
from __future__ import annotations

__A				=list[list[int]]

# assigning initial values to the grid
__A				=[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
__A				=[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]





def 			lowerCamelCase_ (				lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__    ):
				for i in range(9    ):
								if grid[row][i] == n or grid[i][column] == n:
												return False

				for i in range(3    ):
								for j in range(3    ):
												if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
																return False

				return True





def 			lowerCamelCase_ (				lowerCamelCase__    ):
				for i in range(9    ):
								for j in range(9    ):
												if grid[i][j] == 0:
																return i, j
				return None





def 			lowerCamelCase_ (				lowerCamelCase__    ):
				if location := find_empty_location(lowerCamelCase__    ):
								lowerCamelCase_	,    lowerCamelCase_						=			location
				else:
								# If the location is ``None``, then the grid is solved.
								return grid

				for digit in range(1	, 1_0    ):
								if is_safe(lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__    ):
												lowerCamelCase_						=			digit

												if sudoku(lowerCamelCase__    ) is not None:
																return grid

												lowerCamelCase_						=			0

				return None





def 			lowerCamelCase_ (				lowerCamelCase__    ):
				for row in grid:
								for cell in row:
												print(lowerCamelCase__	, end=" "    )
								print()


if __name__ == "__main__":
			# make a copy of grid so that you can compare with the unmodified grid
			for example_grid in (initial_grid, no_solution):
						print('''\nExample grid:\n''' + '''=''' * 2_0)
						print_solution(example_grid)
						print('''\nExample grid solution:''')
						__A				=sudoku(example_grid)
						if solution is not None:
									print_solution(solution)
						else:
									print('''Cannot find a solution.''')




import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
			import torch_xla.core.xla_model as xm
			import torch_xla.debug.metrics as met




class     _SCREAMING_SNAKE_CASE     (      snake_case_						):



	def __init__(    self						,  *lowercase						,  lowercase=None						,  lowercase=None						,  **lowercase )				->       List[str]:
					super().__init__(*lowercase						,  **lowercase )
					lowerCamelCase_						=			eval_examples
					lowerCamelCase_						=			post_process_function



	def     SCREAMING_SNAKE_CASE_(    self						,  lowercase = None						,  lowercase=None						,  lowercase = None						,  lowercase = "eval"						,  **lowercase						,  )				->       Dict[str, float]:
					lowerCamelCase_						=			gen_kwargs.copy()
					lowerCamelCase_						=			(
					    gen_kwargs["max_length"] if gen_kwargs.get("max_length" ) is not None else self.args.generation_max_length
					)
					lowerCamelCase_						=			(
					    gen_kwargs["num_beams"] if gen_kwargs.get("num_beams" ) is not None else self.args.generation_num_beams
					)
					lowerCamelCase_						=			gen_kwargs

					lowerCamelCase_						=			self.eval_dataset if eval_dataset is None else eval_dataset
					lowerCamelCase_						=			self.get_eval_dataloader(lowercase )
					lowerCamelCase_						=			self.eval_examples if eval_examples is None else eval_examples

					# Temporarily disable metric computation, we will do it in the loop here.
					lowerCamelCase_						=			self.compute_metrics
					lowerCamelCase_						=			None
					lowerCamelCase_						=			time.time()
					lowerCamelCase_						=			self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
					try:
									lowerCamelCase_						=			eval_loop(
									    lowercase						,  description="Evaluation"						,  prediction_loss_only=True if compute_metrics is None else None						,  ignore_keys=lowercase						,  metric_key_prefix=lowercase						,  )
					finally:
									lowerCamelCase_						=			compute_metrics
					lowerCamelCase_						=			self.args.eval_batch_size * self.args.world_size
					if f'{metric_key_prefix}_jit_compilation_time' in output.metrics:
									start_time += output.metrics[f'{metric_key_prefix}_jit_compilation_time']
					output.metrics.update(
					    speed_metrics(
					        lowercase						,  lowercase						,  num_samples=output.num_samples						,  num_steps=math.ceil(output.num_samples / total_batch_size )						,  ) )

					if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
									# Only the main node write the results by default
									lowerCamelCase_						=			self.post_process_function(lowercase						,  lowercase						,  lowercase )
									lowerCamelCase_						=			self.compute_metrics(lowercase )

									# Prefix all keys with metric_key_prefix + '_'
									for key in list(metrics.keys() ):
													if not key.startswith(f'{metric_key_prefix}_' ):
																	lowerCamelCase_						=			metrics.pop(lowercase )

									metrics.update(output.metrics )
					else:
									lowerCamelCase_						=			output.metrics

					if self.args.should_log:
									# Only the main node log the results by default
									self.log(lowercase )

					if self.args.tpu_metrics_debug or self.args.debug:
									# tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
									xm.master_print(met.metrics_report() )

					lowerCamelCase_						=			self.callback_handler.on_evaluate(self.args						,  self.state						,  self.control						,  lowercase )
					return metrics



	def     SCREAMING_SNAKE_CASE_(    self						,  lowercase						,  lowercase						,  lowercase=None						,  lowercase = "test"						,  **lowercase )				->       Union[str, Any]:
					lowerCamelCase_						=			gen_kwargs.copy()

					lowerCamelCase_						=			self.get_test_dataloader(lowercase )

					# Temporarily disable metric computation, we will do it in the loop here.
					lowerCamelCase_						=			self.compute_metrics
					lowerCamelCase_						=			None
					lowerCamelCase_						=			time.time()
					lowerCamelCase_						=			self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
					try:
									lowerCamelCase_						=			eval_loop(
									    lowercase						,  description="Prediction"						,  prediction_loss_only=True if compute_metrics is None else None						,  ignore_keys=lowercase						,  metric_key_prefix=lowercase						,  )
					finally:
									lowerCamelCase_						=			compute_metrics

					lowerCamelCase_						=			self.args.eval_batch_size * self.args.world_size
					if f'{metric_key_prefix}_jit_compilation_time' in output.metrics:
									start_time += output.metrics[f'{metric_key_prefix}_jit_compilation_time']
					output.metrics.update(
					    speed_metrics(
					        lowercase						,  lowercase						,  num_samples=output.num_samples						,  num_steps=math.ceil(output.num_samples / total_batch_size )						,  ) )
					if self.post_process_function is None or self.compute_metrics is None:
									return output

					lowerCamelCase_						=			self.post_process_function(lowercase						,  lowercase						,  lowercase						,  "predict" )
					lowerCamelCase_						=			self.compute_metrics(lowercase )

					# Prefix all keys with metric_key_prefix + '_'
					for key in list(metrics.keys() ):
									if not key.startswith(f'{metric_key_prefix}_' ):
													lowerCamelCase_						=			metrics.pop(lowercase )
					metrics.update(output.metrics )
					return PredictionOutput(predictions=predictions.predictions						,  label_ids=predictions.label_ids						,  metrics=lowercase )


