





import enum
import shutil
import sys


_UpperCAmelCase     ,_UpperCAmelCase       : List[Any]			     =       shutil.get_terminal_size()

_UpperCAmelCase       : Union[str, Any]			     =       {"""UP""": """A""", """DOWN""": """B""", """RIGHT""": """C""", """LEFT""": """D"""}

class      lowerCAmelCase							(      enum.Enum    ):
 UpperCAmelCase__									=	0
 UpperCAmelCase__									=	1


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase=""				)    ->  int:
    sys.stdout.write(str(_UpperCAmelCase				) + end				)
    sys.stdout.flush()


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase		,			_UpperCAmelCase=""				)    ->  Union[str, Any]:
    forceWrite(F"""\u001b[{color}m{content}\u001b[0m"""		,			_UpperCAmelCase				)


def  SCREAMING_SNAKE_CASE   ( )    ->  Dict:
    forceWrite('\r'				)


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase		,			_UpperCAmelCase				)    ->  Optional[Any]:
    forceWrite(F"""\033[{num_lines}{CURSOR_TO_CHAR[direction.upper()]}"""				)


def  SCREAMING_SNAKE_CASE   ( )    ->  int:
    forceWrite(' ' * TERMINAL_WIDTH				)
    reset_cursor()


def  SCREAMING_SNAKE_CASE   ( )    ->  Optional[Any]:
    reset_cursor()
    forceWrite('-' * TERMINAL_WIDTH				)












from collections import defaultdict
from math import ceil, sqrt


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 100_0000		,			_UpperCAmelCase = 10				)    ->  int:
    lowerCamelCase__					:   defaultdict      				=	defaultdict(_UpperCAmelCase				)

    for outer_width in range(3		,			(t_limit // 4) + 2				):
        if outer_width * outer_width > t_limit:
            lowerCamelCase__					:   List[str]      				=	max(
                ceil(sqrt(outer_width * outer_width - t_limit				)				)		,			1				)
        else:
            lowerCamelCase__					:   int      				=	1

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(_UpperCAmelCase		,			outer_width - 1		,			2				):
            count[outer_width * outer_width - hole_width * hole_width] += 1

    return sum(1 for n in count.values() if 1 <= n <= 10				)


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





