Fox and Meteor Shower

Description:

Input:

The first line contains an integer n (1 ≤ n ≤ 1000). Each of the next n lines contains six integers: t₁, x₁, y₁, t₂, x₂, y₂ — the description of a meteor's orbit: at time t₁, the current meteor is located at the point (x₁, y₁) and at time t₂, the meteor is located at point (x₂, y₂) ( - 10⁶ ≤ t₁, x₁, y₁, t₂, x₂, y₂ ≤ 10⁶; t₁ ≠ t₂).

There will be no two meteors are always in the same position for any time.

Output:

Print a single integer — the maximum number of meteors such that any pair met at the same position at a certain time.

Sample Input:

2
0 0 1 1 0 2
0 1 0 1 2 0

Sample Output:

2

Sample Input:

3
-1 -1 0 3 3 0
0 2 -1 -1 3 -2
-2 0 -1 6 0 3

Sample Output:

3

Sample Input:

4
0 0 0 1 0 1
0 0 1 1 1 1
0 1 1 1 1 0
0 1 0 1 0 0

Sample Output:

1

Sample Input:

1
0 0 0 1 0 0

Sample Output:

1

Note:

In example 1, meteor 1 and 2 meet in t=-1 at (0, 0).

In example 2, meteor 1 and 2 meet in t=1 at (1, 0), meteor 1 and 3 meet in t=0 at (0, 0) and meteor 2 and 3 meet in t=2 at (0, 1).

In example 3, no two meteor meet.

In example 4, there is only 1 meteor, and its velocity is zero.

If your browser doesn't support animation png, please see the gif version here:

http://assets.codeforces.com/images/388e/example1.gif

http://assets.codeforces.com/images/388e/example2.gif

http://assets.codeforces.com/images/388e/example3.gif

http://assets.codeforces.com/images/388e/example4.gif