'''simple docstring'''
from .balanced_parentheses import balanced_parentheses
from .stack import Stack







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	int:
  return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(__UpperCAmelCase ,   -1			)







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	str:
  if not balanced_parentheses(__UpperCAmelCase			):
    raise ValueError('''Mismatched parentheses'''			)
  lowercase				:							Stack[str]									=   Stack()
  lowercase				:							Union[str, 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()
 _A		:      Optional[int]						   ='''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))
'''simple docstring'''
from __future__ import annotations

import math
import random







def 				__UpperCamelCase (					__UpperCAmelCase  :					int ,   __UpperCAmelCase  :					int ,   __UpperCAmelCase  :					int			)							->	list[int]:
  lowercase				:							Union[str, Any]									=   d * e - 1
  lowercase				:							List[str]									=   0
  lowercase				:							Tuple									=   0
  while p == 0:
    lowercase				:							Optional[Any]									=   random.randint(2 ,   n - 1			)
    lowercase				:							Dict									=   k
    while True:
      if t % 2 == 0:
        lowercase				:							List[Any]									=   t // 2
        lowercase				:							Union[str, Any]									=   (g**t) % n
        lowercase				:							Optional[Any]									=   math.gcd(x - 1 ,   __UpperCAmelCase			)
        if x > 1 and y > 1:
          lowercase				:							Dict									=   y
          lowercase				:							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()