DWITE Online Computer Programming Contest, October 2010, Problem 4

You are considering planting trees around your house, but there are only a few good sites to do so. Furthermore, it would be best if the planted trees surrounded the house — that is, the house is within the area formed between all the trees.

The input will contain 5 test cases, an integer ~3 \le N \le 30~, followed by ~N~ lines of integer ~X\ Y~ pairs, ~-1000 \le X, Y \le 1000~, describing possible plant locations. Consider the house to be a single point at location ~0,0~.

The output will contain 5 lines, an integer number of possible valid configurations for exactly 3 trees.

Notes: the order in which the trees are planted does not matter. The house must be strictly contained within the area; that is, if the house is exactly on the line between two trees, then this configuration does not count.

Sample Input

4
0 1
-1 -1
0 -1
1 -1
6
-1 1
0 1
1 1
-1 -1
0 -1
1 -1

Sample Output

1
2

Problem Resource: DWITE