





from string import ascii_uppercase

_UpperCAmelCase				:       List[str]	   =				{str(ord(c) - 55): c for c in ascii_uppercase}


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase )			->     str:
    if isinstance(_UpperCAmelCase						,	_UpperCAmelCase ):
        raise TypeError('int() can\'t convert non-string with explicit base' )
    if num < 0:
        raise ValueError('parameter must be positive int' )
    if isinstance(_UpperCAmelCase						,	_UpperCAmelCase ):
        raise TypeError('\'str\' object cannot be interpreted as an integer' )
    if isinstance(_UpperCAmelCase						,	_UpperCAmelCase ):
        raise TypeError('\'float\' object cannot be interpreted as an integer' )
    if base in (0, 1):
        raise ValueError('base must be >= 2' )
    if base > 36:
        raise ValueError('base must be <= 36' )
    lowerCamelCase__    :      Optional[Any]					 =		''
    lowerCamelCase__    :      List[str]					 =		0
    lowerCamelCase__    :      Dict					 =		0
    while div != 1:
        lowerCamelCase__ ,							lowerCamelCase__    :      List[str]					 =		divmod(_UpperCAmelCase						,	_UpperCAmelCase )
        if base >= 11 and 9 < mod < 36:
            lowerCamelCase__    :      Dict					 =		ALPHABET_VALUES[str(_UpperCAmelCase )]
        else:
            lowerCamelCase__    :      int					 =		str(_UpperCAmelCase )
        new_value += actual_value
        lowerCamelCase__    :      List[Any]					 =		num // base
        lowerCamelCase__    :      Optional[int]					 =		div
        if div == 0:
            return str(new_value[::-1] )
        elif div == 1:
            new_value += str(_UpperCAmelCase )
            return str(new_value[::-1] )

    return new_value[::-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    for base in range(2, 37):
        for num in range(10_00):
            assert int(decimal_to_any(num, base), base) == num, (
                num,
                base,
                decimal_to_any(num, base),
                int(decimal_to_any(num, base), base),
            )












from __future__ import annotations


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase )			->     list[tuple[int, int]]:
    lowerCamelCase__ ,							lowerCamelCase__    :      Union[str, Any]					 =		position
    lowerCamelCase__    :      Optional[Any]					 =		[
        (y + 1, x + 2),
        (y - 1, x + 2),
        (y + 1, x - 2),
        (y - 1, x - 2),
        (y + 2, x + 1),
        (y + 2, x - 1),
        (y - 2, x + 1),
        (y - 2, x - 1),
    ]
    lowerCamelCase__    :      Dict					 =		[]

    for position in positions:
        lowerCamelCase__ ,							lowerCamelCase__    :      Optional[int]					 =		position
        if 0 <= y_test < n and 0 <= x_test < n:
            permissible_positions.append(_UpperCAmelCase )

    return permissible_positions


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase )			->     bool:
    return not any(elem == 0 for row in board for elem in row )


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase )			->     bool:

    if is_complete(_UpperCAmelCase ):
        return True

    for position in get_valid_pos(_UpperCAmelCase						,	len(_UpperCAmelCase ) ):
        lowerCamelCase__ ,							lowerCamelCase__    :      Optional[int]					 =		position

        if board[y][x] == 0:
            lowerCamelCase__    :      List[Any]					 =		curr + 1
            if open_knight_tour_helper(_UpperCAmelCase						,	_UpperCAmelCase						,	curr + 1 ):
                return True
            lowerCamelCase__    :      Optional[Any]					 =		0

    return False


def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase )			->     list[list[int]]:
    lowerCamelCase__    :      Any					 =		[[0 for i in range(_UpperCAmelCase )] for j in range(_UpperCAmelCase )]

    for i in range(_UpperCAmelCase ):
        for j in range(_UpperCAmelCase ):
            lowerCamelCase__    :      Optional[int]					 =		1
            if open_knight_tour_helper(_UpperCAmelCase						,	(i, j)						,	1 ):
                return board
            lowerCamelCase__    :      Optional[Any]					 =		0

    lowerCamelCase__    :      Any					 =		F"""Open Kight Tour cannot be performed on a board of size {n}"""
    raise ValueError(_UpperCAmelCase )


if __name__ == "__main__":
    import doctest

    doctest.testmod()





