code: 
  """simple docstring"""
  import timeit
  
  
  class    _lowerCAmelCase						:
  
  
  
  							def __init__(      self ,						a_   )							->							List[str]:
  								if isinstance(a_ ,						a_   ):  # Initializes a matrix identical to the one provided.
  									_UpperCAmelCase =						arg
  									_UpperCAmelCase =						len(a_   )
  								else:  # Initializes a square matrix of the given size and set values to zero.
  									_UpperCAmelCase =						arg
  									_UpperCAmelCase =						[[0 for _ in range(self.n   )] for _ in range(self.n   )]
  
  
  
  							def __mul__(      self ,						a_   )							->							int:
  								_UpperCAmelCase =						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__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						Matrix([[1, 0], [0, 1]]      )
  	while b > 0:
  		if b & 1:
  			matrix *= a
  		a *= a
  		b >>= 1
  	return matrix
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if n == 1:
  		return fa
  	elif n == 2:
  		return fa
  	_UpperCAmelCase =						Matrix([[1, 1], [1, 0]]      )
  	_UpperCAmelCase =						modular_exponentiation(UpperCamelCase__				,     n - 2      )
  	return fa * matrix.t[0][0] + fa * matrix.t[0][1]
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	if n == 1:
  		return fa
  	elif n == 2:
  		return fa
  
  	_UpperCAmelCase =						fa
  	_UpperCAmelCase =						fa
  	n -= 2
  
  	while n > 0:
  		_UpperCAmelCase ,      _UpperCAmelCase =						fn_a + fn_a, fn_a
  		n -= 1
  
  	return fn_a
  
  
  
  
  def     __lowerCamelCase  (		):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						"\nfrom random import randint\nfrom __main__ import fibonacci_with_matrix_exponentiation\n"
  	_UpperCAmelCase =						"fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"
  	_UpperCAmelCase =						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  (		):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						"\nfrom random import randint\nfrom __main__ import simple_fibonacci\n"
  	_UpperCAmelCase =						"simple_fibonacci(randint(1,70000), 1, 1)"
  	_UpperCAmelCase =						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  (		):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	matrix_exponentiation_time()
  	simple_fibonacci_time()
  
  
  if __name__ == "__main__":
  			main()
  
  
  
  
  
style_context: 
  """simple docstring"""
  from .stack import Stack
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						Stack()
  	_UpperCAmelCase =						{"(": ")", "[": "]", "{": "}"}
  	for bracket in parentheses:
  		if bracket in bracket_pairs:
  			stack.push(UpperCamelCase__      )
  		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()
  
  			__magic_name__		       =				['''((()))''', '''((())''', '''(()))''']
  			print('''Balanced parentheses demonstration:\n''')
  			for example in examples:
  						__magic_name__		       =				'''''' if balanced_parentheses(example) else '''not '''
  						print(f'''{example} is {not_str}balanced''')
  
  
  
  
  