


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 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    torch.Tensor       ,     lowercase__     :    bool     ):






				'''simple docstring'''






				if not inplace:
								_lowerCAmelCase  						=ma + ma
				else:
								ma += ma

				return ma

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    List[int]     ):






				'''simple docstring'''






				_lowerCAmelCase  						=-1 * len(lowercase__     )
				_lowerCAmelCase  						=list(range(len(tensor.shape[:zero_index]     )     )     )
				return tensor.permute(first_inds + [zero_index + i for i in inds]     )

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    int     ):






				'''simple docstring'''






				return t.reshape(t.shape[:-no_dims] + (-1,)     )

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    torch.Tensor       ,     lowercase__     :    int       ,     lowercase__     :    float = 1e-4     ):






				'''simple docstring'''






				_lowerCAmelCase  						=mask.expand(*value.shape     )
				return torch.sum(mask * value       ,     dim=lowercase__     ) / (eps + torch.sum(lowercase__       ,     dim=lowercase__     ))

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    torch.types.Number = 2.3_1_2_5       ,     lowercase__     :    torch.types.Number = 2_1.6_8_7_5       ,     lowercase__     :    int = 64     ):






				'''simple docstring'''






				_lowerCAmelCase  						=torch.linspace(lowercase__       ,     lowercase__       ,     no_bins - 1       ,     device=pts.device     )
				_lowerCAmelCase  						=torch.sqrt(torch.sum((pts.unsqueeze(-2     ) - pts.unsqueeze(-3     )) ** 2       ,     dim=-1     )     )
				return torch.bucketize(lowercase__       ,     lowercase__     )

def 		snake_case_   (				lowercase__     :    Callable[[list], Any]       ,     lowercase__     :    List[dict]     ):






				'''simple docstring'''






				_lowerCAmelCase  						=dicts[0]
				_lowerCAmelCase  						={}
				for k, v in first.items():
								_lowerCAmelCase  						=[d[k] for d in dicts]
								if isinstance(lowercase__       ,     lowercase__     ):
												_lowerCAmelCase  						=dict_multimap(lowercase__       ,     lowercase__     )
								else:
												_lowerCAmelCase  						=fn(lowercase__     )

				return new_dict

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    torch.Tensor     ):






				'''simple docstring'''






				_lowerCAmelCase  						=v_bins.view(((1,) * len(x.shape     )) + (len(lowercase__     ),)     )
				_lowerCAmelCase  						=x[..., None] - reshaped_bins
				_lowerCAmelCase  						=torch.argmin(torch.abs(lowercase__     )       ,     dim=-1     )
				return nn.functional.one_hot(lowercase__       ,     num_classes=len(lowercase__     )     ).float()

def 		snake_case_   (				lowercase__     :    torch.Tensor       ,     lowercase__     :    torch.Tensor       ,     lowercase__     :    int = 0       ,     lowercase__     :    int = 0     ):






				'''simple docstring'''






				_lowerCAmelCase  						=[]
				for i, s in enumerate(data.shape[:no_batch_dims]     ):
								_lowerCAmelCase  						=torch.arange(lowercase__     )
								_lowerCAmelCase  						=r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape     ) - i - 1)))     )
								ranges.append(lowercase__     )

				_lowerCAmelCase  						=[slice(lowercase__     ) for _ in range(len(data.shape     ) - no_batch_dims     )]
				_lowerCAmelCase  						=inds
				ranges.extend(lowercase__     )
				# 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(lowercase__     )]


__SCREAMING_SNAKE_CASE	:							str           =  TypeVar('''T''')

def 		snake_case_   (				lowercase__     :    Callable[[T], Any]       ,     lowercase__     :    Dict[Any, Union[dict, list, tuple, T]]       ,     lowercase__     :    Type[T]     ):






				'''simple docstring'''






				_lowerCAmelCase  						={}
				for k, v in dic.items():
								if isinstance(lowercase__       ,     lowercase__     ):
												_lowerCAmelCase  						=dict_map(lowercase__       ,     lowercase__       ,     lowercase__     )
								else:
												_lowerCAmelCase  						=tree_map(lowercase__       ,     lowercase__       ,     lowercase__     )

				return new_dict

@overload
def 		snake_case_   (				lowercase__     :    Callable[[T], Any]       ,     lowercase__     :    T       ,     lowercase__     :    Type[T]     ):






				'''simple docstring'''






				...

