def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Tuple			,					__UpperCamelCase   :	Dict     ):







  """simple docstring"""





  while b:
    SCREAMING_SNAKE_CASE__      							=				b, a % b
  return a



def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Dict			,					__UpperCamelCase   :	Optional[Any]     ):







  """simple docstring"""





  return a if b == 0 else euclidean_gcd_recursive(__UpperCamelCase			,					a % b     )



def      __SCREAMING_SNAKE_CASE  ( ):







  """simple docstring"""





  print(f"""euclidean_gcd(3, 5) = {euclidean_gcd(3			,					5     )}"""     )
  print(f"""euclidean_gcd(5, 3) = {euclidean_gcd(5			,					3     )}"""     )
  print(f"""euclidean_gcd(1, 3) = {euclidean_gcd(1			,					3     )}"""     )
  print(f"""euclidean_gcd(3, 6) = {euclidean_gcd(3			,					6     )}"""     )
  print(f"""euclidean_gcd(6, 3) = {euclidean_gcd(6			,					3     )}"""     )

  print(f"""euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3			,					5     )}"""     )
  print(f"""euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5			,					3     )}"""     )
  print(f"""euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1			,					3     )}"""     )
  print(f"""euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3			,					6     )}"""     )
  print(f"""euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6			,					3     )}"""     )


if __name__ == "__main__":
   main()

from __future__ import annotations

__lowerCamelCase      :			Tuple							       =		list[list[int]]

# assigning initial values to the grid
__lowerCamelCase      :			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
__lowerCamelCase      :			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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int			,					__UpperCamelCase   :	int     )							-> 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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> 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      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> Matrix | None:







  """simple docstring"""





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

  for digit in range(1			,					10     ):
    if is_safe(__UpperCamelCase			,					__UpperCamelCase			,					__UpperCamelCase			,					__UpperCamelCase     ):
      SCREAMING_SNAKE_CASE__      							=				digit

      if sudoku(__UpperCamelCase     ) is not None:
        return grid

      SCREAMING_SNAKE_CASE__      							=				0

  return None



def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Matrix     )							-> None:







  """simple docstring"""





  for row in grid:
    for cell in row:
      print(__UpperCamelCase			,					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:''')
      __lowerCamelCase      :			str							       =		sudoku(example_grid)
      if solution is not None:
         print_solution(solution)
      else:
         print('''Cannot find a solution.''')
