Forest

# B. Forest

#### Problem Statement

Andrew went for a walk in the forest behind LHS and got lost. As he sat there waiting for help, he came up with a problem. Of course, he managed to solve it easily, can you do it too?
The forest is a 2D plane, and you are given the coordinates of $$N$$ $$(1 \leq N \leq 100)$$ trees $$(x, y)$$ $$(1 \leq x, y \leq 10^9)$$. Your job is to find the largest number of trees that lie on the same line. Note that all coordinates are distinct.

Time Limit:
C++: 2.5 seconds
Java, Python: 5 seconds
Memory Limit: 128mb

#### Constraints

$$1 \leq N \leq 100$$
$$1 \leq x, y \leq 10^9$$

#### Input format

The first line has one integer $$N$$ ― the number of trees.
Each of the next $$N$$ lines has two integers $$x$$ and $$y$$ ― the coordinates of a tree.

#### Output format

Output one number, the maximum number of trees that lie on the same line.

5
1 1
2 4
2 2
4 2
3 3

3

#### Sample Explanation

The maximum number of points on a single line is 3. You can have $$(1,1)$$, $$(2,2)$$, and $$(3,3)$$. Another solution is $$(2,4)$$, $$(3,3)$$, and $$(4,2)$$.