Migrated from Lutece 484 Division

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Description

On a two dimension plane, you are given a convex polygon and a point which is out of the polygon. You should find a ray whose endpoint is the given point, and divides the convex polygon into two parts with equal area.

Input

First an integer $T$ indicates the number of test cases.

Every test case begins with an integer $N$, which is the number of vertexes of the convex polygon. Then $N$ points follow, specifying the convex polygon in counterclockwise. Finally a point which is the endpoint of the ray ends the test case. A point is consist of two integers $(x, y)$, and the area of the convex polygon is positive.

$T \leq 100$;

$3 \leq N \leq 100$;

$-10000 \leq x, y \leq 10000$;

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and starts at $1$. Then output the unit direction vector of the ray rounding to four digits after the decimal point. See sample for more details.

Samples

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

Case #1: 0.7071 0.7071
Case #2: 1.0000 0.0000

Resources

Sichuan State Programming Contest 2011