Problem Statement

There are N people in a three-dimensional space. The i-th person is at the coordinates (X_i,Y_i,Z_i).
All people are at different coordinates, and we have X_i>0 for every i.
You will choose a point p=(x,y,z) such that x<0, and take a photo in the positive x-direction.
If the point p and the positions A, B of two people are on the same line in the order p,A,B, then the person at B will not be in the photo.
There are no other potential obstacles.
Find the number of people in the photo when p is chosen to minimize this number.

Input

The input is given from Standard Input in the following format:
N
X_1 Y_1 Z_1
$\vdots$
X_N Y_N Z_N

Output

Print the answer.

Constraints

• $1 \leq N \leq 50$
• $0 < X_i \leq 1000$
• -$1000 \leq Y_i,Z_i \leq 1000$
• The triples (X_i,Y_i,Z_i) are distinct.
• All values in the input are integers.

Sample Input 1

3
1 1 1
2 2 2
100 99 98

Sample Output 1

2

For instance, if you take the photo from the point (-0.5,-0.5,-0.5), it will not show the second person.

Sample Input 2

8
1 1 1
1 1 -1
1 -1 1
1 -1 -1
3 2 2
3 2 -2
3 -2 2
3 -2 -2

Sample Output 2

4

If you take the photo from the point (-1,0,0), it will show four people.

见题面 Input 部分

见题面 Output 部分