code: 
  '''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 			A							:
  
  
  
  			def __init__(					self       ,     lowerCamelCase__       )			->		None:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       -1
  									lowercase__							 =       -1
  									lowercase__							 =       [-1] * length
  									lowercase__							 =       None
  									lowercase__							 =       None
  
  
  
  			def __repr__(					self       )			->		str:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									return F'''Node(min_value={self.minn} max_value={self.maxx})'''
  
  
  
  
  
  def  _A		(							lowercase__	):
  						lowercase__							 =       Node(len(lowercase__	)	)
  						lowercase__ ,						lowercase__							 =       min(lowercase__	), max(lowercase__	)
  						# 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(lowercase__	):
  												if num <= pivot:
  																		left_arr.append(lowercase__	)
  												else:
  																		right_arr.append(lowercase__	)
  												lowercase__							 =       len(lowercase__	)
  						lowercase__							 =       build_tree(lowercase__	)
  						lowercase__							 =       build_tree(lowercase__	)
  						return root
  
  
  
  
  
  def  _A		(							lowercase__		,		lowercase__		,		lowercase__	):
  						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		,		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  _A		(							lowercase__		,		lowercase__		,		lowercase__		,		lowercase__	):
  						if start > end:
  												return 0
  						lowercase__							 =       rank_till_index(lowercase__		,		lowercase__		,		lowercase__	)
  						lowercase__							 =       rank_till_index(lowercase__		,		lowercase__		,		start - 1	)
  						return rank_till_end - rank_before_start
  
  
  
  
  
  def  _A		(							lowercase__		,		lowercase__		,		lowercase__		,		lowercase__	):
  						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		,		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  _A		(							lowercase__		,		lowercase__		,		lowercase__		,		lowercase__		,		lowercase__	):
  						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		,		lowercase__		,		lowercase__		,		)
  						lowercase__							 =       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()
  
  
  
  
  
  
  
style_context: 
  '''simple docstring'''
  
  
  
  # DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch
  
  from dataclasses import dataclass
  from typing import Optional, Tuple, Union
  
  import flax
  import jax.numpy as jnp
  from jax import random
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left
  
  
  
  
  
  @flax.struct.dataclass
  class 			A							:
  			# setable values
  			lowerCamelCase							:							Optional[jnp.ndarray]       		=  None
  			lowerCamelCase							:							Optional[jnp.ndarray]       		=  None
  			lowerCamelCase							:							Optional[jnp.ndarray]       		=  None
  
  
  
  			@classmethod
  			def A__ (					cls       )			->		Optional[int]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									return cls()
  
  
  
  
  
  @dataclass
  class 			A							(       __UpperCAmelCase				):
  			lowerCamelCase							:							ScoreSdeVeSchedulerState
  			lowerCamelCase							:							jnp.ndarray
  			lowerCamelCase							:							Optional[jnp.ndarray]       		=  None
  
  
  
  
  
  class 			A							(       __UpperCAmelCase		,						__UpperCAmelCase				):
  
  
  
  			@property
  			def A__ (					self       )			->		Tuple:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									return True
  
  
  
  			@register_to_config
  			def __init__(					self       ,     lowerCamelCase__ = 2_000       ,     lowerCamelCase__ = 0.15       ,     lowerCamelCase__ = 0.01       ,     lowerCamelCase__ = 13_48.0       ,     lowerCamelCase__ = 1e-5       ,     lowerCamelCase__ = 1       ,     )			->		str:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									pass
  
  
  
  			def A__ (					self       )			->		List[Any]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       ScoreSdeVeSchedulerState.create()
  									return self.set_sigmas(
  									    lowerCamelCase__       ,     self.config.num_train_timesteps       ,     self.config.sigma_min       ,     self.config.sigma_max       ,     self.config.sampling_eps       ,     )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__ = ()       ,     lowerCamelCase__ = None       )			->		ScoreSdeVeSchedulerState:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       sampling_eps if sampling_eps is not None else self.config.sampling_eps
  
  									lowercase__							 =       jnp.linspace(1       ,     lowerCamelCase__       ,     lowerCamelCase__       )
  									return state.replace(timesteps=lowerCamelCase__       )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__ = None       ,     lowerCamelCase__ = None       ,     lowerCamelCase__ = None       ,     )			->		ScoreSdeVeSchedulerState:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									lowercase__							 =       sigma_min if sigma_min is not None else self.config.sigma_min
  									lowercase__							 =       sigma_max if sigma_max is not None else self.config.sigma_max
  									lowercase__							 =       sampling_eps if sampling_eps is not None else self.config.sampling_eps
  									if state.timesteps is None:
  															lowercase__							 =       self.set_timesteps(lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       )
  
