

from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass
@dataclass
class     SCREAMING_SNAKE_CASE__     :





       '''simple docstring'''




       UpperCamelCase__ :     int
       UpperCamelCase__ :     TreeNode | None				    =       None
       UpperCamelCase__ :     TreeNode | None				    =       None





def 			_lowercase    (      ):
      return TreeNode(3   ,       TreeNode(9 )   ,       TreeNode(20   ,       TreeNode(15 )   ,       TreeNode(7 ) ) )





def 			_lowercase    (      __UpperCamelCase     :		TreeNode ):

      def depth_first_search(
          __UpperCamelCase     :		TreeNode | None   ,       __UpperCamelCase     :		int   ,       __UpperCamelCase     :		list[int] ) -> 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 )

      snake_case__					=   []
      if not root:
            return right_view

      depth_first_search(__UpperCamelCase   ,       0   ,       __UpperCamelCase )
      return right_view





def 			_lowercase    (      __UpperCamelCase     :		TreeNode ):

      def depth_first_search(
          __UpperCamelCase     :		TreeNode | None   ,       __UpperCamelCase     :		int   ,       __UpperCamelCase     :		list[int] ) -> 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 )

      snake_case__					=   []
      if not root:
            return left_view

      depth_first_search(__UpperCamelCase   ,       0   ,       __UpperCamelCase )
      return left_view





def 			_lowercase    (      __UpperCamelCase     :		TreeNode ):

      def breadth_first_search(__UpperCamelCase     :		TreeNode   ,       __UpperCamelCase     :		list[int] ) -> None:
            snake_case__					=   [(root, 0)]
            snake_case__					=   defaultdict(__UpperCamelCase )

            while queue:
                  snake_case__					=   queue.pop(0 )
                  snake_case__	,			snake_case__					=   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] )

      snake_case__					=   []
      if not root:
            return top_view

      breadth_first_search(__UpperCamelCase   ,       __UpperCamelCase )
      return top_view





def 			_lowercase    (      __UpperCamelCase     :		TreeNode ):
      from collections import defaultdict

      def breadth_first_search(__UpperCamelCase     :		TreeNode   ,       __UpperCamelCase     :		list[int] ) -> None:
            snake_case__					=   [(root, 0)]
            snake_case__					=   defaultdict(__UpperCamelCase )

            while queue:
                  snake_case__					=   queue.pop(0 )
                  snake_case__	,			snake_case__					=   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] )

      snake_case__					=   []
      if not root:
            return bottom_view

      breadth_first_search(__UpperCamelCase   ,       __UpperCamelCase )
      return bottom_view


if __name__ == "__main__":
       import doctest

       doctest.testmod()









class     SCREAMING_SNAKE_CASE__     :





       '''simple docstring'''




       def __init__(						self       :						Tuple							)			->    None:
             # numbermap keys are the number and its values are lists of indexes sorted
             # in ascending order
             snake_case__					=   {}
             # indexmap keys are an index and it's values are the number at that index
             snake_case__					=   {}

       def UpperCAmelCase_						(						self       :						Optional[int]    ,		lowerCAmelCase__       :						list | str | range    ,		lowerCAmelCase__       :						int							)			->    list[int]:
             if isinstance(lowerCAmelCase__    ,		(range, str)							):
                   snake_case__					=   list(lowerCAmelCase__							)
             elif not isinstance(lowerCAmelCase__    ,		lowerCAmelCase__							):
                   raise TypeError(
                       """binary_search_delete() only accepts either a list, range or str"""							)

             snake_case__					=   0
             snake_case__					=   len(lowerCAmelCase__							) - 1

             while low <= high:
                   snake_case__					=   (low + high) // 2
                   if array[mid] == item:
                         array.pop(lowerCAmelCase__							)
                         return array
                   elif array[mid] < item:
                         snake_case__					=   mid + 1
                   else:
                         snake_case__					=   mid - 1
             raise ValueError(
                 """Either the item is not in the array or the array was unsorted"""							)

       def UpperCAmelCase_						(						self       :						Optional[Any]    ,		lowerCAmelCase__       :						list | str | range    ,		lowerCAmelCase__       :						int							)			->    list[int]:
             if isinstance(lowerCAmelCase__    ,		(range, str)							):
                   snake_case__					=   list(lowerCAmelCase__							)
             elif not isinstance(lowerCAmelCase__    ,		lowerCAmelCase__							):
                   raise TypeError(
                       """binary_search_insert() only accepts either a list, range or str"""							)

             snake_case__					=   0
             snake_case__					=   len(lowerCAmelCase__							) - 1

             while low <= high:
                   snake_case__					=   (low + high) // 2
                   if array[mid] == index:
                         # If the item already exists in the array,
                         # insert it after the existing item
                         array.insert(mid + 1    ,		lowerCAmelCase__							)
                         return array
                   elif array[mid] < index:
                         snake_case__					=   mid + 1
                   else:
                         snake_case__					=   mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
             array.insert(lowerCAmelCase__    ,		lowerCAmelCase__							)
             return array

       def UpperCAmelCase_						(						self       :						str    ,		lowerCAmelCase__       :						int    ,		lowerCAmelCase__       :						int							)			->    None:
             # Remove previous index
             if index in self.indexmap:
                   snake_case__					=   self.indexmap[index]
                   if len(self.numbermap[n]							) == 1:
                         del self.numbermap[n]
                   else:
                         snake_case__					=   self.binary_search_delete(self.numbermap[n]    ,		lowerCAmelCase__							)

        # Set new index
             snake_case__					=   number

             # Number not seen before or empty so insert number value
             if number not in self.numbermap:
                   snake_case__					=   [index]

             # Here we need to perform a binary search insertion in order to insert
             # The item in the correct place
             else:
                   snake_case__					=   self.binary_search_insert(
                       self.numbermap[number]    ,		lowerCAmelCase__							)

       def UpperCAmelCase_						(						self       :						Any    ,		lowerCAmelCase__       :						int							)			->    int:
             return self.numbermap.get(lowerCAmelCase__    ,		[-1]							)[0]


if __name__ == "__main__":
       import doctest

       doctest.testmod()






