'''simple docstring'''





from __future__ import annotations

A           =   [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]



class  lowerCAmelCase__   :



  '''simple docstring'''






  def __init__(self  : Optional[int]	, lowerCAmelCase_  : int    )   ->       None:
        snake_case_						       =							-1
        snake_case_						       =							-1
        snake_case_						       =							[-1] * length
        snake_case_						       =							None
        snake_case_						       =							None


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

def   snake_case_       (							_a     :							list[int]			):
      snake_case_						       =							Node(len(_a			)			)
      snake_case_       ,	snake_case_						       =							min(_a			), max(_a			)
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
            return root
      snake_case_						       =							(root.minn + root.maxx) // 2

      snake_case_						       =							[]
      snake_case_						       =							[]

      for index, num in enumerate(_a			):
            if num <= pivot:
                  left_arr.append(_a			)
            else:
                  right_arr.append(_a			)
            snake_case_						       =							len(_a			)
      snake_case_						       =							build_tree(_a			)
      snake_case_						       =							build_tree(_a			)
      return root
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int			):
      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
      snake_case_						       =							(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 ,					_a ,					node.map_left[index] - 1			)
      else:
            # go to the right subtree and map index to the right subtree
            return rank_till_index(node.right ,					_a ,					index - node.map_left[index]			)
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      if start > end:
            return 0
      snake_case_						       =							rank_till_index(_a ,					_a ,					_a			)
      snake_case_						       =							rank_till_index(_a ,					_a ,					start - 1			)
      return rank_till_end - rank_before_start
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      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]
      snake_case_						       =							node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
            return quantile(
                node.left ,					_a ,					(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   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      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
      snake_case_						       =							range_counting(
          node.left ,					(node.map_left[start - 1] if start else 0) ,					node.map_left[end] - 1 ,					_a ,					_a ,					)
      snake_case_						       =							range_counting(
          node.right ,					start - (node.map_left[start - 1] if start else 0) ,					end - node.map_left[end] ,					_a ,					_a ,					)
      return left + right


if __name__ == "__main__":
     import doctest

     doctest.testmod()



'''simple docstring'''





from __future__ import annotations

import random



class  lowerCAmelCase__   :



  '''simple docstring'''






  _UpperCamelCase						= 6

  def __init__(self  : List[Any]    )   ->       Optional[Any]:
        snake_case_						       =							list(range(1	, Dice.NUM_SIDES + 1    )    )


  def 		_lowerCamelCase	(self  : Optional[int]    )   ->       int:
        return random.choice(self.sides    )

def   snake_case_       (							_a     :							int ,					_a     :							int = 2			):
      snake_case_						       =							[Dice() for i in range(_a			)]
      snake_case_						       =							[0] * (len(_a			) * Dice.NUM_SIDES + 1)
      for _ in range(_a			):
            count_of_sum[sum(dice.roll() for dice in dices			)] += 1
      snake_case_						       =							[round((count * 100) / num_throws ,					2			) for count in count_of_sum]
      return probability[num_dice:]  # remove probability of sums that never appear


if __name__ == "__main__":
     import doctest

     doctest.testmod()

