PRISMSA - TRIANGULAR PRISM


In a far away nation, all the liquid substance are stored in a can of shape of a triangular prism. According to belief, this will bring security to their children. As they are very resource conservative people, unlike the earth natives, they want to use as less as possible amount of the raw material to be used for producing the can, which directly depends on the surface area of the can. Mr. Buzz Light Year, of Star Command, is provided with the responsiblity to find the minimal suface area required to prodce a can of a given volume.

Notes:

  • Consider the material the can is made of to be infinitely thin.
  • The base of the prism is equilateral triangle.
  • Some formulas:
    • a: triangle side's length.
    • h: height of the prism.
    • Volume, V =  (a2 * sin(60°) * h)/2
    • Surface Area, S = a2*sin(60°) + 3*a*h
  • If not provided by a library, use the alue of 2*acos(0) for PI(π).
  • Reminder:
    • If your result is within 10-2 of the expected result, your solution will be evaluated as correct.
    • If your result is between (1-10-2)*expected and (1+10-2)*expected, it will be evaluated as correct.

Prism

Constraints

Given volume will be an integer between 1 and 100000, inclusive.

Input

Input begins with a integer t, number of test cases. Then follows t lines, each one containing an integer, V, given volume.

Output

For each volume, print the minimum surface area required to produce the can in separate line.

Example

Input:
5
10
5
100
245
5421

Output:
30.3872837089
19.1427891970
141.0452767471
256.3318686611
2020.2796324002

Explanation for test case 1:
Volume = 10, a = 3.41995, h = 1.97451, Minimum Surface Area = 30.3872837089


hide comments
rohit9934: 2017-03-11 18:54:36

Spelling of precision as **son cost me 1WA. Try at your own risk because ultimately you'll learn nothing except simple math which you have studied in high school.AC in 2nd Go. 0.00 s.

taiken: 2017-02-02 22:00:15

Take into consideration the precision. Solution was right, but precision was set too low, so it gave WA. Set precision higher and AC.

ROHIT Kumar: 2015-08-11 22:12:51

easy clas 12 level ....after this learned two new thing in c++ ...specially use of built in functions..

Daljeet Singh: 2015-03-23 21:11:40

very easy only 6 line of code

Last edit: 2015-03-23 21:13:28
Alexandre Henrique Afonso Campos: 2014-03-11 03:03:52

I enjoyed very much solving this problem :) I filled one page with math equations. Coding was a detail.

Anmol Pandey: 2014-01-18 10:18:49

Easy Problem completes my 50..

pika_pika: 2013-07-07 13:52:49

python nails it... AC in 1st attempt

ওয়াসী (Wasi): 2013-05-29 16:57:38

Nice and easy!
Solved it with python 3
run time 0.11
:D

Anirudh: 2013-02-18 17:42:53

Use double if getting stuck !

Jhoan Es Un Bruto: 2012-08-02 21:25:25

very easy, sure tutorial


Added by:abhiranjan
Date:2011-02-18
Time limit:0.375s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:IIITM Local Contest