





def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase = 100_0000 )			->     int:
    lowerCamelCase__    :      int					 =		limit + 1
    lowerCamelCase__    :      Optional[Any]					 =		[0] * limit
    for first_term in range(1						,	_UpperCAmelCase ):
        for n in range(_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase ):
            lowerCamelCase__    :      Optional[Any]					 =		first_term + n / first_term
            if common_difference % 4:  # d must be divisble by 4
                continue
            else:
                common_difference /= 4
                if (
                    first_term > common_difference
                    and first_term < 4 * common_difference
                ):  # since x,y,z are positive integers
                    frequency[n] += 1  # so z>0 and a>d ,also 4d<a

    lowerCamelCase__    :      List[str]					 =		sum(1 for x in frequency[1:limit] if x == 10 )

    return count


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












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()





