



"""simple docstring"""






from itertools import permutations






def 	snake_case__  (						__lowerCamelCase							:       int = 5      ):
			"""simple docstring"""
			if gon_side < 3 or gon_side > 5:
						raise ValueError('''gon_side must be in the range [3, 5]'''      )

			# Since it's 16, we know 10 is on the outer ring
			# Put the big numbers at the end so that they are never the first number
			lowerCamelCase__						:						Tuple						      =list(range(gon_side + 1				,						0				,						-1      )      )
			lowerCamelCase__						:						List[str]						      =list(range(gon_side + 2				,						gon_side * 2 + 1      )      )

			for perm in permutations(small_numbers + big_numbers      ):
						lowerCamelCase__						:						Optional[int]						      =generate_gon_ring(__lowerCamelCase				,						list(__lowerCamelCase      )      )
						if is_magic_gon(__lowerCamelCase      ):
									return int(''''''.join(str(__lowerCamelCase      ) for n in numbers      )      )

			lowerCamelCase__						:						List[Any]						      =f'''Magic {gon_side}-gon ring is impossible'''
			raise ValueError(__lowerCamelCase      )






def 	snake_case__  (						__lowerCamelCase							:       int				,						__lowerCamelCase							:       list[int]      ):
			"""simple docstring"""
			lowerCamelCase__						:						Any						      =[0] * (gon_side * 3)
			lowerCamelCase__						:						Optional[Any]						      =perm[0:3]
			perm.append(perm[1]      )

			lowerCamelCase__						:						Optional[Any]						      =1 if gon_side < 5 else 2

			for i in range(1				,						len(__lowerCamelCase      ) // 3 + magic_number      ):
						lowerCamelCase__						:						Union[str, Any]						      =perm[2 * i + 1]
						lowerCamelCase__						:						int						      =result[3 * i - 1]
						lowerCamelCase__						:						List[Any]						      =perm[2 * i + 2]

			return result






def 	snake_case__  (						__lowerCamelCase							:       list[int]      ):
			"""simple docstring"""
			if len(__lowerCamelCase      ) % 3 != 0:
						raise ValueError('''a gon ring should have a length that is a multiple of 3'''      )

			if min(numbers[::3]      ) != numbers[0]:
						return False

			lowerCamelCase__						:						Dict						      =sum(numbers[:3]      )

			return all(sum(numbers[i : i + 3]      ) == total for i in range(3				,						len(__lowerCamelCase      )				,						3      )      )


if __name__ == "__main__":
		print(solution())










import argparse
import os
import re

import numpy as np
import PIL
import torch
from timm import create_model
from torch.optim.lr_scheduler import OneCycleLR
from torch.utils.data import DataLoader, Dataset
from torchvision.transforms import Compose, RandomResizedCrop, Resize, ToTensor

from accelerate import Accelerator


def 				__SCREAMING_SNAKE_CASE    (     snake_case_		):

						'''simple docstring'''


						_UpperCAmelCase						=	fname.split(os.path.sep		)[-1]
						return re.search(R"^(.*)_\d+\.jpg$"      ,       snake_case_		).groups()[0]






class        __lowerCAmelCase					(			UpperCAmelCase__					):







			def __init__(			self       :     Union[str, Any]       ,       snake_case__       :     Tuple       ,       snake_case__       :     Dict=None       ,       snake_case__       :     Union[str, Any]=None ):




									"""simple docstring"""


									_UpperCAmelCase						=	file_names
									_UpperCAmelCase						=	image_transform
									_UpperCAmelCase						=	label_to_id







			def __len__(			self       :     Tuple ):




									"""simple docstring"""


									return len(self.file_names )







			def __getitem__(			self       :     List[str]       ,       snake_case__       :     Tuple ):




									"""simple docstring"""


