You are given $N$ points on a 2D plane. The coordinates of the $i$-th point are $(x_i, y_i)$. You will mark some of these $N$ points such that the following condition is satisfied:

• There is no convex quadrilateral whose four distinct vertices are among the marked points.

Find the maximum possible number of marked points.

Definition of Convex Quadrilateral

A quadrilateral formed by four distinct points on a plane is a convex quadrilateral if it satisfies all of the following conditions:

• No three vertices are collinear.
• Non-adjacent edges do not share a common point.
• Every interior angle of the quadrilateral is strictly less than $180$ degrees.

Input

The input is given in the following format:

$$\begin{aligned} &N \\ &x_1 \ y_1 \\ &x_2 \ y_2 \\ &\vdots \\ &x_N \ y_N \end{aligned}$$

• All input values are integers.
• $4 \le N \le 500$
• $|x_i|, |y_i| \le 10^8$
• $(x_i, y_i) \ne (x_j, y_j)$ for $i \ne j$.

Output

Print the answer on a single line.

Examples

Input 1

5
0 0
-1 0
0 -1
1 0
0 1

Output 1

4

Input 2

5
0 0
1 1
2 2
2 3
3 2

Output 2

5

Input 3

7
-1 8
11 8
-4 -2
19 12
-8 -6
7 6
-1 2

Output 3

6

Input 4

4
0 0
2 0
1 -1
0 1

Output 4

3

Note

In the first example, you can mark four points excluding $(-1, 0)$. If you mark all points, there exists a convex quadrilateral whose vertices are four points excluding $(0, 0)$, which violates the condition.