
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  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		bool:
			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_     )				->		tuple[int, int] | None:
			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 | None:
			if location := find_empty_location(SCREAMING_SNAKE_CASE_     ):
						lowerCAmelCase__      ,				lowerCAmelCase__      :      Any         =		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_     ):
									lowerCAmelCase__      :      Optional[Any]         =		digit

									if sudoku(SCREAMING_SNAKE_CASE_     ) is not None:
												return grid

									lowerCAmelCase__      :      List[Any]         =		0

			return None
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		None:
			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:""")
										lowerCamelCase__          =		sudoku(example_grid)
										if solution is not None:
															print_solution(solution)
										else:
															print("""Cannot find a solution.""")

from __future__ import annotations

import math

lowerCamelCase__          =		"""2020.9.26"""
lowerCamelCase__          =		"""xcodz-dot, cclaus, dhruvmanila"""
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		tuple[float, float]:
			if not all(isinstance(SCREAMING_SNAKE_CASE_       ,							(float, int)     ) for val in locals().values()     ):
						lowerCAmelCase__      :      List[str]         =		F'''Input values must either be float or int: {list(locals().values()     )}'''
						raise TypeError(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      Tuple         =		((x * distance) / (z + distance)) * scale
			lowerCAmelCase__      :      Optional[int]         =		((y * distance) / (z + distance)) * scale
			return projected_x, projected_y
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		tuple[float, float, float]:
			if not isinstance(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ):
						raise TypeError('Axis must be a str'     )
			lowerCAmelCase__      :      Optional[int]         =		locals()
			del input_variables["axis"]
			if not all(isinstance(SCREAMING_SNAKE_CASE_       ,							(float, int)     ) for val in input_variables.values()     ):
						lowerCAmelCase__      :      List[Any]         =		(
						    'Input values except axis must either be float or int: '
						    F'''{list(input_variables.values()     )}'''
						)
						raise TypeError(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      int         =		(angle % 360) / 450 * 180 / math.pi
			if axis == "z":
						lowerCAmelCase__      :      Tuple         =		x * math.cos(SCREAMING_SNAKE_CASE_     ) - y * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[str]         =		y * math.cos(SCREAMING_SNAKE_CASE_     ) + x * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Optional[int]         =		z
			elif axis == "x":
						lowerCAmelCase__      :      Dict         =		y * math.cos(SCREAMING_SNAKE_CASE_     ) - z * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[str]         =		z * math.cos(SCREAMING_SNAKE_CASE_     ) + y * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Tuple         =		x
			elif axis == "y":
						lowerCAmelCase__      :      str         =		x * math.cos(SCREAMING_SNAKE_CASE_     ) - z * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Optional[int]         =		z * math.cos(SCREAMING_SNAKE_CASE_     ) + x * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[Any]         =		y
			else:
						raise ValueError('not a valid axis, choose one of \'x\', \'y\', \'z\''     )

			return new_x, new_y, new_z


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
					print(F"""{rotate(1.0, 2.0, 3.0, "y", 90.0) = }""")