QUADAREA  Maximal Quadrilateral Area
You are trying to build a house, but unfortunately you currently have only four available walls with side lengths a, b, c, and d. You want your house to be as big as possible, so you would like to know the largest possible area of any quadrilateral you can construct with these four side lengths.
Input
The first line contains the integer T (1 ≤ T ≤ 2,000), the number of tests. Each test contains a single line with four real numbers: a, b, c, and d (0 < a, b, c, d < 1,000). Note that it will always be possible to form a valid quadrilateral with these lengths; that is, the sum of any three side lengths will be strictly larger than the other one.
Output
For each test case, print a single line containing the largest possible area. Your output will be accepted if it is within 0.01 of the official answer.
Example
Input: 2 1 2 1 2 0.5 0.5 0.5 0.5 Output: 2.00 0.25
For the first test case, it is optimal to construct a rectangle, and for the second, a square is optimal.
hide comments
gohanssj9:
20150427 11:14:00
Exactly Abhishek...Thanks to Brahmagupta...but the problem doesnt mention if its cyclic or not...that is a confusion


Jerry Goyal:
20150405 23:20:49
how to know whether it's a cyclic quad.? 

Abhishek Kainth:
20150404 21:05:22
Thanks to Brahmagupta!! :D 

pvkcse:
20140517 07:21:11
just a four lines of code in python and AC at first attempt...!!! 

RAJAT SINGH:
20140313 13:47:19
got AC in first attempt easiest problem in spoj .....if you know some math 

ppppppp:
20140217 15:42:31
use double dont use float in c,c++ 

Aragon!!!:
20140121 19:25:28
just a formula.. :) ... 

Praveen :
20140117 18:46:38
My 25th problem on SPOJ...:) 

jiglipufff:
20131230 16:40:57
ma 100th... :) 

Vaibhav Yenamandra:
20130804 12:43:38
Nice, and easy :D Last edit: 20130804 17:19:58 
Added by:  Neal Wu 
Date:  20080524 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 