






import timeit







class 							UpperCAmelCase_     :




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




					def __mul__(							self  ,	_lowerCAmelCase		):
										UpperCAmelCase__			:     Tuple										= 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	(	__lowerCamelCase   ,       __lowerCamelCase					)   -> List[str]:

					'''simple docstring'''
					UpperCAmelCase__			:     Dict										= Matrix([[1, 0], [0, 1]]					)
					while b > 0:
										if b & 1:
															matrix *= a
										a *= a
										b >>= 1
					return matrix





def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> Union[str, Any]:

					'''simple docstring'''





					if n == 1:
										return fa
					elif n == 2:
										return fa
					UpperCAmelCase__			:     Optional[Any]										= Matrix([[1, 1], [1, 0]]					)
					UpperCAmelCase__			:     List[Any]										= modular_exponentiation(__a   ,       n - 2					)
					return fa * matrix.t[0][0] + fa * matrix.t[0][1]





def    _lowerCamelCase	(	__lowerCamelCase   ,       __lowerCamelCase   ,       __lowerCamelCase					)   -> List[Any]:

					'''simple docstring'''





					if n == 1:
										return fa
					elif n == 2:
										return fa

					UpperCAmelCase__			:     Optional[Any]										= fa
					UpperCAmelCase__			:     Any										= fa
					n -= 2

					while n > 0:
										UpperCAmelCase__			:     int										= fn_a + fn_a, fn_a
										n -= 1

					return fn_a





def    _lowerCamelCase	(	)   -> str:

					'''simple docstring'''
					UpperCAmelCase__			:     str										= '''
from random import randint
from __main__ import fibonacci_with_matrix_exponentiation
'''
					UpperCAmelCase__			:     int										= '''fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)'''
					UpperCAmelCase__			:     Tuple										= timeit.timeit(setup=__a   ,       stmt=__a   ,       number=100					)
					print("""With matrix exponentiation the average execution time is """   ,       exec_time / 100					)
					return exec_time





def    _lowerCamelCase	(	)   -> int:

					'''simple docstring'''
					UpperCAmelCase__			:     Any										= '''
from random import randint
from __main__ import simple_fibonacci
'''
					UpperCAmelCase__			:     Tuple										= '''simple_fibonacci(randint(1,70000), 1, 1)'''
					UpperCAmelCase__			:     List[Any]										= timeit.timeit(setup=__a   ,       stmt=__a   ,       number=100					)
					print(
					    """Without matrix exponentiation the average execution time is """   ,       exec_time / 100					)
					return exec_time





def    _lowerCamelCase	(	)   -> List[str]:

					'''simple docstring'''
					matrix_exponentiation_time()
					simple_fibonacci_time()


if __name__ == "__main__":
						main()














from .stack import Stack





def    _lowerCamelCase	(	__lowerCamelCase					)   -> bool:

     '''simple docstring'''
     UpperCAmelCase__			:     Stack[str]										= Stack()
     UpperCAmelCase__			:     str										= {"""(""": """)""", """[""": """]""", """{""": """}"""}
     for bracket in parentheses:
          if bracket in bracket_pairs:
               stack.push(__lowerCamelCase					)
          elif bracket in (")", "]", "}"):
               if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                    return False
     return stack.is_empty()


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

      testmod()

      SCREAMING_SNAKE_CASE__		:       Any   							=							["""((()))""", """((())""", """(()))"""]
      print("""Balanced parentheses demonstration:\n""")
      for example in examples:
            SCREAMING_SNAKE_CASE__		:       List[str]   							=							"""""" if balanced_parentheses(example) else """not """
            print(f'''{example} is {not_str}balanced''')






