code: from __future__ import annotations
  
  from collections import deque
  from enum import Enum
  from math import atana, degrees
  from sys import maxsize
  
  class 				_lowercase						(    UpperCAmelCase__ ):
  
  
  
  
  
  
      '''simple docstring'''
      SCREAMING_SNAKE_CASE:							Optional[Any]        =						1
      SCREAMING_SNAKE_CASE:							Any        =						2
      SCREAMING_SNAKE_CASE:							str        =						3
  
  
  
  
      def __repr__(						self   ):
         return F'''{self.__class__.__name__}.{self.name}'''
  
  
  
  
  
  def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase				):
     lowerCAmelCase_:       str         =  point
     return degrees(atana(y - miny       ,							x - minx				)				)
  def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase				):
     lowerCAmelCase_:       List[str]         =  starting
     lowerCAmelCase_:       str         =  via
     lowerCAmelCase_:       Optional[Any]         =  target
     lowerCAmelCase_:       Optional[Any]         =  degrees(atana(ya - ya       ,							xa - xa				)				)
     via_angle %= 360
     lowerCAmelCase_:       str         =  degrees(atana(ya - ya       ,							xa - xa				)				)
     target_angle %= 360
     # t-
     #  \ \
     #   \ v
     #    \|
     #     s
     # via_angle is always lower than target_angle, if direction is left.
     # If they are same, it means they are on a same line of convex hull.
     if target_angle > via_angle:
        return Direction.left
     elif target_angle == via_angle:
        return Direction.straight
     else:
        return Direction.right
  
  
  
  
  
  
  
  def 		snake_case__  (		lowercase				):
  
     if len(UpperCamelCase__				) <= 2:
        # There is no convex hull
        raise ValueError("graham_scan: argument must contain more than 3 points."				)
     if len(UpperCamelCase__				) == 3:
        return points
     # find the lowest and the most left point
     lowerCAmelCase_:       Union[str, Any]         =  0
     lowerCAmelCase_:       List[Any]         =  maxsize, maxsize
     for i, point in enumerate(UpperCamelCase__				):
        lowerCAmelCase_:       Dict         =  point[0]
        lowerCAmelCase_:       List[Any]         =  point[1]
        if y < miny:
           lowerCAmelCase_:       str         =  y
           lowerCAmelCase_:       Any         =  x
           lowerCAmelCase_:       Optional[Any]         =  i
        if y == miny and x < minx:
           lowerCAmelCase_:       int         =  x
           lowerCAmelCase_:       Optional[Any]         =  i
  
      # remove the lowest and the most left point from points for preparing for sort
     points.pop(UpperCamelCase__				)
  
     lowerCAmelCase_:       str         =  sorted(UpperCamelCase__       ,							key=lambda lowercase				: angle_comparer(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)				)
     # This insert actually costs complexity,
     # and you should instead add (minx, miny) into stack later.
     # I'm using insert just for easy understanding.
     sorted_points.insert(0       ,							(minx, miny)				)
  
     lowerCAmelCase_:       deque[tuple[int, int]]         =  deque()
     stack.append(sorted_points[0]				)
     stack.append(sorted_points[1]				)
     stack.append(sorted_points[2]				)
     # In any ways, the first 3 points line are towards left.
     # Because we sort them the angle from minx, miny.
     lowerCAmelCase_:       List[Any]         =  Direction.left
  
     for i in range(3       ,							len(UpperCamelCase__				)				):
        while True:
           lowerCAmelCase_:       Optional[Any]         =  stack[-2]
           lowerCAmelCase_:       Any         =  stack[-1]
           lowerCAmelCase_:       Optional[Any]         =  sorted_points[i]
           lowerCAmelCase_:       str         =  check_direction(UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__				)
  
           if next_direction == Direction.left:
              lowerCAmelCase_:       Union[str, Any]         =  Direction.left
              break
           if next_direction == Direction.straight:
              if current_direction == Direction.left:
                 # We keep current_direction as left.
                 # Because if the straight line keeps as straight,
                 # we want to know if this straight line is towards left.
                 break
              elif current_direction == Direction.right:
                 # If the straight line is towards right,
                 # every previous points on those straigh line is not convex hull.
                 stack.pop()
           if next_direction == Direction.right:
              stack.pop()
        stack.append(sorted_points[i]				)
     return list(UpperCamelCase__				)
style_context: from .balanced_parentheses import balanced_parentheses
  from .stack import Stack
  def 		snake_case__  (		lowercase				):
     return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(lowercase       ,							-1				)
  def 		snake_case__  (		lowercase				):
     if not balanced_parentheses(lowercase				):
        raise ValueError("Mismatched parentheses"				)
     lowerCAmelCase_:       Stack[str]         =  Stack()
     lowerCAmelCase_:       Union[str, Any]         =  []
     for char in expression_str:
        if char.isalpha() or char.isdigit():
           postfix.append(lowercase				)
        elif char == "(":
           stack.push(lowercase				)
        elif char == ")":
           while not stack.is_empty() and stack.peek() != "(":
              postfix.append(stack.pop()				)
           stack.pop()
        else:
           while not stack.is_empty() and precedence(lowercase				) <= precedence(stack.peek()				):
              postfix.append(stack.pop()				)
           stack.push(lowercase				)
     while not stack.is_empty():
        postfix.append(stack.pop()				)
     return " ".join(lowercase				)
  
  
  if __name__ == "__main__":
   from doctest import testmod
  
   testmod()
   a     :			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))