





from itertools import permutations


def 				SCREAMING_SNAKE_CASE__    (     __a = 5 ):
	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
	snake_case_		:      List[Any]           =						list(range(gon_side + 1 ,			0 ,			-1 ) )
	snake_case_		:      int           =						list(range(gon_side + 2 ,			gon_side * 2 + 1 ) )

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

	snake_case_		:      Dict           =						f"""Magic {gon_side}-gon ring is impossible"""
	raise ValueError(__a )


def 				SCREAMING_SNAKE_CASE__    (     __a ,			__a ):
	snake_case_		:      Union[str, Any]           =						[0] * (gon_side * 3)
	snake_case_		:      Tuple           =						perm[0:3]
	perm.append(perm[1] )

	snake_case_		:      Tuple           =						1 if gon_side < 5 else 2

	for i in range(1 ,			len(__a ) // 3 + magic_number ):
		snake_case_		:      List[Any]           =						perm[2 * i + 1]
		snake_case_		:      Tuple           =						result[3 * i - 1]
		snake_case_		:      Optional[int]           =						perm[2 * i + 2]

	return result


def 				SCREAMING_SNAKE_CASE__    (     __a ):
	if len(__a ) % 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

	snake_case_		:      List[Any]           =						sum(numbers[:3] )

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


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


'''simple docstring'''




import logging
from pathlib import Path

import numpy as np
import pytorch_lightning as pl
import torch
from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
from pytorch_lightning.utilities import rank_zero_only

from utils import save_json

def _UpperCamelCase (							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							Optional[Any]  					=       filter(lambda SCREAMING_SNAKE_CASE_				: p.requires_grad	,							model.parameters()				)
     lowercase_       :							Tuple  					=       sum([np.prod(p.size()				) for p in model_parameters]				)
     return params


_A										= logging.getLogger(__name__)


class    UpperCAmelCase__	(							pl.Callback      ):






   """simple docstring"""
   def 		_lowerCamelCase			(self							,					_a							,					_a					)     ->  str:
        lowercase_       :							List[str]  					=       {f'''lr_group_{i}''': param['lr'] for i, param in enumerate(pl_module.trainer.optimizers[0].param_groups					)}
        pl_module.logger.log_metrics(_a					)
   @rank_zero_only
   def 		_lowerCamelCase			(self							,					_a							,					_a							,					_a							,					_a=True					)     ->  None:
        logger.info(f'''***** {type_path} results at step {trainer.global_step:05d} *****'''					)
        lowercase_       :							Union[str, Any]  					=       trainer.callback_metrics
        trainer.logger.log_metrics({k: v for k, v in metrics.items() if k not in ['log', 'progress_bar', 'preds']}					)
        # Log results
        lowercase_       :							Optional[int]  					=       Path(pl_module.hparams.output_dir					)
        if type_path == "test":
             lowercase_       :							Union[str, Any]  					=       od / 'test_results.txt'
             lowercase_       :							Tuple  					=       od / 'test_generations.txt'
        else:
             # this never gets hit. I prefer not to save intermediate generations, and results are in metrics.json
             # If people want this it will be easy enough to add back.
             lowercase_       :							List[str]  					=       od / f'''{type_path}_results/{trainer.global_step:05d}.txt'''
             lowercase_       :							int  					=       od / f'''{type_path}_generations/{trainer.global_step:05d}.txt'''
             results_file.parent.mkdir(exist_ok=_a					)
             generations_file.parent.mkdir(exist_ok=_a					)
        with open(_a							,					'a+'					) as writer:
             for key in sorted(_a					):
                  if key in ["log", "progress_bar", "preds"]:
                       continue
                  lowercase_       :							Any  					=       metrics[key]
                  if isinstance(_a							,					torch.Tensor					):
                       lowercase_       :							Any  					=       val.item()
                  lowercase_       :							List[str]  					=       f'''{key}: {val:.6f}\n'''
                  writer.write(_a					)

        if not save_generations:
             return

        if "preds" in metrics:
             lowercase_       :							Optional[Any]  					=       '\n'.join(metrics['preds']					)
             generations_file.open('w+'					).write(_a					)
   @rank_zero_only
   def 		_lowerCamelCase			(self							,					_a							,					_a					)     ->  Tuple:
        try:
             lowercase_       :							List[Any]  					=       pl_module.model.model.num_parameters()
        except AttributeError:
             lowercase_       :							Dict  					=       pl_module.model.num_parameters()

        lowercase_       :							Optional[Any]  					=       count_trainable_parameters(_a					)
        # mp stands for million parameters
        trainer.logger.log_metrics({'n_params': npars, 'mp': npars / 1e6, 'grad_mp': n_trainable_pars / 1e6}					)
   @rank_zero_only
   def 		_lowerCamelCase			(self							,					_a							,					_a					)     ->  int:
        save_json(pl_module.metrics							,					pl_module.metrics_save_path					)
        return self._write_logs(_a							,					_a							,					'test'					)





   @rank_zero_only
   def 		_lowerCamelCase			(self							,					_a							,					_a					)     ->  List[str]:
        save_json(pl_module.metrics							,					pl_module.metrics_save_path					)
        # Uncommenting this will save val generations
        # return self._write_logs(trainer, pl_module, "valid")



def _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_=1	,							SCREAMING_SNAKE_CASE_=False				):
     if metric == "rouge2":
          lowercase_       :							Optional[int]  					=       '{val_avg_rouge2:.4f}-{step_count}'
     elif metric == "bleu":
          lowercase_       :							int  					=       '{val_avg_bleu:.4f}-{step_count}'
     elif metric == "loss":
          lowercase_       :							List[Any]  					=       '{val_avg_loss:.4f}-{step_count}'
     else:
          raise NotImplementedError(
              f'''seq2seq callbacks only support rouge2, bleu and loss, got {metric}, You can make your own by adding to'''
              ' this function.'				)

     lowercase_       :							Tuple  					=       ModelCheckpoint(
         dirpath=SCREAMING_SNAKE_CASE_	,							filename=SCREAMING_SNAKE_CASE_	,							monitor=f'''val_{metric}'''	,							mode='min' if 'loss' in metric else 'max'	,							save_top_k=SCREAMING_SNAKE_CASE_	,							)
     return checkpoint_callback






def _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_				):
     return EarlyStopping(
         monitor=f'''val_{metric}'''	,							mode='min' if 'loss' in metric else 'max'	,							patience=SCREAMING_SNAKE_CASE_	,							verbose=SCREAMING_SNAKE_CASE_	,							)




