There is an old country and the king fell in love with a devil. The devil always asks the king to do some crazy things. Although the king used to be wise and beloved by his people. Now he is just like a boy in love and can’t refuse any request from the devil. Also, this devil is looking like a very cute Loli.
Y*wan find that the only way to save this country is to kill every loli. Y*wan is fine about that because he doesn't like loli. But the princess's knight's member just thinks he is insane. So they compete in an algorithm contest.
In this contest, Y*wan suck at this problem, if y*wan can't win, the mankind will become extinct, so it's your turn to help y*wan solve this problem.
There are n points in the plane, you pick a random point in [0,X] x [0,Y], after that you output the second nearest squared distance from this point to those n points. What is the expectation of your output?
The first line contains an integer T, denoting the number of the test cases.
For each test case, the first line contains 3 integers n,X,Y.
The next n lines, each contains 2 integers x, y, denote that there is a point x,y.
0<=X,Y<=100 , -200<=x,y<=200
For each test case, output the answer in one line.
This problem is special judged. The relative error less than 1e-6 will be accepted.
2 10 10
- Hero’s assistant