





from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
  import torch

UpperCAmelCase__            =							logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
  from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):
  def     UpperCAmelCase_ (							cls						)					->      Any:







   """simple docstring"""


   return cls
def     UpperCAmelCase_ (							__snake_case					,						__snake_case = None					,						__snake_case = None					,						__snake_case = None					,						__snake_case = None					,						)					->      Dict:







 """simple docstring"""


 _lowercase											=device
 _lowercase											=shape[0]

 _lowercase											=layout or torch.strided
 _lowercase											=device or torch.device('''cpu'''						)

 if generator is not None:
  _lowercase											=generator.device.type if not isinstance(__snake_case					,						__snake_case						) else generator[0].device.type
  if gen_device_type != device.type and gen_device_type == "cpu":
   _lowercase											='''cpu'''
   if device != "mps":
    logger.info(
        F"The passed generator was created on 'cpu' even though a tensor on {device} was expected."
        F" Tensors will be created on 'cpu' and then moved to {device}. Note that one can probably"
        F" slighly speed up this function by passing a generator that was created on the {device} device."						)
  elif gen_device_type != device.type and gen_device_type == "cuda":
   raise ValueError(F"Cannot generate a {device} tensor from a generator of type {gen_device_type}."						)

 if isinstance(__snake_case					,						__snake_case						):
  _lowercase											=(1,) + shape[1:]
  _lowercase											=[
      torch.randn(__snake_case					,						generator=generator[i]					,						device=__snake_case					,						dtype=__snake_case					,						layout=__snake_case						)
      for i in range(__snake_case						)
  ]
  _lowercase											=torch.cat(__snake_case					,						dim=0						).to(__snake_case						)
 else:
  _lowercase											=torch.randn(__snake_case					,						generator=__snake_case					,						device=__snake_case					,						dtype=__snake_case					,						layout=__snake_case						).to(__snake_case						)

 return latents



def     UpperCAmelCase_ (							__snake_case						)					->      Tuple:







 """simple docstring"""


 if is_torch_version('''<'''					,						'''2.0.0'''						) or not hasattr(__snake_case					,						'''_dynamo'''						):
  return False
 return isinstance(__snake_case					,						torch._dynamo.eval_frame.OptimizedModule						)





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__       :





     def __init__(self		,					UpperCAmelCase	)					->       None:
      _lowercase											=-1
      _lowercase											=-1
      _lowercase											=[-1] * length
      _lowercase											=None
      _lowercase											=None





     def __repr__(self	)					->       str:
      return f"Node(min_value={self.minn} max_value={self.maxx})"



def     UpperCAmelCase_ (							__snake_case						)					->      Node | None:







 """simple docstring"""


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

 _lowercase											=[]
 _lowercase											=[]

 for index, num in enumerate(__snake_case						):
  if num <= pivot:
   left_arr.append(__snake_case						)
  else:
   right_arr.append(__snake_case						)
  _lowercase											=len(__snake_case						)
 _lowercase											=build_tree(__snake_case						)
 _lowercase											=build_tree(__snake_case						)
 return root
def     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case						)					->      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
 _lowercase											=(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					,						__snake_case					,						node.map_left[index] - 1						)
 else:
  # go to the right subtree and map index to the right subtree
  return rank_till_index(node.right					,						__snake_case					,						index - node.map_left[index]						)
def     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__snake_case						)					->      int:







 """simple docstring"""


 if start > end:
  return 0
 _lowercase											=rank_till_index(__snake_case					,						__snake_case					,						__snake_case						)
 _lowercase											=rank_till_index(__snake_case					,						__snake_case					,						start - 1						)
 return rank_till_end - rank_before_start
def     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__snake_case						)					->      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]
 _lowercase											=node.map_left[end] - (
     node.map_left[start - 1] if start else 0
 )
 if num_elements_in_left_tree > index:
  return quantile(
      node.left					,						__snake_case					,						(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     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__snake_case					,						__snake_case						)					->      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
 _lowercase											=range_counting(
     node.left					,						(node.map_left[start - 1] if start else 0)					,						node.map_left[end] - 1					,						__snake_case					,						__snake_case					,						)
 _lowercase											=range_counting(
     node.right					,						start - (node.map_left[start - 1] if start else 0)					,						end - node.map_left[end]					,						__snake_case					,						__snake_case					,						)
 return left + right


if __name__ == "__main__":
  import doctest

  doctest.testmod()

