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Description

After $23$ o'clock, our school has turned off the lights. QiQi has nothing to do but count the stars in the sky. Suddenly, a new idea comes to QiQi. He wants to choose no more than four stars as a simple polygon's (not intersect with itself) vertexes, how large can the polygon be?

Input

The first line of the input is an integer $T$ ($T\leq 50$), which stands for the number of test cases you need to solve.

Every test case begins with an integer $N$ ($1\leq N\leq 1000$), indicating the number of stars in the sky. Then $N$ lines follow, every line is a pair of integers $(x, y)$ ($-10000\leq x, y\leq 10000$), indicating the coordinate of a star.

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and starts at $1$. Then output the largest area of the simple polygon. To ensure the answer is an integer, you should double the area. See sample for more details.

Samples

3
3
0 0
1 0
2 0
3
0 0
1 0
0 1
4
0 0
1 0
1 1
0 1

Case #1: 0
Case #2: 1
Case #3: 2

Resources

The 9th UESTC Programming Contest Final