import math





class 			__snake_case  :




					def __init__(       self   ,	__UpperCamelCase		)					->  List[Any]:



									'''simple docstring'''







									snake_case__ :     Optional[int] 							=				len(__UpperCamelCase		)
									snake_case__ :     List[str] 							=				[0] * (
									    4 * self.N
									)  # approximate the overall size of segment tree with array N
									self.build(1   ,	0   ,	self.N - 1		)




					def       __a      (       self   ,	__UpperCamelCase		)					->  Dict:



									'''simple docstring'''







									return idx * 2




					def       __a      (       self   ,	__UpperCamelCase		)					->  Union[str, Any]:



									'''simple docstring'''







									return idx * 2 + 1




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  List[Any]:  # noqa: E741



									'''simple docstring'''







									if l == r:
													snake_case__ :     List[str] 							=				A[l]
									else:
													snake_case__ :     Dict 							=				(l + r) // 2
													self.build(self.left(__UpperCamelCase		)   ,	__UpperCamelCase   ,	__UpperCamelCase		)
													self.build(self.right(__UpperCamelCase		)   ,	mid + 1   ,	__UpperCamelCase		)
													snake_case__ :     Union[str, Any] 							=				max(self.st[self.left(__UpperCamelCase		)]   ,	self.st[self.right(__UpperCamelCase		)]		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  Union[str, Any]:



									'''simple docstring'''







									return self.update_recursive(1   ,	0   ,	self.N - 1   ,	a - 1   ,	b - 1   ,	__UpperCamelCase		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  Dict:  # noqa: E741



									'''simple docstring'''







									if r < a or l > b:
													return True
									if l == r:
													snake_case__ :     Any 							=				val
													return True
									snake_case__ :     Tuple 							=				(l + r) // 2
									self.update_recursive(self.left(__UpperCamelCase		)   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									self.update_recursive(self.right(__UpperCamelCase		)   ,	mid + 1   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									snake_case__ :     Optional[Any] 							=				max(self.st[self.left(__UpperCamelCase		)]   ,	self.st[self.right(__UpperCamelCase		)]		)
									return True




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  Optional[Any]:



									'''simple docstring'''







									return self.query_recursive(1   ,	0   ,	self.N - 1   ,	a - 1   ,	b - 1		)




					def       __a      (       self   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)					->  str:  # noqa: E741



									'''simple docstring'''







									if r < a or l > b:
													return -math.inf
									if l >= a and r <= b:
													return self.st[idx]
									snake_case__ :     Optional[int] 							=				(l + r) // 2
									snake_case__ :     int 							=				self.query_recursive(self.left(__UpperCamelCase		)   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									snake_case__ :     Tuple 							=				self.query_recursive(self.right(__UpperCamelCase		)   ,	mid + 1   ,	__UpperCamelCase   ,	__UpperCamelCase   ,	__UpperCamelCase		)
									return max(__UpperCamelCase   ,	__UpperCamelCase		)




					def       __a      (       self		)					->  Union[str, Any]:



									'''simple docstring'''







									snake_case__ :     Tuple 							=				[]
									for i in range(1   ,	N + 1		):
													show_list += [self.query(__UpperCamelCase   ,	__UpperCamelCase		)]
									print(__UpperCamelCase		)


if __name__ == "__main__":
				lowerCAmelCase__					:       Dict		=       [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
				lowerCAmelCase__					:       Optional[Any]		=       15
				lowerCAmelCase__					:       Dict		=       SegmentTree(A)
				print(segt.query(4, 6))
				print(segt.query(7, 11))
				print(segt.query(7, 12))
				segt.update(1, 3, 1_11)
				print(segt.query(1, 15))
				segt.update(7, 8, 2_35)
				segt.show_data()



import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_multi_gpu,
    require_single_gpu,
    test_sync,
)
from accelerate.utils import patch_environment





class 			__snake_case  (      unittest.TestCase     ):




					def       __a      (       self		)					->  Union[str, Any]:



									'''simple docstring'''







									snake_case__ :     List[Any] 							=				inspect.getfile(accelerate.test_utils		)
									snake_case__ :     Tuple 							=				os.path.sep.join(mod_file.split(os.path.sep		)[:-1] + ['scripts', 'test_sync.py']		)




					@require_cpu
					def       __a      (       self		)					->  int:



									'''simple docstring'''







									debug_launcher(test_sync.main   ,	num_processes=1		)




					@require_cpu
					def       __a      (       self		)					->  Dict:



									'''simple docstring'''







									debug_launcher(test_sync.main		)




					@require_single_gpu
					def       __a      (       self		)					->  int:



									'''simple docstring'''







									test_sync.main()




					@require_multi_gpu
					def       __a      (       self		)					->  str:



									'''simple docstring'''







									print(F"""Found {torch.cuda.device_count()} devices."""		)
									snake_case__ :     Any 							=				['torchrun', F"""--nproc_per_node={torch.cuda.device_count()}""", self.test_file_path]
									with patch_environment(omp_num_threads=1		):
													execute_subprocess_async(__UpperCamelCase   ,	env=os.environ.copy()		)


