



"""simple docstring"""




from itertools import product


def 	lowercase__  (      _UpperCAmelCase = 15					)  ->      int:






      '''simple docstring'''


      lowercase	:   float											= 0.0
      lowercase	:   float
      lowercase	:   int
      lowercase	:   int
      lowercase	:   int
      lowercase	:   int
      lowercase	:   tuple[int, ...]

      for series in product(range(2					)						,   repeat=_UpperCAmelCase					):
            lowercase	:   Optional[Any]											= series.count(1					)
            lowercase	:   Optional[Any]											= num_turns - num_blue
            if num_red >= num_blue:
                  continue
            lowercase	:   Tuple											= 1.0
            for ind, col in enumerate(_UpperCAmelCase						,   2					):
                  if col == 0:
                        prob *= (ind - 1) / ind
                  else:
                        prob *= 1 / ind

            total_prob += prob

      return int(1 / total_prob					)


if __name__ == "__main__":
     print(f'''{solution() = }''')





"""simple docstring"""




from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass


@dataclass
class 	a__		:
   _lowerCamelCase       				=					42
   _lowerCamelCase       				=					None
   _lowerCamelCase       				=					None




def 	lowercase__  (      )  ->      TreeNode:






      '''simple docstring'''


      return TreeNode(3						,   TreeNode(9					)						,   TreeNode(20						,   TreeNode(15					)						,   TreeNode(7					)					)					)


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def depth_first_search(
          _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            if not root:
                  return

            if depth == len(_UpperCAmelCase					):
                  right_view.append(root.val					)

            depth_first_search(root.right						,   depth + 1						,   _UpperCAmelCase					)
            depth_first_search(root.left						,   depth + 1						,   _UpperCAmelCase					)

      lowercase	:   list											= []
      if not root:
            return right_view

      depth_first_search(_UpperCAmelCase						,   0						,   _UpperCAmelCase					)
      return right_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def depth_first_search(
          _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            if not root:
                  return

            if depth == len(_UpperCAmelCase					):
                  left_view.append(root.val					)

            depth_first_search(root.left						,   depth + 1						,   _UpperCAmelCase					)
            depth_first_search(root.right						,   depth + 1						,   _UpperCAmelCase					)

      lowercase	:   list											= []
      if not root:
            return left_view

      depth_first_search(_UpperCAmelCase						,   0						,   _UpperCAmelCase					)
      return left_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            lowercase	:   List[str]											= [(root, 0)]
            lowercase	:   List[Any]											= defaultdict(_UpperCAmelCase					)

            while queue:
                  lowercase	:   Union[str, Any]											= queue.pop(0					)
                  lowercase						,     lowercase	:   str											= first

                  lookup[hd].append(node.val					)

                  if node.left:
                        queue.append((node.left, hd - 1)					)
                  if node.right:
                        queue.append((node.right, hd + 1)					)

            for pair in sorted(lookup.items()						,   key=lambda _UpperCAmelCase					: each[0]					):
                  top_view.append(pair[1][0]					)

      lowercase	:   list											= []
      if not root:
            return top_view

      breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					)
      return top_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      from collections import defaultdict

      def breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            lowercase	:   Any											= [(root, 0)]
            lowercase	:   Dict											= defaultdict(_UpperCAmelCase					)

            while queue:
                  lowercase	:   str											= queue.pop(0					)
                  lowercase						,     lowercase	:   List[Any]											= first
                  lookup[hd].append(node.val					)

                  if node.left:
                        queue.append((node.left, hd - 1)					)
                  if node.right:
                        queue.append((node.right, hd + 1)					)

            for pair in sorted(lookup.items()						,   key=lambda _UpperCAmelCase					: each[0]					):
                  bottom_view.append(pair[1][-1]					)

      lowercase	:   list											= []
      if not root:
            return bottom_view

      breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					)
      return bottom_view


if __name__ == "__main__":
     import doctest

     doctest.testmod()
