
"""simple docstring"""





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__		(			__snake_case,     __snake_case,     __snake_case,     __snake_case	)							->		bool:


					"""simple docstring"""





					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__		(			__snake_case	)							->		tuple[int, int] | None:


					"""simple docstring"""





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



def       lowerCamelCase__		(			__snake_case	)							->		Matrix | None:


					"""simple docstring"""





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

					for digit in range(1,     10	):
										if is_safe(__snake_case,     __snake_case,     __snake_case,     __snake_case	):
															_UpperCamelCase							 =  digit

															if sudoku(__snake_case	) is not None:
																				return grid

															_UpperCamelCase							 =  0

					return None



def       lowerCamelCase__		(			__snake_case	)							->		None:


					"""simple docstring"""





					for row in grid:
										for cell in row:
															print(__snake_case,     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""" + """=""" * 20)
								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.""")








"""simple docstring"""





from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_a														=		{
    """configuration_autoformer""": [
        """AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """AutoformerConfig""",
    ],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_a														=		[
				    """AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
				    """AutoformerForPrediction""",
				    """AutoformerModel""",
				    """AutoformerPreTrainedModel""",
				]


if TYPE_CHECKING:
				from .configuration_autoformer import (
				    AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    AutoformerConfig,
				)

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_autoformer import (
								    AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
								    AutoformerForPrediction,
								    AutoformerModel,
								    AutoformerPreTrainedModel,
								)

else:
				import sys

				_a														=		_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)






