



def 				A			(		__UpperCAmelCase	)       ->       int:



						'''simple docstring'''






						UpperCAmelCase_     							=     len(__UpperCAmelCase	)
						if n in (0, 1):
												return 0
						return sum(query * (n - i - 1) for i, query in enumerate(sorted(__UpperCAmelCase	)	)	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()










from __future__ import annotations

from pathlib import Path







def 				A			(		__UpperCAmelCase							,					__UpperCAmelCase	)       ->       int:



						'''simple docstring'''






						return pointa[0] * pointa[1] - pointa[1] * pointa[0]







def 				A			(		__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase							,					__UpperCAmelCase	)       ->       bool:



						'''simple docstring'''






						UpperCAmelCase_     							=     (xa, ya)
						UpperCAmelCase_     							=     (xa - xa, ya - ya)
						UpperCAmelCase_     							=     (xa - xa, ya - ya)
						UpperCAmelCase_     							=     -vector_product(__UpperCAmelCase							,					__UpperCAmelCase	) / vector_product(
						    __UpperCAmelCase							,					__UpperCAmelCase	)
						UpperCAmelCase_     							=     +vector_product(__UpperCAmelCase							,					__UpperCAmelCase	) / vector_product(
						    __UpperCAmelCase							,					__UpperCAmelCase	)

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







def 				A			(		__UpperCAmelCase = "p102_triangles.txt"	)       ->       int:



						'''simple docstring'''






						UpperCAmelCase_     							=     Path(__UpperCAmelCase	).parent.joinpath(__UpperCAmelCase	).read_text(encoding='''utf-8'''	)

						UpperCAmelCase_     							=     []
						for line in data.strip().split('''\n'''	):
												triangles.append([int(__UpperCAmelCase	) for number in line.split(''','''	)]	)

						UpperCAmelCase_     							=     0
						UpperCAmelCase_     							=     42

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

						return ret


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





