Chef and Triangles

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Chef has come to a 2 dimensional garden in which there are N points. Each point has coordinates (x, y), where x can either be 1 or 2 or 3. Chef will now choose every triplet of these N points and make a triangle from it. You need to tell the sum of areas of all the triangles the Chef makes.
Note that some of the triplets might not form proper triangles, and would end up as a line or a point (ie. degenerate), but that is fine because their area will be zero.
Input
 The first line contains a single integer T, the number of test cases. The description of each testcase follows.
 The first line of each test case contains an integer N denoting the number of points on the plane.
 The next N lines contain 2 space separated integers x and y denoting the coordinates of the points.
Output
For each test case, output a single line containing the answer. Your answer will be considered correct if the absolute error is less than or equal to 10^{2}.
Constraints
 1 ≤ T ≤ 20
 1 ≤ N ≤ 2000
 1 ≤ x ≤ 3
 1 ≤ y ≤10^{6}
 All (x, y) pairs are distinct
Example
Input: 2 3 1 1 2 1 3 3 4 1 1 2 2 2 1 3 3 Output: 1.0 2.0
Explanation:
Test Case 1: There is only one triangle which has nonzero area, and it's area is 1, hence the output.
Test Case 2: Let the points be A(1,1), B(2,2), C(2,1), D(3,3). There are 3 non degenerate triangles possible.
Author:  usaxena95 
Tags  easymedium, geometry, gwr17rol, usaxena95 
Date Added:  8122017 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY 
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