





from __future__ import annotations

from typing import Any



class  __lowerCAmelCase	:






			def __init__(self ,							__magic_name__ ,							__magic_name__ ,							__magic_name__ = 0   )					->       None:


							'''simple docstring'''



							snake_case_      ,							snake_case_						:   Tuple           =  row, column
							snake_case_						:   Optional[int]           =  [[default_value for c in range(__magic_name__   )] for r in range(__magic_name__   )]






			def __str__(self   )					->       str:


							'''simple docstring'''



							snake_case_						:   Optional[Any]           =  F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

							# Make string identifier
							snake_case_						:   Dict           =  0
							for row_vector in self.array:
											for obj in row_vector:
															snake_case_						:   Tuple           =  max(__magic_name__ ,							len(str(__magic_name__   )   )   )
							snake_case_						:   Dict           =  F'''%{max_element_length}s'''

							# Make string and return
							def single_line(__magic_name__   ) -> str:
											nonlocal string_format_identifier
											snake_case_						:   Any           =  '''['''
											line += ", ".join(string_format_identifier % (obj,) for obj in row_vector   )
											line += "]"
											return line

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






			def __repr__(self   )					->       str:


							'''simple docstring'''



							return str(self   )






			def       lowerCamelCase  (self ,							__magic_name__   )					->       bool:


							'''simple docstring'''



							if not (isinstance(__magic_name__ ,							(list, tuple)   ) and len(__magic_name__   ) == 2):
											return False
							elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
											return False
							else:
											return True






			def __getitem__(self ,							__magic_name__   )					->       Any:


							'''simple docstring'''



							assert self.validate_indicies(__magic_name__   )
							return self.array[loc[0]][loc[1]]






			def __setitem__(self ,							__magic_name__ ,							__magic_name__   )					->       None:


							'''simple docstring'''



							assert self.validate_indicies(__magic_name__   )
							snake_case_						:   List[str]           =  value






			def __add__(self ,							__magic_name__   )					->       Matrix:


							'''simple docstring'''



							assert isinstance(__magic_name__ ,							__magic_name__   )
							assert self.row == another.row and self.column == another.column

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






			def __neg__(self   )					->       Matrix:


							'''simple docstring'''



							snake_case_						:   Optional[Any]           =  Matrix(self.row ,							self.column   )
							for r in range(self.row   ):
											for c in range(self.column   ):
															snake_case_						:   int           =  -self[r, c]
							return result






			def __sub__(self ,							__magic_name__   )					->       Matrix:


							'''simple docstring'''



							return self + (-another)






			def __mul__(self ,							__magic_name__   )					->       Matrix:


							'''simple docstring'''



							if isinstance(__magic_name__ ,							(int, float)   ):  # Scalar multiplication
											snake_case_						:   Tuple           =  Matrix(self.row ,							self.column   )
											for r in range(self.row   ):
															for c in range(self.column   ):
																			snake_case_						:   Dict           =  self[r, c] * another
											return result
							elif isinstance(__magic_name__ ,							__magic_name__   ):  # Matrix multiplication
											assert self.column == another.row
											snake_case_						:   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:
											snake_case_						:   str           =  F'''Unsupported type given for another ({type(__magic_name__   )})'''
											raise TypeError(__magic_name__   )






			def       lowerCamelCase  (self   )					->       Matrix:


							'''simple docstring'''



							snake_case_						:   Tuple           =  Matrix(self.column ,							self.row   )
							for r in range(self.row   ):
											for c in range(self.column   ):
															snake_case_						:   Tuple           =  self[r, c]
							return result






			def       lowerCamelCase  (self ,							__magic_name__ ,							__magic_name__   )					->       Any:


							'''simple docstring'''



							assert isinstance(__magic_name__ ,							__magic_name__   ) and isinstance(__magic_name__ ,							__magic_name__   )
							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
							snake_case_						:   str           =  v.transpose()
							snake_case_						:   Dict           =  (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 					lowerCamelCase_						(    )		->						None:






					"""simple docstring"""


					snake_case_						:   Optional[int]           =  Matrix(3			,    3			,    0			)
					for i in range(3			):
									snake_case_						:   Any           =  1
					print(f'''a^(-1) is {ainv}'''			)
					# u, v
					snake_case_						:   List[str]           =  Matrix(3			,    1			,    0			)
					snake_case_      ,							snake_case_      ,							snake_case_						:   Optional[Any]           =  1, 2, -3
					snake_case_						:   Union[str, Any]           =  Matrix(3			,    1			,    0			)
					snake_case_      ,							snake_case_      ,							snake_case_						:   Tuple           =  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(_UpperCamelCase			,    _UpperCamelCase			)}'''			)






	def 					lowerCamelCase_						(    )		->						None:






					"""simple docstring"""


					import doctest

					doctest.testmod()





	testa()







import random

from .binary_exp_mod import bin_exp_mod






def 					lowerCamelCase_						(    _UpperCamelCase			,    _UpperCamelCase=1_000			)		->						str:






				"""simple docstring"""


				if n < 2:
								return False

				if n % 2 == 0:
								return n == 2

				# this means n is odd
				snake_case_						:   int           =  n - 1
				snake_case_						:   Union[str, Any]           =  0
				while d % 2 == 0:
								d /= 2
								exp += 1

				# n - 1=d*(2**exp)
				snake_case_						:   List[Any]           =  0
				while count < prec:
								snake_case_						:   Tuple           =  random.randint(2			,    n - 1			)
								snake_case_						:   List[Any]           =  bin_exp_mod(_UpperCamelCase			,    _UpperCamelCase			,    _UpperCamelCase			)
								if b != 1:
												snake_case_						:   Any           =  True
												for _ in range(_UpperCamelCase			):
																if b == n - 1:
																				snake_case_						:   Tuple           =  False
																				break
																snake_case_						:   List[Any]           =  b * b
																b %= n
												if flag:
																return False
												count += 1
				return True


if __name__ == "__main__":
	lowerCAmelCase_    =    abs(int(input('''Enter bound : ''').strip()))
	print('''Here\'s the list of primes:''')
	print(''', '''.join(str(i) for i in range(n + 1) if is_prime_big(i)))