  									lowercase__							 =       jnp.exp(jnp.linspace(jnp.log(lowerCamelCase__       )       ,     jnp.log(lowerCamelCase__       )       ,     lowerCamelCase__       )       )
  									lowercase__							 =       jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]       )
  
  									return state.replace(discrete_sigmas=lowerCamelCase__       ,     sigmas=lowerCamelCase__       )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       )			->		List[str]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									return jnp.where(timesteps == 0       ,     jnp.zeros_like(lowerCamelCase__       )       ,     state.discrete_sigmas[timesteps - 1]       )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__ = True       ,     )			->		Union[FlaxSdeVeOutput, Tuple]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									if state.timesteps is None:
  															raise ValueError(
  															    """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""       )
  
  									lowercase__							 =       timestep * jnp.ones(
  									    sample.shape[0]       ,     )
  									lowercase__							 =       (timestep * (len(state.timesteps       ) - 1)).long()
  
  									lowercase__							 =       state.discrete_sigmas[timesteps]
  									lowercase__							 =       self.get_adjacent_sigma(lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       )
  									lowercase__							 =       jnp.zeros_like(lowerCamelCase__       )
  									lowercase__							 =       (sigma**2 - adjacent_sigma**2) ** 0.5
  
  									# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
  									# also equation 47 shows the analog from SDE models to ancestral sampling methods
  									lowercase__							 =       diffusion.flatten()
  									lowercase__							 =       broadcast_to_shape_from_left(lowerCamelCase__       ,     sample.shape       )
  									lowercase__							 =       drift - diffusion**2 * model_output
  
  									#  equation 6: sample noise for the diffusion term of
  									lowercase__							 =       random.split(lowerCamelCase__       ,     num=1       )
  									lowercase__							 =       random.normal(key=lowerCamelCase__       ,     shape=sample.shape       )
  									lowercase__							 =       sample - drift  # subtract because `dt` is a small negative timestep
  									# TODO is the variable diffusion the correct scaling term for the noise?
  									lowercase__							 =       prev_sample_mean + diffusion * noise  # add impact of diffusion field g
  
  									if not return_dict:
  															return (prev_sample, prev_sample_mean, state)
  
  									return FlaxSdeVeOutput(prev_sample=lowerCamelCase__       ,     prev_sample_mean=lowerCamelCase__       ,     state=lowerCamelCase__       )
  
  
  
  			def A__ (					self       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__       ,     lowerCamelCase__ = True       ,     )			->		Union[FlaxSdeVeOutput, Tuple]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									if state.timesteps is None:
  															raise ValueError(
  															    """`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"""       )
  
  									# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
  									# sample noise for correction
  									lowercase__							 =       random.split(lowerCamelCase__       ,     num=1       )
  									lowercase__							 =       random.normal(key=lowerCamelCase__       ,     shape=sample.shape       )
  
  									# compute step size from the model_output, the noise, and the snr
  									lowercase__							 =       jnp.linalg.norm(lowerCamelCase__       )
  									lowercase__							 =       jnp.linalg.norm(lowerCamelCase__       )
  									lowercase__							 =       (self.config.snr * noise_norm / grad_norm) ** 2 * 2
  									lowercase__							 =       step_size * jnp.ones(sample.shape[0]       )
  
  									# compute corrected sample: model_output term and noise term
  									lowercase__							 =       step_size.flatten()
  									lowercase__							 =       broadcast_to_shape_from_left(lowerCamelCase__       ,     sample.shape       )
  									lowercase__							 =       sample + step_size * model_output
  									lowercase__							 =       prev_sample_mean + ((step_size * 2) ** 0.5) * noise
  
  									if not return_dict:
  															return (prev_sample, state)
  
  									return FlaxSdeVeOutput(prev_sample=lowerCamelCase__       ,     state=lowerCamelCase__       )
  
  
  
  			def __len__(					self       )			->		Union[str, Any]:
  
  
  
  
  									'''simple docstring'''
  
  
  
  									return self.config.num_train_timesteps
  
  
  
  
  
  
  