AT_abc422_e [ABC422E] Colinear

There are $ N $ points on a two-dimensional plane. $ N $ is odd. The $ i $ -th point is at $ (x_i, y_i) $ . All point coordinates are distinct. Determine whether there exists a line passing through more than half of the $ N $ points, and if so, output it. For any input satisfying the constraints, if a line satisfying the condition exists, it can be expressed as $ ax+by+c=0 $ using integers $ a,b,c $ with $ -10^{18} \leq a,b,c \leq 10^{18} $ (where $ (a,b,c) \neq (0,0,0) $ ). Output these $ a,b,c $ .

The input is given from Standard Input in the following format: > $ N $ $ x_1 $ $ y_1 $ $ x_2 $ $ y_2 $ $ \vdots $ $ x_N $ $ y_N $

If no line satisfying the condition exists, output `No`. If a line satisfying the condition exists, output two lines. On the first line, output `Yes`, and on the second line, output $ a,b,c $ in this order separated by spaces. $ a,b,c $ must satisfy $ -10^{18} \leq a,b,c \leq 10^{18} $ and $ (a,b,c) \neq (0,0,0) $ . If there are multiple solutions, any of them will be considered correct.

### Sample Explanation 1 The line $ 2x+y-8=0 $ passes through the $ 2 $ nd and $ 3 $ rd points, so it satisfies the condition. ### Sample Explanation 2 No line satisfying the condition exists. ### Constraints - $ 3 \leq N \leq 5 \times 10^5 $ - $ N $ is odd. - $ -10^8 \leq x_i \leq 10^8 $ - $ -10^8 \leq y_i \leq 10^8 $ - If $ i \neq j $ , then $ (x_i, y_i) \neq (x_j, y_j) $ . - All input values are integers.