]      =      value





	def __add__(   self      :				Optional[Any]			,			lowerCAmelCase_      :				Matrix		)		->    Matrix:
				assert isinstance(lowerCAmelCase_			,			lowerCAmelCase_		)
				assert self.row == another.row and self.column == another.column

				# Add
				UpperCAmelCase_  :				Dict      =      Matrix(self.row			,			self.column		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase_  :				Dict      =      self[r, c] + another[r, c]
				return result





	def __neg__(   self      :				int		)		->    Matrix:
				UpperCAmelCase_  :				Optional[Any]      =      Matrix(self.row			,			self.column		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase_  :				Union[str, Any]      =      -self[r, c]
				return result





	def __sub__(   self      :				List[Any]			,			lowerCAmelCase_      :				Matrix		)		->    Matrix:
				return self + (-another)





	def __mul__(   self      :				Optional[Any]			,			lowerCAmelCase_      :				int | float | Matrix		)		->    Matrix:

				if isinstance(lowerCAmelCase_			,			(int, float)		):  # Scalar multiplication
							UpperCAmelCase_  :				int      =      Matrix(self.row			,			self.column		)
							for r in range(self.row		):
										for c in range(self.column		):
													UpperCAmelCase_  :				Tuple      =      self[r, c] * another
							return result
				elif isinstance(lowerCAmelCase_			,			lowerCAmelCase_		):  # Matrix multiplication
							assert self.column == another.row
							UpperCAmelCase_  :				List[str]      =      Matrix(self.row			,			another.column		)
							for r in range(self.row		):
										for c in range(another.column		):
													for i in range(self.column		):
																result[r, c] += self[r, i] * another[i, c]
							return result
				else:
							UpperCAmelCase_  :				Dict      =      f"""Unsupported type given for another ({type(lowerCAmelCase_		)})"""
							raise TypeError(lowerCAmelCase_		)





	def   _SCREAMING_SNAKE_CASE   (   self      :				Any		)		->    Matrix:
				UpperCAmelCase_  :				List[str]      =      Matrix(self.column			,			self.row		)
				for r in range(self.row		):
							for c in range(self.column		):
										UpperCAmelCase_  :				int      =      self[r, c]
				return result





	def   _SCREAMING_SNAKE_CASE   (   self      :				Optional[Any]			,			lowerCAmelCase_      :				Matrix			,			lowerCAmelCase_      :				Matrix		)		->    Any:
				assert isinstance(lowerCAmelCase_			,			lowerCAmelCase_		) and isinstance(lowerCAmelCase_			,			lowerCAmelCase_		)
				assert self.row == self.column == u.row == v.row  # u, v should be column vector
				assert u.column == v.column == 1  # u, v should be column vector

				# Calculate
				UpperCAmelCase_  :				Dict      =      v.transpose()
				UpperCAmelCase_  :				int      =      (v_t * self * u)[0, 0] + 1
				if numerator_factor == 0:
							return None  # It's not invertable
				return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

						def        snake_case   (     ):
									# a^(-1)
									UpperCAmelCase_  :				str      =      Matrix(3			,3			,0		)
									for i in range(3		):
												UpperCAmelCase_  :				Optional[Any]      =      1
									print(F"""a^(-1) is {ainv}"""		)
									# u, v
									UpperCAmelCase_  :				Union[str, Any]      =      Matrix(3			,1			,0		)
									UpperCAmelCase_  :				Any      =      1, 2, -3
									UpperCAmelCase_  :				int      =      Matrix(3			,1			,0		)
									UpperCAmelCase_  :				List[Any]      =      4, -2, 5
									print(F"""u is {u}"""		)
									print(F"""v is {v}"""		)
									print(F"""uv^T is {u * v.transpose()}"""		)
									# Sherman Morrison
									print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(A__			,A__		)}"""		)

						def        snake_case   (     ):
									import doctest

									doctest.testmod()




						testa()











"""simple docstring"""
from __future__ import annotations

import math

def        snake_case   (     A__		):

			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(A__		) + 1		)			,6		):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True


lowerCamelCase_       			=   [num for num in range(3, 10_0001, 2) if not is_prime(num)]

def        snake_case   (     A__		):
			if not isinstance(A__			,A__		):
						raise ValueError("n must be an integer"		)
			if n <= 0:
						raise ValueError("n must be >= 0"		)

			UpperCAmelCase_  :				List[str]      =      []
			for num in range(len(A__		)		):
						UpperCAmelCase_  :				Dict      =      0
						while 2 * i * i <= odd_composites[num]:
									UpperCAmelCase_  :				List[str]      =      odd_composites[num] - 2 * i * i
									if is_prime(A__		):
												break
									i += 1
						else:
									list_nums.append(odd_composites[num]		)
									if len(A__		) == n:
												return list_nums

			return []

def        snake_case   (     ):
			return compute_nums(1		)[0]


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



