

import inspect
import os
import unittest

import torch

import accelerate
from accelerate import Accelerator
from accelerate.test_utils import execute_subprocess_async, require_multi_gpu
from accelerate.utils import patch_environment
class        snake_case_		(			unittest.TestCase):







		def 			__lowercase   (		self   )				->   int:
				lowerCamelCase   : int								=inspect.getfile(accelerate.test_utils   )
				lowerCamelCase   : Optional[int]								=os.path.sep.join(mod_file.split(os.path.sep   )[:-1] + ['''scripts''', '''test_script.py''']   )
				lowerCamelCase   : str								=os.path.sep.join(
				    mod_file.split(os.path.sep   )[:-1] + ['''scripts''', '''test_distributed_data_loop.py''']   )
				lowerCamelCase   : int								=os.path.sep.join(mod_file.split(os.path.sep   )[:-1] + ['''scripts''', '''test_ops.py''']   )







		@require_multi_gpu
		def 			__lowercase   (		self   )				->   int:
				print(F"Found {torch.cuda.device_count()} devices."   )
				lowerCamelCase   : Optional[Any]								=['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", self.test_file_path]
				with patch_environment(omp_num_threads=1   ):
						execute_subprocess_async(__a			,     env=os.environ.copy()   )







		@require_multi_gpu
		def 			__lowercase   (		self   )				->   str:
				print(F"Found {torch.cuda.device_count()} devices."   )
				lowerCamelCase   : Tuple								=['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", self.operation_file_path]
				print(F"Command: {cmd}"   )
				with patch_environment(omp_num_threads=1   ):
						execute_subprocess_async(__a			,     env=os.environ.copy()   )







		@require_multi_gpu
		def 			__lowercase   (		self   )				->   Any:
				lowerCamelCase   : str								=['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", inspect.getfile(self.__class__   )]
				with patch_environment(omp_num_threads=1   ):
						execute_subprocess_async(__a			,     env=os.environ.copy()   )







		@require_multi_gpu
		def 			__lowercase   (		self   )				->   Optional[int]:
				print(F"Found {torch.cuda.device_count()} devices, using 2 devices only"   )
				lowerCamelCase   : Any								=['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", self.data_loop_file_path]
				with patch_environment(omp_num_threads=1			,     cuda_visible_devices='''0,1'''   ):
						execute_subprocess_async(__a			,     env=os.environ.copy()   )


if __name__ == "__main__":
				snake_case_							=			Accelerator()
				snake_case_							=			(accelerator.state.process_index + 2, 1_0)
				snake_case_							=			torch.randint(0, 1_0, shape).to(accelerator.device)

				snake_case_							=			''''''

				snake_case_							=			accelerator.pad_across_processes(tensor)
				if tensora.shape[0] != accelerator.state.num_processes + 1:
								error_msg += F"Found shape {tensora.shape} but should have {accelerator.state.num_processes + 1} at dim 0."
				if not torch.equal(tensora[: accelerator.state.process_index + 2], tensor):
								error_msg += "Tensors have different values."
				if not torch.all(tensora[accelerator.state.process_index + 2 :] == 0):
								error_msg += "Padding was not done with the right value (0)."

				snake_case_							=			accelerator.pad_across_processes(tensor, pad_first=True)
				if tensora.shape[0] != accelerator.state.num_processes + 1:
								error_msg += F"Found shape {tensora.shape} but should have {accelerator.state.num_processes + 1} at dim 0."
				snake_case_							=			accelerator.state.num_processes - accelerator.state.process_index - 1
				if not torch.equal(tensora[index:], tensor):
								error_msg += "Tensors have different values."
				if not torch.all(tensora[:index] == 0):
								error_msg += "Padding was not done with the right value (0)."

				# Raise error at the end to make sure we don't stop at the first failure.
				if len(error_msg) > 0:
								raise ValueError(error_msg)








from collections import defaultdict
from math import ceil, sqrt


def 					A__	(       SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0							,       SCREAMING_SNAKE_CASE_ = 1_0		)   ->     int:
		lowerCamelCase   : defaultdict								=defaultdict(SCREAMING_SNAKE_CASE_		)

		for outer_width in range(3							,       (t_limit // 4) + 2		):
				if outer_width * outer_width > t_limit:
						lowerCamelCase   : Any								=max(
						    ceil(sqrt(outer_width * outer_width - t_limit		)		)							,       1		)
				else:
						lowerCamelCase   : str								=1

				hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

				for hole_width in range(SCREAMING_SNAKE_CASE_							,       outer_width - 1							,       2		):
						count[outer_width * outer_width - hole_width * hole_width] += 1

		return sum(1 for n in count.values() if 1 <= n <= 1_0		)


if __name__ == "__main__":
				print(F"""{solution() = }""")

