TRICENTR - Triangle From Centroid

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Given the length of side a of a triangle and the distances from the centroid (the point of concurrence of the medians - red in the picture) to all sides: a, b and c, calculate this triangle's area and the distance (blue line) from the orthocenter (the point of concurrence of the heights - green in the picture) to the centroid.

Input

In the first line integer n - the number of test cases (equal to about 1000). The next n lines - 4 floating point values: the length of side a, and distances from the centroid to sides a, b and c.

Output

n lines consisting of 2 floating point values with 3 digits after the decimal point: the area of the triangle and the distance from the orthocenter to centroid.

Example

Input:
2
3.0 0.8660254038 0.8660254038 0.8660254038
657.8256599140 151.6154399062 213.5392629932 139.4878846649

Output:
3.897 0.000
149604.790 150.275


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つ ◕_◕ ༽つ GIFF AC: 2011-10-18 17:11:27

yeah case 2 area is wrong, should be .797
Disregard this, the test case is correct

Last edit: 2011-10-20 04:50:44
bashrc is back: 2011-07-04 11:31:15

@prab are you printing new line after every case?I got 3 WA's coz of dat

__Pra: 2011-03-12 09:04:24

well my formula is correct but i'm getting different area ..even from scientif calc for case 2!!

Lewin Gan: 2010-04-25 20:22:25

Of course this can be done in java, it's just plugging numbers into a formula: O(1) time


Added by:Patryk Pomykalski
Date:2004-05-22
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