

'''simple docstring'''



from __future__ import annotations

__lowercase     :						int	=     list[list[int]]

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






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Matrix       ):
					if location := find_empty_location(_SCREAMING_SNAKE_CASE       ):
										__a      :	str    =  location
					else:
										# If the location is ``None``, then the grid is solved.
										return grid

					for digit in range(1						,				10       ):
										if is_safe(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       ):
															__a      :	Optional[int]    =  digit

															if sudoku(_SCREAMING_SNAKE_CASE       ) is not None:
																				return grid

															__a      :	Tuple    =  0

					return None






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       Matrix       ):
					for row in grid:
										for cell in row:
															print(_SCREAMING_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:')
		__lowercase     :						List[str]	=     sudoku(example_grid)
		if solution is not None:
			print_solution(solution)
		else:
			print('Cannot find a solution.')







'''simple docstring'''



import sys

__lowercase     :						Union[str, Any]	=     (
    '73167176531330624919225119674426574742355349194934'
    '96983520312774506326239578318016984801869478851843'
    '85861560789112949495459501737958331952853208805511'
    '12540698747158523863050715693290963295227443043557'
    '66896648950445244523161731856403098711121722383113'
    '62229893423380308135336276614282806444486645238749'
    '30358907296290491560440772390713810515859307960866'
    '70172427121883998797908792274921901699720888093776'
    '65727333001053367881220235421809751254540594752243'
    '52584907711670556013604839586446706324415722155397'
    '53697817977846174064955149290862569321978468622482'
    '83972241375657056057490261407972968652414535100474'
    '82166370484403199890008895243450658541227588666881'
    '16427171479924442928230863465674813919123162824586'
    '17866458359124566529476545682848912883142607690042'
    '24219022671055626321111109370544217506941658960408'
    '07198403850962455444362981230987879927244284909188'
    '84580156166097919133875499200524063689912560717606'
    '05886116467109405077541002256983155200055935729725'
    '71636269561882670428252483600823257530420752963450'
)






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       str       ):
					__a      :	List[str]    =  1
					for digit in s:
										product *= int(_SCREAMING_SNAKE_CASE       )
					return product






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       str = N       ):
					__a      :	Optional[int]    =  -sys.maxsize - 1
					__a      :	Optional[Any]    =  n[:13]
					__a      :	int    =  13
					while cur_index < len(_SCREAMING_SNAKE_CASE       ) - 13:
										if int(n[cur_index]       ) >= int(substr[0]       ):
															__a      :	List[Any]    =  substr[1:] + n[cur_index]
															cur_index += 1
										else:
															__a      :	Dict    =  max(_SCREAMING_SNAKE_CASE						,				str_eval(_SCREAMING_SNAKE_CASE       )       )
															__a      :	Optional[Any]    =  n[cur_index : cur_index + 13]
															cur_index += 13
					return largest_product


if __name__ == "__main__":
	print(f'''{solution() = }''')



