C - Collinearity

Score : $300$ points

Problem Statement

We have $N$ points on a two-dimensional infinite coordinate plane.

The $i$-th point is at $(x_i,y_i)$.

Is there a triple of distinct points lying on the same line among the $N$ points?

Constraints

• All values in input are integers.
• $3 \leq N \leq 10^2$
• $|x_i|, |y_i| \leq 10^3$
• If $i \neq j$, $(x_i, y_i) \neq (x_j, y_j)$.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$\vdots$

$x_N$ $y_N$

Output

If there is a triple of distinct points lying on the same line, print Yes; otherwise, print No.

4
0 1
0 2
0 3
1 1

Yes

The three points $(0, 1), (0, 2), (0, 3)$ lie on the line $x = 0$.

14
5 5
0 1
2 5
8 0
2 1
0 0
3 6
8 6
5 9
7 9
3 4
9 2
9 8
7 2

No

9
8 2
2 3
1 3
3 7
1 0
8 8
5 6
9 7
0 1

Yes