


from itertools import permutations



def      __lowerCAmelCase    (				snake_case						:     Tuple = 5			)							->				str:
   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:					Optional[int]	 =						list(range(gon_side + 1    ,   0    ,   -1			)			)
   __lowerCamelCase:					str	 =						list(range(gon_side + 2    ,   gon_side * 2 + 1			)			)

   for perm in permutations(small_numbers + big_numbers			):
      __lowerCamelCase:					int	 =						generate_gon_ring(SCREAMING_SNAKE_CASE_    ,   list(SCREAMING_SNAKE_CASE_			)			)
      if is_magic_gon(SCREAMING_SNAKE_CASE_			):
         return int("""""".join(str(SCREAMING_SNAKE_CASE_			) for n in numbers			)			)

   __lowerCamelCase:					Any	 =						f'Magic {gon_side}-gon ring is impossible'
   raise ValueError(SCREAMING_SNAKE_CASE_			)



def      __lowerCAmelCase    (				snake_case						:     List[str]    ,   snake_case						:     Any			)							->				List[Any]:
   __lowerCamelCase:					Union[str, Any]	 =						[0] * (gon_side * 3)
   __lowerCamelCase:					Any	 =						perm[0:3]
   perm.append(perm[1]			)

   __lowerCamelCase:					Union[str, Any]	 =						1 if gon_side < 5 else 2

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

   return result



def      __lowerCAmelCase    (				snake_case						:     int			)							->				List[str]:
   if len(SCREAMING_SNAKE_CASE_			) % 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:					Tuple	 =						sum(numbers[:3]			)

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


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




"""simple docstring"""




import gym
import numpy as np
import torch
from mujoco_py import GlfwContext

from transformers import DecisionTransformerModel


GlfwContext(offscreen=True)  # Create a window to init GLFW.

def     UpperCamelCase_    (						SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_,	SCREAMING_SNAKE_CASE_     ):
					# we don't care about the past rewards in this model

					SCREAMING_SNAKE_CASE           =      states.reshape(1,	-1,	model.config.state_dim     )
					SCREAMING_SNAKE_CASE           =      actions.reshape(1,	-1,	model.config.act_dim     )
					SCREAMING_SNAKE_CASE           =      returns_to_go.reshape(1,	-1,	1     )
					SCREAMING_SNAKE_CASE           =      timesteps.reshape(1,	-1     )

					if model.config.max_length is not None:
										SCREAMING_SNAKE_CASE           =      states[:, -model.config.max_length :]
										SCREAMING_SNAKE_CASE           =      actions[:, -model.config.max_length :]
										SCREAMING_SNAKE_CASE           =      returns_to_go[:, -model.config.max_length :]
										SCREAMING_SNAKE_CASE           =      timesteps[:, -model.config.max_length :]

										# pad all tokens to sequence length
										SCREAMING_SNAKE_CASE           =      torch.cat(
										    [torch.zeros(model.config.max_length - states.shape[1]     ), torch.ones(states.shape[1]     )]     )
										SCREAMING_SNAKE_CASE           =      attention_mask.to(dtype=torch.long,	device=states.device     ).reshape(1,	-1     )
										SCREAMING_SNAKE_CASE           =      torch.cat(
										    [
										        torch.zeros(
										            (states.shape[0], model.config.max_length - states.shape[1], model.config.state_dim),	device=states.device,	),
										        states,
										    ],	dim=1,	).to(dtype=torch.floataa     )
										SCREAMING_SNAKE_CASE           =      torch.cat(
										    [
										        torch.zeros(
										            (actions.shape[0], model.config.max_length - actions.shape[1], model.config.act_dim),	device=actions.device,	),
										        actions,
										    ],	dim=1,	).to(dtype=torch.floataa     )
										SCREAMING_SNAKE_CASE           =      torch.cat(
										    [
										        torch.zeros(
										            (returns_to_go.shape[0], model.config.max_length - returns_to_go.shape[1], 1),	device=returns_to_go.device,	),
										        returns_to_go,
										    ],	dim=1,	).to(dtype=torch.floataa     )
										SCREAMING_SNAKE_CASE           =      torch.cat(
										    [
										        torch.zeros(
										            (timesteps.shape[0], model.config.max_length - timesteps.shape[1]),	device=timesteps.device     ),
										        timesteps,
										    ],	dim=1,	).to(dtype=torch.long     )
					else:
										SCREAMING_SNAKE_CASE           =      None

