"""simple docstring"""






from __future__ import annotations

lowerCAmelCase__    :    Optional[Any]			=      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
class 							snake_case			:




					"""simple docstring"""

					def __init__(							self  :      Dict       ,lowerCamelCase__  :      Dict     ):
									UpperCAmelCase__			 =				-1
									UpperCAmelCase__			 =				-1
									UpperCAmelCase__			 =				[-1] * length
									UpperCAmelCase__			 =				None
									UpperCAmelCase__			 =				None







					def __repr__(							self  :      Union[str, Any]     ):
									return f'''Node(min_value={self.minn} max_value={self.maxx})'''






def     a_		(   lowerCamelCase			):
				UpperCAmelCase__			 =				Node(len(lowerCAmelCase_			)			)
				UpperCAmelCase__			 =				min(lowerCAmelCase_			), max(lowerCAmelCase_			)
				# Leaf node case where the node contains only one unique value
				if root.minn == root.maxx:
								return root
				UpperCAmelCase__			 =				(root.minn + root.maxx) // 2

				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[]

				for index, num in enumerate(lowerCAmelCase_			):
								if num <= pivot:
												left_arr.append(lowerCAmelCase_			)
								else:
												right_arr.append(lowerCAmelCase_			)
								UpperCAmelCase__			 =				len(lowerCAmelCase_			)
				UpperCAmelCase__			 =				build_tree(lowerCAmelCase_			)
				UpperCAmelCase__			 =				build_tree(lowerCAmelCase_			)
				return root



def     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):


				if index < 0 or node is None:
								return 0
				# Leaf node cases
				if node.minn == node.maxx:
								return index + 1 if node.minn == num else 0
				UpperCAmelCase__			 =				(node.minn + node.maxx) // 2
				if num <= pivot:
								# go the left subtree and map index to the left subtree
								return rank_till_index(node.left   ,     lowerCAmelCase_   ,     node.map_left[index] - 1			)
				else:
								# go to the right subtree and map index to the right subtree
								return rank_till_index(node.right   ,     lowerCAmelCase_   ,     index - node.map_left[index]			)



def     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):


				if start > end:
								return 0
				UpperCAmelCase__			 =				rank_till_index(lowerCAmelCase_   ,     lowerCAmelCase_   ,     lowerCAmelCase_			)
				UpperCAmelCase__			 =				rank_till_index(lowerCAmelCase_   ,     lowerCAmelCase_   ,     start - 1			)
				return rank_till_end - rank_before_start



def     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):


				if index > (end - start) or start > end or node is None:
								return -1
				# Leaf node case
				if node.minn == node.maxx:
								return node.minn
				# Number of elements in the left subtree in interval [start, end]
				UpperCAmelCase__			 =				node.map_left[end] - (
				    node.map_left[start - 1] if start else 0
				)
				if num_elements_in_left_tree > index:
								return quantile(
								    node.left   ,     lowerCAmelCase_   ,     (node.map_left[start - 1] if start else 0)   ,     node.map_left[end] - 1   ,     )
				else:
								return quantile(
								    node.right   ,     index - num_elements_in_left_tree   ,     start - (node.map_left[start - 1] if start else 0)   ,     end - node.map_left[end]   ,     )



def     a_		(   lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase   ,     lowerCamelCase			):


				if (
				    start > end
				    or node is None
				    or start_num > end_num
				    or node.minn > end_num
				    or node.maxx < start_num
				):
								return 0
				if start_num <= node.minn and node.maxx <= end_num:
								return end - start + 1
				UpperCAmelCase__			 =				range_counting(
				    node.left   ,     (node.map_left[start - 1] if start else 0)   ,     node.map_left[end] - 1   ,     lowerCAmelCase_   ,     lowerCAmelCase_   ,     )
				UpperCAmelCase__			 =				range_counting(
				    node.right   ,     start - (node.map_left[start - 1] if start else 0)   ,     end - node.map_left[end]   ,     lowerCAmelCase_   ,     lowerCAmelCase_   ,     )
				return left + right


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''






from __future__ import annotations

A_				:					Tuple							=      """Alexander Joslin"""




def        snake_case_   (	lowerCAmelCase_						)->						int:





       '''simple docstring'''


       if number <= 0:
              _UpperCAmelCase    :		Union[str, Any]     	=					F'''n must be greater than 0. Got n = {number}'''
              raise ValueError(lowerCAmelCase_						)

       _UpperCAmelCase    :		List[str]     	=					[number + 1] * (number + 1)

       # starting position
       _UpperCAmelCase    :		Dict     	=					0
       for i in range(1			,  lowerCAmelCase_						):
              _UpperCAmelCase    :		int     	=					min(table[i + 1]			,  table[i] + 1						)
              # check if out of bounds
              if i * 2 <= number:
                     _UpperCAmelCase    :		Dict     	=					min(table[i * 2]			,  table[i] + 1						)
              # check if out of bounds
              if i * 3 <= number:
                     _UpperCAmelCase    :		Tuple     	=					min(table[i * 3]			,  table[i] + 1						)
       return table[number]


if __name__ == "__main__":
   import doctest

   doctest.testmod()