									_UpperCAmelCase						=	self.file_names[idx]
									_UpperCAmelCase						=	PIL.Image.open(snake_case__ )
									_UpperCAmelCase						=	raw_image.convert("RGB" )
									if self.image_transform is not None:
															_UpperCAmelCase						=	self.image_transform(snake_case__ )
									_UpperCAmelCase						=	extract_label(snake_case__ )
									if self.label_to_id is not None:
															_UpperCAmelCase						=	self.label_to_id[label]
									return {"image": image, "label": label}




def 				__SCREAMING_SNAKE_CASE    (     snake_case_      ,       snake_case_		):

						'''simple docstring'''


						_UpperCAmelCase						=	Accelerator(cpu=args.cpu      ,       mixed_precision=args.mixed_precision		)

						# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
						_UpperCAmelCase						=	config["lr"]
						_UpperCAmelCase						=	int(config["num_epochs"]		)
						_UpperCAmelCase						=	int(config["seed"]		)
						_UpperCAmelCase						=	int(config["batch_size"]		)
						_UpperCAmelCase						=	config["image_size"]
						if not isinstance(snake_case_      ,       (list, tuple)		):
												_UpperCAmelCase						=	(image_size, image_size)

						# Grab all the image filenames
						_UpperCAmelCase						=	[os.path.join(args.data_dir      ,       snake_case_		) for fname in os.listdir(args.data_dir		) if fname.endswith(".jpg"		)]

						# Build the label correspondences
						_UpperCAmelCase						=	[extract_label(snake_case_		) for fname in file_names]
						_UpperCAmelCase						=	list(set(snake_case_		)		)
						id_to_label.sort()
						_UpperCAmelCase						=	{lbl: i for i, lbl in enumerate(snake_case_		)}

						# Set the seed before splitting the data.
						np.random.seed(snake_case_		)
						torch.manual_seed(snake_case_		)
						torch.cuda.manual_seed_all(snake_case_		)

						# Split our filenames between train and validation
						_UpperCAmelCase						=	np.random.permutation(len(snake_case_		)		)
						_UpperCAmelCase						=	int(0.8 * len(snake_case_		)		)
						_UpperCAmelCase						=	random_perm[:cut]
						_UpperCAmelCase						=	random_perm[cut:]

						# For training we use a simple RandomResizedCrop
						_UpperCAmelCase						=	Compose([RandomResizedCrop(snake_case_      ,       scale=(0.5, 1.0)		), ToTensor()]		)
						_UpperCAmelCase						=	PetsDataset(
						    [file_names[i] for i in train_split]      ,       image_transform=snake_case_      ,       label_to_id=snake_case_		)

						# For evaluation, we use a deterministic Resize
						_UpperCAmelCase						=	Compose([Resize(snake_case_		), ToTensor()]		)
						_UpperCAmelCase						=	PetsDataset([file_names[i] for i in eval_split]      ,       image_transform=snake_case_      ,       label_to_id=snake_case_		)

						# Instantiate dataloaders.
						_UpperCAmelCase						=	DataLoader(snake_case_      ,       shuffle=snake_case_      ,       batch_size=snake_case_      ,       num_workers=4		)
						_UpperCAmelCase						=	DataLoader(snake_case_      ,       shuffle=snake_case_      ,       batch_size=snake_case_      ,       num_workers=4		)

						# Instantiate the model (we build the model here so that the seed also control new weights initialization)
						_UpperCAmelCase						=	create_model("resnet50d"      ,       pretrained=snake_case_      ,       num_classes=len(snake_case_		)		)

						# We could avoid this line since the accelerator is set with `device_placement=True` (default value).
						# Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
						# creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
						_UpperCAmelCase						=	model.to(accelerator.device		)

						# Freezing the base model
						for param in model.parameters():
												_UpperCAmelCase						=	False
						for param in model.get_classifier().parameters():
												_UpperCAmelCase						=	True

						# We normalize the batches of images to be a bit faster.
						_UpperCAmelCase						=	torch.tensor(model.default_cfg["mean"]		)[None, :, None, None].to(accelerator.device		)
						_UpperCAmelCase						=	torch.tensor(model.default_cfg["std"]		)[None, :, None, None].to(accelerator.device		)

