


'''simple docstring'''



import random






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       Optional[Any]					    =  num - 1
					__a			:       List[str]					    =  0

					while s % 2 == 0:
										__a			:       Any					    =  s // 2
										t += 1

					for _ in range(5   ):
										__a			:       Tuple					    =  random.randrange(2						,      num - 1   )
										__a			:       int					    =  pow(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
										if v != 1:
															__a			:       List[str]					    =  0
															while v != (num - 1):
																				if i == t - 1:
																									return False
																				else:
																									__a			:       Union[str, Any]					    =  i + 1
																									__a			:       Union[str, Any]					    =  (v**2) % num
					return True






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					if num < 2:
										return False

					__a			:       str					    =  [
					    2,
					    3,
					    5,
					    7,
					    11,
					    13,
					    17,
					    19,
					    23,
					    29,
					    31,
					    37,
					    41,
					    43,
					    47,
					    53,
					    59,
					    61,
					    67,
					    71,
					    73,
					    79,
					    83,
					    89,
					    97,
					    101,
					    103,
					    107,
					    109,
					    113,
					    127,
					    131,
					    137,
					    139,
					    149,
					    151,
					    157,
					    163,
					    167,
					    173,
					    179,
					    181,
					    191,
					    193,
					    197,
					    199,
					    211,
					    223,
					    227,
					    229,
					    233,
					    239,
					    241,
					    251,
					    257,
					    263,
					    269,
					    271,
					    277,
					    281,
					    283,
					    293,
					    307,
					    311,
					    313,
					    317,
					    331,
					    337,
					    347,
					    349,
					    353,
					    359,
					    367,
					    373,
					    379,
					    383,
					    389,
					    397,
					    401,
					    409,
					    419,
					    421,
					    431,
					    433,
					    439,
					    443,
					    449,
					    457,
					    461,
					    463,
					    467,
					    479,
					    487,
					    491,
					    499,
					    503,
					    509,
					    521,
					    523,
					    541,
					    547,
					    557,
					    563,
					    569,
					    571,
					    577,
					    587,
					    593,
					    599,
					    601,
					    607,
					    613,
					    617,
					    619,
					    631,
					    641,
					    643,
					    647,
					    653,
					    659,
					    661,
					    673,
					    677,
					    683,
					    691,
					    701,
					    709,
					    719,
					    727,
					    733,
					    739,
					    743,
					    751,
					    757,
					    761,
					    769,
					    773,
					    787,
					    797,
					    809,
					    811,
					    821,
					    823,
					    827,
					    829,
					    839,
					    853,
					    857,
					    859,
					    863,
					    877,
					    881,
					    883,
					    887,
					    907,
					    911,
					    919,
					    929,
					    937,
					    941,
					    947,
					    953,
					    967,
					    971,
					    977,
					    983,
					    991,
					    997,
					]

					if num in low_primes:
										return True

					for prime in low_primes:
										if (num % prime) == 0:
															return False

					return rabin_miller(_SCREAMING_SNAKE_CASE   )






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 1_024   ):
					while True:
										__a			:       Any					    =  random.randrange(2 ** (keysize - 1)						,      2 ** (keysize)   )
										if is_prime_low_num(_SCREAMING_SNAKE_CASE   ):
															return num


if __name__ == "__main__":
	__lowercase	:						List[str]       =	generate_large_prime()
	print(('Prime number:', num))
	print(('is_prime_low_num:', is_prime_low_num(num)))








from PIL import Image






def 				A				(					_lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase   ,    _lowerCAmelCase     :							int    =    image.size
							_lowerCAmelCase     :							Any    =    0
							_lowerCAmelCase     :							Tuple    =    image.load()
							for i in range(_lowerCamelCase  ):
														for j in range(_lowerCamelCase  ):
																					_lowerCAmelCase     :							Union[str, Any]    =    pixels[j, i]
																					mean += pixel
							mean //= width * height

							for j in range(_lowerCamelCase  ):
														for i in range(_lowerCamelCase  ):
																					_lowerCAmelCase     :							Optional[Any]    =    255 if pixels[i, j] > mean else 0
							return image


if __name__ == "__main__":
						_snake_case		=  mean_threshold(Image.open("path_to_image").convert("L"))
						image.save("output_image_path")
