code: 
  
  
  """simple docstring"""
  from .balanced_parentheses import balanced_parentheses
  from .stack import Stack
  
  def 							_snake_case			(      __snake_case       :			Optional[Any]      ):
  
  
  
  
  			"""simple docstring"""
  
  
  
  
  
  
  
  			return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(UpperCamelCase__	,   -1      )
  
  def 							_snake_case			(      __snake_case       :			int      ):
  
  
  
  
  			"""simple docstring"""
  
  
  
  
  
  
  
  			if not balanced_parentheses(UpperCamelCase__      ):
  						raise ValueError("""Mismatched parentheses"""      )
  			_lowerCamelCase  :				List[Any]      =		Stack()
  			_lowerCamelCase  :				Any      =		[]
  			for char in expression_str:
  						if char.isalpha() or char.isdigit():
  									postfix.append(UpperCamelCase__      )
  						elif char == "(":
  									stack.push(UpperCamelCase__      )
  						elif char == ")":
  									while not stack.is_empty() and stack.peek() != "(":
  												postfix.append(stack.pop()      )
  									stack.pop()
  						else:
  									while not stack.is_empty() and precedence(UpperCamelCase__      ) <= precedence(stack.peek()      ):
  												postfix.append(stack.pop()      )
  									stack.push(UpperCamelCase__      )
  			while not stack.is_empty():
  						postfix.append(stack.pop()      )
  			return " ".join(UpperCamelCase__      )
  
  
  if __name__ == "__main__":
  	from doctest import testmod
  
  	testmod()
  	UpperCAmelCase   =	"""a+b*(c^d-e)^(f+g*h)-i"""
  
  	print("""Infix to Postfix Notation demonstration:\n""")
  	print("""Infix notation: """ + expression)
  	print("""Postfix notation: """ + infix_to_postfix(expression))
  
  
style_context: 
  
  
  """simple docstring"""
  import timeit
  
  
  
  
  class   lowercase__							:
  
  
  
  
  
     def __init__(       self			,      SCREAMING_SNAKE_CASE)     ->     Tuple:
        if isinstance(SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE):  # Initializes a matrix identical to the one provided.
           _lowerCamelCase  :				List[str]      =		arg
           _lowerCamelCase  :				List[str]      =		len(SCREAMING_SNAKE_CASE)
        else:  # Initializes a square matrix of the given size and set values to zero.
           _lowerCamelCase  :				List[Any]      =		arg
           _lowerCamelCase  :				Union[str, Any]      =		[[0 for _ in range(self.n)] for _ in range(self.n)]
  
  
  
  
  
     def __mul__(       self			,      SCREAMING_SNAKE_CASE)     ->     Optional[Any]:
        _lowerCamelCase  :				List[Any]      =		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 							_snake_case			(      __snake_case       :			Union[str, Any]	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				List[Any]      =		Matrix([[1, 0], [0, 1]]      )
     while b > 0:
        if b & 1:
           matrix *= a
        a *= a
        b >>= 1
     return matrix
  
  def 							_snake_case			(      __snake_case       :			List[str]	,   __snake_case       :			str	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if n == 1:
        return fa
     elif n == 2:
        return fa
     _lowerCamelCase  :				Any      =		Matrix([[1, 1], [1, 0]]      )
     _lowerCamelCase  :				List[str]      =		modular_exponentiation(__snake_case	,   n - 2      )
     return fa * matrix.t[0][0] + fa * matrix.t[0][1]
  
  def 							_snake_case			(      __snake_case       :			int	,   __snake_case       :			Optional[int]	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if n == 1:
        return fa
     elif n == 2:
        return fa
  
     _lowerCamelCase  :				Optional[Any]      =		fa
     _lowerCamelCase  :				int      =		fa
     n -= 2
  
     while n > 0:
        _lowerCamelCase      ,						_lowerCamelCase  :				Tuple      =		fn_a + fn_a, fn_a
        n -= 1
  
     return fn_a
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				List[str]      =		"""
  from random import randint
  from __main__ import fibonacci_with_matrix_exponentiation
  """
     _lowerCamelCase  :				int      =		"""fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"""
     _lowerCamelCase  :				Tuple      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
     print("""With matrix exponentiation the average execution time is """	,   exec_time / 100      )
     return exec_time
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				Dict      =		"""
  from random import randint
  from __main__ import simple_fibonacci
  """
     _lowerCamelCase  :				Optional[int]      =		"""simple_fibonacci(randint(1,70000), 1, 1)"""
     _lowerCamelCase  :				List[Any]      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
     print(
         """Without matrix exponentiation the average execution time is """	,   exec_time / 100      )
     return exec_time
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     matrix_exponentiation_time()
     simple_fibonacci_time()
  
  
  if __name__ == "__main__":
   main()
  
  