


def  _UpperCAmelCase						( __lowerCamelCase							)		->list:


 '''simple docstring'''
 snake_case :			int							=   [True for i in range(n + 1							)]
 snake_case :			List[str]							=   [i - 1 for i in range(n + 1							)]
 snake_case :			Optional[Any]							=   []
 for i in range(2			,  n + 1							):
  if is_prime[i]:
   primes.append(__a							)
  for j in range(0			,  len(__a							)							):
   if i * primes[j] >= n:
    break
   snake_case :			Optional[int]							=   False

   if i % primes[j] == 0:
    snake_case :			Dict							=   totients[i] * primes[j]
    break

   snake_case :			List[Any]							=   totients[i] * (primes[j] - 1)

 return totients


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''

from .balanced_parentheses import balanced_parentheses
from .stack import Stack



def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(__a			,      -1      )



def  _lowerCAmelCase				(				__a      )  ->      str:
     '''simple docstring'''







     if not balanced_parentheses(__a      ):
          raise ValueError("""Mismatched parentheses"""      )
     _UpperCamelCase  :Stack[str]       =Stack()
     _UpperCamelCase  :Optional[int]       =[]
     for char in expression_str:
          if char.isalpha() or char.isdigit():
               postfix.append(__a      )
          elif char == "(":
               stack.push(__a      )
          elif char == ")":
               while not stack.is_empty() and stack.peek() != "(":
                    postfix.append(stack.pop()      )
               stack.pop()
          else:
               while not stack.is_empty() and precedence(__a      ) <= precedence(stack.peek()      ):
                    postfix.append(stack.pop()      )
               stack.push(__a      )
     while not stack.is_empty():
          postfix.append(stack.pop()      )
     return " ".join(__a      )


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

      testmod()
      _lowerCamelCase :				Tuple														= """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))