After a successful day at the casino, you're heading back to the exchange machine with your chips when someone accidentally bumps into you, scattering them across the floor. As you begin to pick them up, you notice something interesting, some of the chips have landed in a perfectly straight line. It looks pretty cool!

What is the maximum number of chips that have landed in a straight line?

Input

The first line consists of an integer ~n~ ~(2 \leq n \leq 1000)~, the number of chips that have fallen on the floor.

The next ~n~ lines contain ~x_i~ and ~y_i~ ~(0 \leq x_i, y_i \leq 10^8)~, representing the position on the floor that the ~i~th chip has landed.

Output

Output the maximum number of chips lying in a straight line.

Clarifications

• For this question, assume chips are points with no width/depth.
• These points must lie on a straight line.

Example

Input

5
1 0
3 1
2 2
5 2
4 0

Output

3

There are ~3~ chips that lie on a single, straight line, which is the maximum you can get.

Input

6
0 1
0 2
0 5
0 10
1 1
2 2

Output

4