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.

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.

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.