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.

给二维平面n个白点和n个黑点，定义一个点被捕获是在另外一种颜色的某三个点组成的三角形内部(包括边界)，问被捕获的黑白点各有多少

Format

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.

Samples

4
0 0
0 2
2 0
2 2
1 1
1 10
-10 3
10 3

1 2

Limitation

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). OUTPUT DETAILS: Team A captures their opponent's stone at (1,1). Team B captures their opponent's stones at (0,2) and (2,2).