Time Limit: 2 Seconds
Memory Limit: 65536 KB
A, B, C and D are four points on Euclidean plane. AB and CD are two line segments without a common point. E1 and E2 are two ellipses without any common area. E1's focuses are A and B, and E2's focuses are C and D. Can you tell the maximum of S1×S2, where S1 and S2 are the areas of E1 and E2.
There are multiple test cases. The first line of input contains an integer T(T≤ 100) indicating the number of test cases. For each test case:
There are 8 integers in one line, indicating the coordinates of A, B, C and D. Each integer in the input is nonnegative and no more than 100.
For each test case, output the the maximum of S1×S2. Relative error no more than 10-6 will be accepted.