


'''simple docstring'''


import math






def 			__lowerCAmelCase			(__lowerCAmelCase ):
		if not isinstance(snake_case_   ,			snake_case_ ):
				_UpperCAmelCase		:							List[Any]             =   F"""Input value of [number={number}] must be an integer"""
				raise TypeError(snake_case_ )
		if number < 1:
				_UpperCAmelCase		:							str             =   F"""Input value of [number={number}] must be a positive integer"""
				raise ValueError(snake_case_ )
		_UpperCAmelCase		:							Union[str, Any]             =   [number]
		while number != 1:
				if number % 2 == 0:
						_UpperCAmelCase		:							Tuple             =   math.floor(math.sqrt(snake_case_ ) )
				else:
						_UpperCAmelCase		:							Optional[int]             =   math.floor(
						    math.sqrt(snake_case_ ) * math.sqrt(snake_case_ ) * math.sqrt(snake_case_ ) )
				sequence.append(snake_case_ )
		return sequence


if __name__ == "__main__":
						import doctest

						doctest.testmod()






'''simple docstring'''







from __future__ import annotations

from pathlib import Path






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_	):
	return pointa[0] * pointa[1] - pointa[1] * pointa[0]






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_							,       snake_case_							,       snake_case_							,       snake_case_							,       snake_case_	):
	_lowercase							=     (xa, ya)
	_lowercase							=     (xa - xa, ya - ya)
	_lowercase							=     (xa - xa, ya - ya)
	_lowercase							=     -vector_product(snake_case_							,       snake_case_	) / vector_product(
	    snake_case_							,       snake_case_	)
	_lowercase							=     +vector_product(snake_case_							,       snake_case_	) / vector_product(
	    snake_case_							,       snake_case_	)

	return a > 0 and b > 0 and a + b < 1






def 					_SCREAMING_SNAKE_CASE		(						snake_case_ = "p102_triangles.txt"	):
	_lowercase							=     Path(snake_case_	).parent.joinpath(snake_case_	).read_text(encoding="""utf-8"""	)

	_lowercase							=     []
	for line in data.strip().split("""\n"""	):
		triangles.append([int(snake_case_	) for number in line.split(""","""	)]	)

	_lowercase							=     0
	_lowercase							=     42

	for triangle in triangles:
		ret += contains_origin(*snake_case_	)

	return ret


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




