code: from __future__ import annotations
  
  from pathlib import Path
  def 		snake_case__  (		lowercase       ,							lowercase				):
     return pointa[0] * pointa[1] - pointa[1] * pointa[0]
  def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase       ,							lowercase       ,							lowercase       ,							lowercase				):
     lowerCAmelCase_:       tuple[int, int]         =  (xa, ya)
     lowerCAmelCase_:       tuple[int, int]         =  (xa - xa, ya - ya)
     lowerCAmelCase_:       tuple[int, int]         =  (xa - xa, ya - ya)
     lowerCAmelCase_:       float         =  -vector_product(lowercase       ,							lowercase				) / vector_product(
         lowercase       ,							lowercase				)
     lowerCAmelCase_:       float         =  +vector_product(lowercase       ,							lowercase				) / vector_product(
         lowercase       ,							lowercase				)
  
     return a > 0 and b > 0 and a + b < 1
  def 		snake_case__  (		lowercase = "p102_triangles.txt"				):
     lowerCAmelCase_:       str         =  Path(lowercase				).parent.joinpath(lowercase				).read_text(encoding="utf-8"				)
  
     lowerCAmelCase_:       list[list[int]]         =  []
     for line in data.strip().split("\n"				):
        triangles.append([int(lowercase				) for number in line.split(","				)]				)
  
     lowerCAmelCase_:       int         =  0
     lowerCAmelCase_:       list[int]
  
     for triangle in triangles:
        ret += contains_origin(*lowercase				)
  
     return ret
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')
style_context: def 		snake_case__  (		lowercase = 998001				):
  
     # fetches the next number
     for number in range(n - 1       ,							9999       ,							-1				):
        lowerCAmelCase_:       str         =  str(lowercase				)
  
        # checks whether 'str_number' is a palindrome.
        if str_number == str_number[::-1]:
           lowerCAmelCase_:       List[str]         =  999
  
           # if 'number' is a product of two 3-digit numbers
           # then number is the answer otherwise fetch next number.
           while divisor != 99:
              if (number % divisor == 0) and (len(str(number // divisor				)				) == 3.0):
                 return number
              divisor -= 1
     raise ValueError("That number is larger than our acceptable range."				)
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')