						# Instantiate optimizer
						_UpperCAmelCase						=	torch.optim.Adam(params=model.parameters()      ,       lr=lr / 25		)

						# Instantiate learning rate scheduler
						_UpperCAmelCase						=	OneCycleLR(optimizer=snake_case_      ,       max_lr=snake_case_      ,       epochs=snake_case_      ,       steps_per_epoch=len(snake_case_		)		)

						# Prepare everything
						# There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
						# prepare method.
						_UpperCAmelCase				,					_UpperCAmelCase				,					_UpperCAmelCase				,					_UpperCAmelCase				,					_UpperCAmelCase						=	accelerator.prepare(
						    snake_case_      ,       snake_case_      ,       snake_case_      ,       snake_case_      ,       snake_case_		)

						# Now we train the model
						for epoch in range(snake_case_		):
												model.train()
												for step, batch in enumerate(snake_case_		):
																		# We could avoid this line since we set the accelerator with `device_placement=True`.
																		_UpperCAmelCase						=	{k: v.to(accelerator.device		) for k, v in batch.items()}
																		_UpperCAmelCase						=	(batch["image"] - mean) / std
																		_UpperCAmelCase						=	model(snake_case_		)
																		_UpperCAmelCase						=	torch.nn.functional.cross_entropy(snake_case_      ,       batch["label"]		)
																		accelerator.backward(snake_case_		)
																		optimizer.step()
																		lr_scheduler.step()
																		optimizer.zero_grad()

												model.eval()
												_UpperCAmelCase						=	0
												_UpperCAmelCase						=	0
												for _, batch in enumerate(snake_case_		):
																		# We could avoid this line since we set the accelerator with `device_placement=True`.
																		_UpperCAmelCase						=	{k: v.to(accelerator.device		) for k, v in batch.items()}
																		_UpperCAmelCase						=	(batch["image"] - mean) / std
																		with torch.no_grad():
																								_UpperCAmelCase						=	model(snake_case_		)
																		_UpperCAmelCase						=	outputs.argmax(dim=-1		)
																		_UpperCAmelCase				,					_UpperCAmelCase						=	accelerator.gather_for_metrics((predictions, batch["label"])		)
																		_UpperCAmelCase						=	predictions == references
																		num_elems += accurate_preds.shape[0]
																		accurate += accurate_preds.long().sum()

												_UpperCAmelCase						=	accurate.item() / num_elems
												# Use accelerator.print to print only on the main process.
												accelerator.print(f"""epoch {epoch}: {100 * eval_metric:.2f}"""		)


def 				__SCREAMING_SNAKE_CASE    (     ):

						'''simple docstring'''


						_UpperCAmelCase						=	argparse.ArgumentParser(description="Simple example of training script."		)
						parser.add_argument("--data_dir"      ,       required=snake_case_      ,       help="The data folder on disk."		)
						parser.add_argument(
						    "--mixed_precision"      ,       type=snake_case_      ,       default=snake_case_      ,       choices=["no", "fp16", "bf16", "fp8"]      ,       help="Whether to use mixed precision. Choose"
						    "between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10."
						    "and an Nvidia Ampere GPU."      ,       )
						parser.add_argument(
						    "--checkpointing_steps"      ,       type=snake_case_      ,       default=snake_case_      ,       help="Whether the various states should be saved at the end of every n steps, or 'epoch' for each epoch."      ,       )
						parser.add_argument("--cpu"      ,       action="store_true"      ,       help="If passed, will train on the CPU."		)
						_UpperCAmelCase						=	parser.parse_args()
						_UpperCAmelCase						=	{"lr": 3e-2, "num_epochs": 3, "seed": 42, "batch_size": 64, "image_size": 224}
						training_function(snake_case_      ,       snake_case_		)


if __name__ == "__main__":
				main()




