






from __future__ import annotations

snake_case__   :						Any													=   list[list[int]]

# assigning initial values to the grid
snake_case__   :						Matrix													=   [
    [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
snake_case__   :						Matrix													=   [
    [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      _snake_case     (__lowercase     ,   __lowercase     ,   __lowercase     ,   __lowercase):
   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      _snake_case     (__lowercase):
   for i in range(9):
      for j in range(9):
         if grid[i][j] == 0:
            return i, j
   return None






def      _snake_case     (__lowercase):
   if location := find_empty_location(__lowercase):
      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(__lowercase     ,   __lowercase     ,   __lowercase     ,   __lowercase):
         UpperCamelCase_						=  digit

         if sudoku(__lowercase) is not None:
            return grid

         UpperCamelCase_						=  0

   return None






def      _snake_case     (__lowercase):
   for row in grid:
      for cell in row:
         print(__lowercase     ,   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:""")
  snake_case__   :						Any													=   sudoku(example_grid)
  if solution is not None:
   print_solution(solution)
  else:
   print("""Cannot find a solution.""")













from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


snake_case__   :						Optional[int]													=   {
    """configuration_pegasus_x""": ["""PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP""", """PegasusXConfig"""],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 snake_case__   :						Dict													=   [
     """PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """PegasusXForConditionalGeneration""",
     """PegasusXModel""",
     """PegasusXPreTrainedModel""",
 ]


if TYPE_CHECKING:
 from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_pegasus_x import (
      PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
      PegasusXForConditionalGeneration,
      PegasusXModel,
      PegasusXPreTrainedModel,
  )


else:
 import sys

 snake_case__   :						Optional[Any]													=   _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





