from __future__ import annotations

import math
import random







def 						UpperCAmelCase							(		lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_							)						->						list[int]:
     a	:     Tuple						      =    d * e - 1
     a	:     Dict						      =    0
     a	:     Any						      =    0
     while p == 0:
          a	:     int						      =    random.randint(2    ,   n - 1							)
          a	:     List[str]						      =    k
          while True:
               if t % 2 == 0:
                    a	:     int						      =    t // 2
                    a	:     Union[str, Any]						      =    (g**t) % n
                    a	:     Tuple						      =    math.gcd(x - 1    ,   UpperCamelCase__							)
                    if x > 1 and y > 1:
                         a	:     Optional[int]						      =    y
                         a	:     Any						      =    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'''






import timeit


class 	_lowercase    :


   def __init__(			self     , _UpperCAmelCase       ):
       if isinstance(_UpperCAmelCase     , _UpperCAmelCase       ):  # Initializes a matrix identical to the one provided.
           A							:							List[Any]				=    arg
           A							:							Dict				=    len(_UpperCAmelCase       )
       else:  # Initializes a square matrix of the given size and set values to zero.
           A							:							str				=    arg
           A							:							Union[str, Any]				=    [[0 for _ in range(self.n       )] for _ in range(self.n       )]


   def __mul__(			self     , _UpperCAmelCase       ):
       A							:							List[str]				=    Matrix(self.n       )
       for i in range(self.n       ):
           for j in range(self.n       ):
               for k in range(self.n       ):
                   matrix.t[i][j] += self.t[i][k] * b.t[k][j]
       return matrix







def 				_lowerCamelCase(	UpperCamelCase__     :			Union[str, Any]     ,							UpperCamelCase__     :			int		)		->	Union[str, Any]:
    A							:							Tuple				=    Matrix([[1, 0], [0, 1]]		)
    while b > 0:
        if b & 1:
            matrix *= a
        a *= a
        b >>= 1
    return matrix
def 				_lowerCamelCase(	UpperCamelCase__     :			int     ,							UpperCamelCase__     :			Tuple     ,							UpperCamelCase__     :			Any		)		->	Any:
    # Trivial Cases
    if n == 1:
        return fa
    elif n == 2:
        return fa
    A							:							Optional[Any]				=    Matrix([[1, 1], [1, 0]]		)
    A							:							int				=    modular_exponentiation(UpperCamelCase__     ,							n - 2		)
    return fa * matrix.t[0][0] + fa * matrix.t[0][1]
def 				_lowerCamelCase(	UpperCamelCase__     :			str     ,							UpperCamelCase__     :			Optional[Any]     ,							UpperCamelCase__     :			Any		)		->	List[Any]:
    # Trivial Cases
    if n == 1:
        return fa
    elif n == 2:
        return fa

    A							:							str				=    fa
    A							:							List[Any]				=    fa
    n -= 2

    while n > 0:
        A,						A							:							List[str]				=    fn_a + fn_a, fn_a
        n -= 1

    return fn_a
def 				_lowerCamelCase(	)		->	Union[str, Any]:
    A							:							Any				=    '''
from random import randint
from __main__ import fibonacci_with_matrix_exponentiation
'''
    A							:							Optional[int]				=    '''fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)'''
    A							:							List[Any]				=    timeit.timeit(setup=UpperCamelCase__     ,							stmt=UpperCamelCase__     ,							number=100		)
    print('''With matrix exponentiation the average execution time is '''     ,							exec_time / 100		)
    return exec_time
def 				_lowerCamelCase(	)		->	List[Any]:
    A							:							str				=    '''
from random import randint
from __main__ import simple_fibonacci
'''
    A							:							Any				=    '''simple_fibonacci(randint(1,70000), 1, 1)'''
    A							:							str				=    timeit.timeit(setup=UpperCamelCase__     ,							stmt=UpperCamelCase__     ,							number=100		)
    print(
        '''Without matrix exponentiation the average execution time is '''     ,							exec_time / 100		)
    return exec_time
def 				_lowerCamelCase(	)		->	Optional[Any]:
    matrix_exponentiation_time()
    simple_fibonacci_time()


if __name__ == "__main__":
     main()
