AT_past202309_m 線分の交差判定

There are two line segments in the $ xy $ -plane. The endpoints of the $ i $ -th line segment are at coordinates $ (a_i,b_i) $ and $ (c_i,d_i) $ . Determine if these two line segments intersect.

The input is given from Standard Input in the following format: > $ a_1 $ $ b_1 $ $ c_1 $ $ d_1 $ $ a_2 $ $ b_2 $ $ c_2 $ $ d_2 $

Print `Yes` if the two line segments intersect, and `No` otherwise.

### Sample Explanation 1 As shown below, the two line segments intersect at coordinates $ (5,5) $ .  ### Sample Explanation 2  ### Sample Explanation 3  ### Constraints - $ -1000 \leq a_i,b_i,c_i,d_i \leq 1000 $ - $ (a_i,b_i)\neq (c_i,d_i) $ - All input values are integers.