



from __future__ import annotations

import math
import random



def  _lowerCAmelCase     (_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase):
					UpperCamelCase_			= d * e - 1
					UpperCamelCase_			= 0
					UpperCamelCase_			= 0
					while p == 0:
										UpperCamelCase_			= random.randint(2 ,						n - 1)
										UpperCamelCase_			= k
										while True:
															if t % 2 == 0:
																				UpperCamelCase_			= t // 2
																				UpperCamelCase_			= (g**t) % n
																				UpperCamelCase_			= math.gcd(x - 1 ,						_lowerCAmelCase)
																				if x > 1 and y > 1:
																									UpperCamelCase_			= y
																									UpperCamelCase_			= n // y
																									break  # find the correct factors
															else:
																				break  # t is not divisible by 2, break and choose another g
					return sorted([p, q])


if __name__ == "__main__":
	import doctest

	doctest.testmod()




"""simple docstring"""






def    A_ ( _lowerCAmelCase  :       str							):






     """simple docstring"""

     return "".join(chr(ord(_lowerCAmelCase							) + 32							) if '''A''' <= char <= '''Z''' else char for char in word							)


if __name__ == "__main__":
   from doctest import testmod

   testmod()