We have two lines on a 2D Cartesian plane. These lines are labeled as AB and CD where first line goes through points A and B and second one goes through C and D. We are interested to know answers of the following three questions:

1. Are the lines parallel or the same line?
2. Do they intersect?
3. Are they perpendicular?

You are given the four points A, B, C, D. Answer all three question mentioned above.

Input

There are multiple test cases. Each test case consists of four lines. Each line contains two integers representing a point on Cartesian plane.

Sequence of points are A, B, C, D.

Output

For each test case output in the following format:

Case $X: ans1 ans2 ans3

Where “X” will be replaced by case number starting from 0. “ans1”, “ans2”, “ans3” will be either “yes” or “no” (without the quote).

Example

Input:
0 0
5 0
1 1
5 1
0 0
5 0
-1 -1
-1 1
0 0
5 0
-1 -1
1 1

Output:
Case $0: yes no no
Case $1: no yes yes
Case $2: no yes no