Description
Cow curling is a popular cold-weather sport played in the Moolympics. Like regular curling, the sport involves two teams, each of which slides N heavy stones (3 <= N <= 50,000) across a sheet of ice. At the end of the game, there are 2N stones on the ice, each located at a distinct 2D point. Scoring in the cow version of curling is a bit curious, however. A stone is said to be "captured" if it is contained inside a triangle whose corners are stones owned by the opponent (a stone on the boundary of such a triangle also counts as being captured). The score for a team is the number of opponent stones that are captured. Please help compute the final score of a cow curling match, given the locations of all 2N stones.
Input
* Line 1: The integer N.
* Lines 2..1+N: Each line contains 2 integers specifying the x and y coordinates of a stone for team A (each coordinate lies in the range -40,000 .. +40,000).
* Lines 2+N..1+2N: Each line contains 2 integers specifying the x and y coordinates of a stone for team B (each coordinate lies in the range -40,000 .. +40,000).
Output
* Line 1: Two space-separated integers, giving the scores for teams A and B.
Sample Input
40 0
0 2
2 0
2 2
1 1
1 10
-10 3
10 3
INPUT DETAILS: Each team owns 4 stones. Team A has stones at (0,0), (0,2), (2,0), and (2,2), and team B has stones at (1,1), (1,10), (-10,3), and (10,3).
Sample Output
1 2OUTPUT DETAILS: Team A captures their opponent's stone at (1,1). Team B captures their opponent's stones at (0,2) and (2,2).