@overload
def 		snake_case_   (				lowercase__     :    Callable[[T], Any]       ,     lowercase__     :    dict       ,     lowercase__     :    Type[T]     ):






				'''simple docstring'''






				...

@overload
def 		snake_case_   (				lowercase__     :    Callable[[T], Any]       ,     lowercase__     :    list       ,     lowercase__     :    Type[T]     ):






				'''simple docstring'''






				...

@overload
def 		snake_case_   (				lowercase__     :    Callable[[T], Any]       ,     lowercase__     :    tuple       ,     lowercase__     :    Type[T]     ):






				'''simple docstring'''






				...

def 		snake_case_   (				lowercase__     :    Optional[Any]       ,     lowercase__     :    str       ,     lowercase__     :    Optional[int]     ):






				'''simple docstring'''






				if isinstance(lowercase__       ,     lowercase__     ):
								return dict_map(lowercase__       ,     lowercase__       ,     lowercase__     )
				elif isinstance(lowercase__       ,     lowercase__     ):
								return [tree_map(lowercase__       ,     lowercase__       ,     lowercase__     ) for x in tree]
				elif isinstance(lowercase__       ,     lowercase__     ):
								return tuple(tree_map(lowercase__       ,     lowercase__       ,     lowercase__     ) for x in tree     )
				elif isinstance(lowercase__       ,     lowercase__     ):
								return fn(lowercase__     )
				else:
								print(type(lowercase__     )     )
								raise ValueError("""Not supported"""     )





__SCREAMING_SNAKE_CASE	:							Any           =  partial(tree_map, leaf_type=torch.Tensor)





from __future__ import annotations

__SCREAMING_SNAKE_CASE	:							Union[str, Any]           =  [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     :    Dict	,							lowerCamelCase_     :    int					):
								_lowerCAmelCase  						=-1
								_lowerCAmelCase  						=-1
								_lowerCAmelCase  						=[-1] * length
								_lowerCAmelCase  						=None
								_lowerCAmelCase  						=None






				def __repr__(				self     :    Tuple					):
								return F"Node(min_value={self.minn} max_value={self.maxx})"

def 		snake_case_   (				lowercase__     :    list[int]     ):






				'''simple docstring'''






				_lowerCAmelCase  						=Node(len(lowercase__     )     )
				_lowerCAmelCase						,							_lowerCAmelCase  						=min(lowercase__     ), max(lowercase__     )
				# 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(lowercase__     ):
								if num <= pivot:
												left_arr.append(lowercase__     )
								else:
												right_arr.append(lowercase__     )
								_lowerCAmelCase  						=len(lowercase__     )
				_lowerCAmelCase  						=build_tree(lowercase__     )
				_lowerCAmelCase  						=build_tree(lowercase__     )
				return root

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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       ,     lowercase__       ,     node.map_left[index] - 1     )
				else:
								# go to the right subtree and map index to the right subtree
								return rank_till_index(node.right       ,     lowercase__       ,     index - node.map_left[index]     )

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






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

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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       ,     lowercase__       ,     (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_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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       ,     lowercase__       ,     lowercase__       ,     )
				_lowerCAmelCase  						=range_counting(
				    node.right       ,     start - (node.map_left[start - 1] if start else 0)       ,     end - node.map_left[end]       ,     lowercase__       ,     lowercase__       ,     )
				return left + right


if __name__ == "__main__":
		import doctest

		doctest.testmod()

