code: 
  """simple docstring"""
  from __future__ import annotations
  
  from collections import deque
  from enum import Enum
  from math import atana, degrees
  from sys import maxsize
  
  
  class    _lowerCAmelCase						(						lowerCamelCase						):
  							lowercase_     :     str       =							1
  							lowercase_     :     Any       =							2
  							lowercase_     :     Dict       =							3
  
  
  
  							def __repr__(      self   )							->							Any:
  								return f"{self.__class__.__name__}.{self.name}"
  
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						point
  	return degrees(atana(y - miny				,     x - minx      )      )
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						starting
  	_UpperCAmelCase =						via
  	_UpperCAmelCase =						target
  	_UpperCAmelCase =						degrees(atana(ya - ya				,     xa - xa      )      )
  	via_angle %= 360
  	_UpperCAmelCase =						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     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	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
  	_UpperCAmelCase =						0
  	_UpperCAmelCase =						maxsize, maxsize
  	for i, point in enumerate(UpperCamelCase__      ):
  		_UpperCAmelCase =						point[0]
  		_UpperCAmelCase =						point[1]
  		if y < miny:
  			_UpperCAmelCase =						y
  			_UpperCAmelCase =						x
  			_UpperCAmelCase =						i
  		if y == miny and x < minx:
  			_UpperCAmelCase =						x
  			_UpperCAmelCase =						i
  
      # remove the lowest and the most left point from points for preparing for sort
  	points.pop(UpperCamelCase__      )
  
  	_UpperCAmelCase =						sorted(UpperCamelCase__				,     key=lambda UpperCamelCase__      : 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)      )
  
  	_UpperCAmelCase =						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.
  	_UpperCAmelCase =						Direction.left
  
  	for i in range(3				,     len(UpperCamelCase__      )      ):
  		while True:
  			_UpperCAmelCase =						stack[-2]
  			_UpperCAmelCase =						stack[-1]
  			_UpperCAmelCase =						sorted_points[i]
  			_UpperCAmelCase =						check_direction(UpperCamelCase__				,     UpperCamelCase__				,     UpperCamelCase__      )
  
  			if next_direction == Direction.left:
  				_UpperCAmelCase =						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: 
  """simple docstring"""
  from .stack import Stack
  
  
  
  
  def     __lowerCamelCase  (		UpperCamelCase__      ):
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  	_UpperCAmelCase =						Stack()
  	_UpperCAmelCase =						{"(": ")", "[": "]", "{": "}"}
  	for bracket in parentheses:
  		if bracket in bracket_pairs:
  			stack.push(UpperCamelCase__      )
  		elif bracket in (")", "]", "}"):
  			if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
  				return False
  	return stack.is_empty()
  
  
  if __name__ == "__main__":
  			from doctest import testmod
  
  			testmod()
  
  			__magic_name__		       =				['''((()))''', '''((())''', '''(()))''']
  			print('''Balanced parentheses demonstration:\n''')
  			for example in examples:
  						__magic_name__		       =				'''''' if balanced_parentheses(example) else '''not '''
  						print(f'''{example} is {not_str}balanced''')
  
  
  
  
  