write a go solution for G. Good Robot Pathstime limit per test7.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputOn a Cartesian plane, there are n distinct points painted black, while all other points are painted white. Each black point has integer coordinates.There is also a robot that can move one unit in any of the directions 'U' (up), 'D' (down), 'L' (left), or 'R' (right) with a single command.A path of the robot from point p_1 to point p_2 is a sequence of commands such that if the robot, starting at point p_1, executes this sequence, it will arrive at point p_2.The shortest path of the robot from point p_1 to point p_2 is a path whose sequence consists of the minimum possible number of commands.You need to count the number of pairs of points p_i, p_j (ineqj) such that for this pair of points the following condition holds:All points with integer coordinates on any shortest path of the robot from point p_i to point p_j are painted black.InputEach test contains multiple test cases. The first line contains the number of test cases t (1<=t<=10^4). The description of the test cases follows. The first line of each test case contains a single integer n (1<=n<=5*10^5) — the number of points painted black.The next n lines of each test case contain two integers x_i,y_i (-10^9<=x_i,y_i<=10^9) — the coordinates of point p_i. All points are pairwise distinct.It is guaranteed that the sum of n across all test cases does not exceed 5*10^5.OutputFor each test case, output a single integer — the answer to the problem.ExampleInput350 01 00 11 12 0180 0-1 0-2 00 -1-1 -10 11 10 21 22 21 36 -25 -25 -36 -34 -33 -35 -43-100 100-101 99-99 101Output16
70
0
NoteIn the first test case, there are 16 suitable pairs of points:  p_1,p_2  p_1,p_3  p_1,p_4  p_1,p_5  p_2,p_1  p_2,p_3  p_2,p_4  p_2,p_5  p_3,p_1  p_3,p_2  p_3,p_4  p_4,p_1  p_4,p_2  p_4,p_3  p_5,p_1  p_5,p_2. Output only the code with no comments, explanation, or additional text.