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 file DATA4.txt will contain 5 sets of input, an integer 3 <= N <= 30, followed by N lines of integer X Y pairs, -1000 <= X, Y <= 1000, describing possible plant locations. Consider the house to be a single point at location 0,0.

The output file OUT4.txt will contain 5 lines of output, 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.

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

1
2