




from __future__ import annotations

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

a_ 		=  TypeVar("T", bound=bool)

class 			_lowerCamelCase    (      Generic[T] ):

      """simple docstring"""

      def __init__(  self       :			Optional[Any]			,							snake_case       :			T					):
          __UpperCamelCase			=    value
          __UpperCamelCase			=    None
          __UpperCamelCase			=    None







      @property
      def    snake_case						(  self       :			Optional[Any]					):
          return self._value







      @staticmethod
      def    snake_case						(  snake_case       :			RandomizedHeapNode[T] | None			,							snake_case       :			RandomizedHeapNode[T] | None					):
          if not roota:
              return roota

          if not roota:
              return roota

          if roota.value > roota.value:
              __UpperCamelCase		,   __UpperCamelCase			=    roota, roota

          if random.choice([True, False]					):
              __UpperCamelCase		,   __UpperCamelCase			=    roota.right, roota.left

          __UpperCamelCase			=    RandomizedHeapNode.merge(roota.left			,							snake_case					)

          return roota







class 			_lowerCamelCase    (      Generic[T] ):

      """simple docstring"""

      def __init__(  self       :			Union[str, Any]			,							snake_case       :			Iterable[T] | None = ()					):
          __UpperCamelCase			=    None

          if data:
              for item in data:
                  self.insert(snake_case					)







      def    snake_case						(  self       :			Any			,							snake_case       :			T					):
          __UpperCamelCase			=    RandomizedHeapNode.merge(self._root			,							RandomizedHeapNode(snake_case					)					)







      def    snake_case						(  self       :			Optional[int]					):
          __UpperCamelCase			=    self.top()

          if self._root is None:
              return None

          __UpperCamelCase			=    RandomizedHeapNode.merge(self._root.left			,							self._root.right					)

          return result







      def    snake_case						(  self       :			Optional[Any]					):
          if not self._root:
              raise IndexError('''Can\'t get top element for the empty heap.'''					)
          return self._root.value







      def    snake_case						(  self       :			Union[str, Any]					):
          __UpperCamelCase			=    None







      def    snake_case						(  self       :			str					):
          __UpperCamelCase			=    []
          while self:
              result.append(self.pop()					)

          return result







      def __bool__(  self       :			List[str]					):
          return self._root is not None


if __name__ == "__main__":
 import doctest

 doctest.testmod()









from math import cos, sin







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE 		=float(lowerCAmelCase_     )
     return [[scaling_factor * int(x == y     ) for x in range(2     )] for y in range(2     )]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     return [[c, -s], [s, c]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[c * c, cs], [cs, s * s]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'    {scaling(5) = }')
print(f'  {rotation(45) = }')
print(f'{projection(45) = }')



print(f'{reflection(45) = }')

