

from __future__ import annotations

__snake_case							:     Tuple 						=	[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]



class    A__:
						"""simple docstring"""






						def __init__(  self       ,     _lowercase  )      ->				None:
									a_		:		int				    =				-1
									a_		:		int				    =				-1
									a_		:		list[int]				    =				[-1] * length
									a_		:		Node | None				    =				None
									a_		:		Node | None				    =				None





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


def 			_UpperCAmelCase							(		a__):

			'''simple docstring'''



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

			a_		:		list[int]				    =				[]
			a_		:		list[int]				    =				[]

			for index, num in enumerate(a__):
						if num <= pivot:
									left_arr.append(a__)
						else:
									right_arr.append(a__)
						a_		:		int				    =				len(a__)
			a_		:		Optional[int]				    =				build_tree(a__)
			a_		:		Optional[Any]				    =				build_tree(a__)
			return root


def 			_UpperCAmelCase							(		a__       ,					a__       ,					a__):

			'''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
			a_		:		Union[str, Any]				    =				(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 			_UpperCAmelCase							(		a__       ,					a__       ,					a__       ,					a__):

			'''simple docstring'''



			if start > end:
						return 0
			a_		:		int				    =				rank_till_index(a__       ,					a__       ,					a__)
			a_		:		Union[str, Any]				    =				rank_till_index(a__       ,					a__       ,					start - 1)
			return rank_till_end - rank_before_start


def 			_UpperCAmelCase							(		a__       ,					a__       ,					a__       ,					a__):

			'''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]
			a_		:		Optional[Any]				    =				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 			_UpperCAmelCase							(		a__       ,					a__       ,					a__       ,					a__       ,					a__):

			'''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
			a_		:		Optional[int]				    =				range_counting(
			    node.left       ,					(node.map_left[start - 1] if start else 0)       ,					node.map_left[end] - 1       ,					a__       ,					a__       ,					)
			a_		:		str				    =				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()





import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin


def 			_UpperCAmelCase							(		a__=2       ,					a__=True       ,					a__=False):

			'''simple docstring'''



			a_		:		Optional[Any]				    =				Accelerator(step_scheduler_with_optimizer=a__       ,					split_batches=a__)
			a_		:		Dict				    =				torch.nn.Linear(2       ,					4)
			a_		:		int				    =				torch.optim.AdamW(model.parameters()       ,					lr=1.0)
			a_		:		Optional[int]				    =				torch.optim.lr_scheduler.OneCycleLR(a__       ,					max_lr=0.01       ,					steps_per_epoch=2       ,					epochs=1)
			a_    ,			a_    ,			a_		:		List[Any]				    =				accelerator.prepare(a__       ,					a__       ,					a__)

			# Optimizer has stepped
			scheduler.step()
			if step_scheduler_with_optimizer or (num_processes == 1):
						assert (
						    scheduler.scheduler.last_epoch == num_processes
						), f'''Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'''
			else:
						assert (
						    scheduler.scheduler.last_epoch != num_processes
						), f'''Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'''


def 			_UpperCAmelCase							(		a__=2       ,					a__=True       ,					a__=False):

			'''simple docstring'''



			a_		:		int				    =				Accelerator(step_scheduler_with_optimizer=a__       ,					split_batches=a__)
			a_		:		Tuple				    =				torch.nn.Linear(2       ,					4)
			a_		:		str				    =				torch.optim.AdamW(model.parameters()       ,					lr=1.0)
			a_		:		Optional[int]				    =				torch.optim.lr_scheduler.LambdaLR(a__       ,					lr_lambda=lambda a__: 1 - n / 1_0)
			a_    ,			a_    ,			a_		:		List[str]				    =				accelerator.prepare(a__       ,					a__       ,					a__)

			# Optimizer has stepped
			a_		:		Optional[Any]				    =				False
			scheduler.step()
			a_		:		Union[str, Any]				    =				1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 1_0
			assert (
			    scheduler.get_last_lr()[0] == expected_lr
			), f'''Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''

			# Optimizer has not stepped
			a_		:		Any				    =				True
			scheduler.step()
			if not step_scheduler_with_optimizer:
						a_		:		Any				    =				1 - 2 / 1_0
			assert (
			    scheduler.get_last_lr()[0] == expected_lr
			), f'''Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'''


def 			_UpperCAmelCase							(		a__ = 2):

			'''simple docstring'''



			from transformers import get_linear_schedule_with_warmup

			a_		:		int				    =				[1, 2, 4]
			for num_steps in steps:
						a_		:		List[str]				    =				GradientAccumulationPlugin(num_steps=a__       ,					adjust_scheduler=num_steps > 1)
						a_		:		List[str]				    =				Accelerator(gradient_accumulation_plugin=a__)
						a_		:		int				    =				torch.nn.Linear(2       ,					4)
						a_		:		Any				    =				torch.optim.AdamW(model.parameters()       ,					lr=10.0)
						a_		:		List[Any]				    =				get_linear_schedule_with_warmup(optimizer=a__       ,					num_warmup_steps=0       ,					num_training_steps=2_0)

						a_    ,			a_    ,			a_		:		int				    =				accelerator.prepare(a__       ,					a__       ,					a__)

						for i in range(1_0 * num_steps):
									with accelerator.accumulate(a__):
												optimizer.step()
												scheduler.step()

									if i == (1_0 * num_steps - 2):
												assert (
												    scheduler.get_last_lr()[0] != 0
												), f'''Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'''
						assert (
						    scheduler.get_last_lr()[0] == 0
						), f'''Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'''
						GradientState._reset_state()



@require_cpu
class    A__(unittest.TestCase    ):
						"""simple docstring"""






						def 	UpperCamelCase__			(  self  )      ->				str:
									debug_launcher(partial(_lowercase       ,     num_processes=1  )       ,     num_processes=1  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Dict:
									debug_launcher(partial(_lowercase       ,     num_processes=1  )       ,     num_processes=1  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     step_scheduler_with_optimizer=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Tuple:
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     step_scheduler_with_optimizer=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				List[Any]:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1       ,     split_batches=_lowercase  )       ,     num_processes=1  )





						def 	UpperCamelCase__			(  self  )      ->				Any:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     step_scheduler_with_optimizer=_lowercase  )  )





						def 	UpperCamelCase__			(  self  )      ->				str:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     step_scheduler_with_optimizer=_lowercase  )  )





						@require_huggingface_suite
						def 	UpperCamelCase__			(  self  )      ->				Optional[int]:
									AcceleratorState._reset_state(_lowercase  )
									debug_launcher(partial(_lowercase       ,     num_processes=1  )  )
									debug_launcher(_lowercase  )


