QUADAREA - Maximal Quadrilateral Area

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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.


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gohanssj9: 2015-04-27 11:14:00

Exactly Abhishek...Thanks to Brahmagupta...but the problem doesnt mention if its cyclic or not...that is a confusion

Jerry Goyal: 2015-04-05 23:20:49

how to know whether it's a cyclic quad.?

Abhishek Kainth: 2015-04-04 21:05:22

Thanks to Brahmagupta!! :D

pvkcse: 2014-05-17 07:21:11

just a four lines of code in python and AC at first attempt...!!!

RAJAT SINGH: 2014-03-13 13:47:19

got AC in first attempt easiest problem in spoj .....if you know some math

ppppppp: 2014-02-17 15:42:31

use double dont use float in c,c++

Aragon!!!: 2014-01-21 19:25:28

just a formula.. :) ...

Praveen : 2014-01-17 18:46:38

My 25th problem on SPOJ...:)

jiglipufff: 2013-12-30 16:40:57

ma 100th... :)

Vaibhav Yenamandra: 2013-08-04 12:43:38

Nice, and easy :D

Last edit: 2013-08-04 17:19:58

Added by:Neal Wu
Date:2008-05-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO