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?

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.

Constraints

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

Sample Input 1

4
0 1
0 2
0 3
1 1

Sample Output 1

Yes

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

Sample Input 2

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

Sample Output 2

No

Sample Input 3

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

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分