'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

_lowerCamelCase :				List[Any]														= TypeVar("""T""", bound=bool)




class    lowerCamelCase__  (   Generic[T]     ):



   def __init__(    self					,      lowerCAmelCase__     )				->     None:
        """simple docstring"""





        _UpperCamelCase  :T       =value
        _UpperCamelCase  :SkewNode[T] | None       =None
        _UpperCamelCase  :SkewNode[T] | None       =None



   @property
   def  _UpperCamelCase		(    self     )				->     T:
        """simple docstring"""





        return self._value




   @staticmethod
   def  _UpperCamelCase		(    lowerCAmelCase__					,      lowerCAmelCase__     )				->     SkewNode[T] | None:
        """simple docstring"""





        if not roota:
             return roota

        if not roota:
             return roota

        if roota.value > roota.value:
             _UpperCamelCase       ,      _UpperCamelCase  :Optional[int]       =roota, roota

        _UpperCamelCase  :Any       =roota
        _UpperCamelCase  :List[Any]       =roota.right
        _UpperCamelCase  :Dict       =roota.left
        _UpperCamelCase  :Optional[int]       =SkewNode.merge(lowerCAmelCase__					,      lowerCAmelCase__     )

        return result




class    lowerCamelCase__  (   Generic[T]     ):



   def __init__(    self					,      lowerCAmelCase__ = ()     )				->     None:
        """simple docstring"""





        _UpperCamelCase  :SkewNode[T] | None       =None
        if data:
             for item in data:
                  self.insert(lowerCAmelCase__     )



   def __bool__(    self     )				->     bool:
        """simple docstring"""





        return self._root is not None



   def __iter__(    self     )				->     Iterator[T]:
        """simple docstring"""





        _UpperCamelCase  :list[Any]       =[]
        while self:
             result.append(self.pop()     )

        # Pushing items back to the heap not to clear it.
        for item in result:
             self.insert(lowerCAmelCase__     )

        return iter(lowerCAmelCase__     )



   def  _UpperCamelCase		(    self					,      lowerCAmelCase__     )				->     None:
        """simple docstring"""





        _UpperCamelCase  :Dict       =SkewNode.merge(self._root					,      SkewNode(lowerCAmelCase__     )     )



   def  _UpperCamelCase		(    self     )				->     T | None:
        """simple docstring"""





        _UpperCamelCase  :Optional[int]       =self.top()
        _UpperCamelCase  :str       =(
            SkewNode.merge(self._root.left					,      self._root.right     ) if self._root else None
        )

        return result



   def  _UpperCamelCase		(    self     )				->     T:
        """simple docstring"""





        if not self._root:
             raise IndexError("""Can't get top element for the empty heap."""     )
        return self._root.value




   def  _UpperCamelCase		(    self     )				->     None:
        """simple docstring"""





        _UpperCamelCase  :int       =None


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))