



'''simple docstring'''







from __future__ import annotations

_UpperCamelCase  						=			[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		:  int   ,		__A		:  int					)     ->			None:




								'''simple docstring'''





								lowerCAmelCase__  =   -1
								lowerCAmelCase__  =   -1
								lowerCAmelCase__  =   [-1] * length
								lowerCAmelCase__  =   None
								lowerCAmelCase__  =   None




	def __repr__(  self		:  Optional[Any]					)     ->			str:




								'''simple docstring'''





								return f'''Node(min_value={self.minn} max_value={self.maxx})'''





def 			_lowerCAmelCase(      UpperCAmelCase_      :	list[int]						) ->							Node | None:
							lowerCAmelCase__  =   Node(len(UpperCAmelCase_						)						)
							lowerCAmelCase__  ,lowerCAmelCase__  =   min(UpperCAmelCase_						), max(UpperCAmelCase_						)
							# Leaf node case where the node contains only one unique value
							if root.minn == root.maxx:
														return root
							lowerCAmelCase__  =   (root.minn + root.maxx) // 2

							lowerCAmelCase__  =   []
							lowerCAmelCase__  =   []

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()










'''simple docstring'''







from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	bool						) ->							torch.Tensor:
							# The first operation in a checkpoint can't be in-place, but it's
							# nice to have in-place addition during inference. Thus...
							if not inplace:
														lowerCAmelCase__  =   ma + ma
							else:
														ma += ma

							return ma
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	List[int]						) ->							torch.Tensor:
							lowerCAmelCase__  =   -1 * len(UpperCAmelCase_						)
							lowerCAmelCase__  =   list(range(len(tensor.shape[:zero_index]						)						)						)
							return tensor.permute(first_inds + [zero_index + i for i in inds]						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	int						) ->							torch.Tensor:
							return t.reshape(t.shape[:-no_dims] + (-1,)						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	int					, UpperCAmelCase_      :	float = 1E-4						) ->							torch.Tensor:
							lowerCAmelCase__  =   mask.expand(*value.shape						)
							return torch.sum(mask * value					, dim=UpperCAmelCase_						) / (eps + torch.sum(UpperCAmelCase_					, dim=UpperCAmelCase_						))
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	torch.types.Number = 2.31_25					, UpperCAmelCase_      :	torch.types.Number = 21.68_75					, UpperCAmelCase_      :	int = 64						) ->							torch.Tensor:
							lowerCAmelCase__  =   torch.linspace(UpperCAmelCase_					, UpperCAmelCase_					, no_bins - 1					, device=pts.device						)
							lowerCAmelCase__  =   torch.sqrt(torch.sum((pts.unsqueeze(-2						) - pts.unsqueeze(-3						)) ** 2					, dim=-1						)						)
							return torch.bucketize(UpperCAmelCase_					, UpperCAmelCase_						)
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[list], Any]					, UpperCAmelCase_      :	List[dict]						) ->							dict:
							lowerCAmelCase__  =   dicts[0]
							lowerCAmelCase__  =   {}
							for k, v in first.items():
														lowerCAmelCase__  =   [d[k] for d in dicts]
														if isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
																					lowerCAmelCase__  =   dict_multimap(UpperCAmelCase_					, UpperCAmelCase_						)
														else:
																					lowerCAmelCase__  =   fn(UpperCAmelCase_						)

							return new_dict
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	torch.Tensor						) ->							torch.Tensor:
							lowerCAmelCase__  =   v_bins.view(((1,) * len(x.shape						)) + (len(UpperCAmelCase_						),)						)
							lowerCAmelCase__  =   x[..., None] - reshaped_bins
							lowerCAmelCase__  =   torch.argmin(torch.abs(UpperCAmelCase_						)					, dim=-1						)
							return nn.functional.one_hot(UpperCAmelCase_					, num_classes=len(UpperCAmelCase_						)						).float()
def 			_lowerCAmelCase(      UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	torch.Tensor					, UpperCAmelCase_      :	int = 0					, UpperCAmelCase_      :	int = 0						) ->							torch.Tensor:
							lowerCAmelCase__  =   []
							for i, s in enumerate(data.shape[:no_batch_dims]						):
														lowerCAmelCase__  =   torch.arange(UpperCAmelCase_						)
														lowerCAmelCase__  =   r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape						) - i - 1)))						)
														ranges.append(UpperCAmelCase_						)

							lowerCAmelCase__  =   [slice(UpperCAmelCase_						) for _ in range(len(data.shape						) - no_batch_dims						)]
							lowerCAmelCase__  =   inds
							ranges.extend(UpperCAmelCase_						)
							# Matt note: Editing this to get around the behaviour of using a list as an array index changing
							# in recent Numpy versions
							return data[tuple(UpperCAmelCase_						)]


_UpperCamelCase  						=			TypeVar("""T""")
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[T], Any]					, UpperCAmelCase_      :	Dict[Any, Union[dict, list, tuple, T]]					, UpperCAmelCase_      :	Type[T]						) ->							Dict[Any, Union[dict, list, tuple, Any]]:
							lowerCAmelCase__  =   {}
							for k, v in dic.items():
														if isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
																					lowerCAmelCase__  =   dict_map(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_						)
														else:
																					lowerCAmelCase__  =   tree_map(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_						)

							return new_dict
@overload
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[T], Any]					, UpperCAmelCase_      :	T					, UpperCAmelCase_      :	Type[T]						) ->							Any:
							...
@overload
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[T], Any]					, UpperCAmelCase_      :	dict					, UpperCAmelCase_      :	Type[T]						) ->							dict:
							...
@overload
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[T], Any]					, UpperCAmelCase_      :	list					, UpperCAmelCase_      :	Type[T]						) ->							list:
							...
@overload
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Callable[[T], Any]					, UpperCAmelCase_      :	tuple					, UpperCAmelCase_      :	Type[T]						) ->							tuple:
							...
def 			_lowerCAmelCase(      UpperCAmelCase_      :	str					, UpperCAmelCase_      :	Dict					, UpperCAmelCase_      :	Union[str, Any]						) ->							List[str]:
							if isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
														return dict_map(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_						)
							elif isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
														return [tree_map(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_						) for x in tree]
							elif isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
														return tuple(tree_map(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_						) for x in tree						)
							elif isinstance(UpperCAmelCase_					, UpperCAmelCase_						):
														return fn(UpperCAmelCase_						)
							else:
														print(type(UpperCAmelCase_						)						)
														raise ValueError("""Not supported"""						)






_UpperCamelCase  						=			partial(tree_map, leaf_type=torch.Tensor)