					SCREAMING_SNAKE_CASE      ,       SCREAMING_SNAKE_CASE      ,       SCREAMING_SNAKE_CASE           =      model(
					    states=SCREAMING_SNAKE_CASE_,	actions=SCREAMING_SNAKE_CASE_,	rewards=SCREAMING_SNAKE_CASE_,	returns_to_go=SCREAMING_SNAKE_CASE_,	timesteps=SCREAMING_SNAKE_CASE_,	attention_mask=SCREAMING_SNAKE_CASE_,	return_dict=SCREAMING_SNAKE_CASE_,	)

					return action_preds[0, -1]


# build the environment

snake_case					  =						gym.make('Hopper-v3')
snake_case					  =						env.observation_space.shape[0]
snake_case					  =						env.action_space.shape[0]
snake_case					  =						1_0_0_0
snake_case					  =						'cuda'
snake_case					  =						1_0_0_0.0  # normalization for rewards/returns
snake_case					  =						3_6_0_0 / scale  # evaluation conditioning targets, 3600 is reasonable from the paper LINK
snake_case					  =						np.array(
    [
        1.3_1_1_2_7_9,
        -0.0_8_4_6_9_5_2_1,
        -0.5_3_8_2_7_1_9,
        -0.0_7_2_0_1_5_7_6,
        0.0_4_9_3_2_3_6_6,
        2.1_0_6_6_8_5_6,
        -0.1_5_0_1_7_3_5_4,
        0.0_0_8_7_8_3_4_5,
        -0.2_8_4_8_1_8_6,
        -0.1_8_5_4_0_0_9_6,
        -0.2_8_4_6_1_2_8_6,
    ]
)
snake_case					  =						np.array(
    [
        0.1_7_7_9_0_7_5_1,
        0.0_5_4_4_4_6_2_1,
        0.2_1_2_9_7_1_3_9,
        0.1_4_5_3_0_4_1_9,
        0.6_1_2_4_4_4_4,
        0.8_5_1_7_4_4_6_5,
        1.4_5_1_5_2_5_2,
        0.6_7_5_1_6_9_6,
        1.5_3_6_2_3_9,
        1.6_1_6_0_7_4_6,
        5.6_0_7_2_5_3_6,
    ]
)
snake_case					  =						torch.from_numpy(state_mean).to(device=device)
snake_case					  =						torch.from_numpy(state_std).to(device=device)

# Create the decision transformer model
snake_case					  =						DecisionTransformerModel.from_pretrained('edbeeching/decision-transformer-gym-hopper-medium')
snake_case					  =						model.to(device)
model.eval()

for ep in range(1_0):
	snake_case  ,     snake_case					  =						0, 0
	snake_case					  =						env.reset()
	snake_case					  =						torch.tensor(TARGET_RETURN, device=device, dtype=torch.floataa).reshape(1, 1)
	snake_case					  =						torch.from_numpy(state).reshape(1, state_dim).to(device=device, dtype=torch.floataa)
	snake_case					  =						torch.zeros((0, act_dim), device=device, dtype=torch.floataa)
	snake_case					  =						torch.zeros(0, device=device, dtype=torch.floataa)

	snake_case					  =						torch.tensor(0, device=device, dtype=torch.long).reshape(1, 1)
	for t in range(max_ep_len):
		env.render()
		# add padding
		snake_case					  =						torch.cat([actions, torch.zeros((1, act_dim), device=device)], dim=0)
		snake_case					  =						torch.cat([rewards, torch.zeros(1, device=device)])

		snake_case					  =						get_action(
		    model,
		    (states.to(dtype=torch.floataa) - state_mean) / state_std,
		    actions.to(dtype=torch.floataa),
		    rewards.to(dtype=torch.floataa),
		    target_return.to(dtype=torch.floataa),
		    timesteps.to(dtype=torch.long),
		)
		snake_case					  =						action
		snake_case					  =						action.detach().cpu().numpy()

		snake_case  ,     snake_case  ,     snake_case  ,     snake_case					  =						env.step(action)

		snake_case					  =						torch.from_numpy(state).to(device=device).reshape(1, state_dim)
		snake_case					  =						torch.cat([states, cur_state], dim=0)
		snake_case					  =						reward

		snake_case					  =						target_return[0, -1] - (reward / scale)
		snake_case					  =						torch.cat([target_return, pred_return.reshape(1, 1)], dim=1)
		snake_case					  =						torch.cat([timesteps, torch.ones((1, 1), device=device, dtype=torch.long) * (t + 1)], dim=1)

		episode_return += reward
		episode_length += 1

		if done:
			break
