





from __future__ import annotations

lowerCamelCase__          =    list[list[int]]

# assigning initial values to the grid
lowerCamelCase__          =    [
    [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__          =    [
    [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       A(__a:			Matrix						,   __a:			int						,   __a:			int						,   __a:			int				):





		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       A(__a:			Matrix				):





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

def       A(__a:			Matrix				):





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

		for digit in range(1						,   10				):
				if is_safe(lowerCamelCase_						,   lowerCamelCase_						,   lowerCamelCase_						,   lowerCamelCase_				):
						lowerCAmelCase_												=				digit

						if sudoku(lowerCamelCase_				) is not None:
								return grid

						lowerCAmelCase_												=				0

		return None

def       A(__a:			Matrix				):





		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''' + '''=''' * 20)
				print_solution(example_grid)
				print('''\nExample grid solution:''')
				lowerCamelCase__          =    sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('''Cannot find a solution.''')







def        __UpperCAmelCase						(							lowerCamelCase_ :     List[str]  ,							lowerCamelCase_ :     Optional[Any]  )       ->  int:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : List[Any]					  =      [0 for i in range(r + 1  )]
			# nc0 = 1
			SCREAMING_SNAKE_CASE_   : Dict					  =      1
			for i in range(1  ,							n + 1  ):
						# to compute current row from previous row.
						SCREAMING_SNAKE_CASE_   : Optional[int]					  =      min(lowerCamelCase_  ,							lowerCamelCase_  )
						while j > 0:
									c[j] += c[j - 1]
									j -= 1
			return c[r]




print(binomial_coefficient(n=10, r=5))



