PROBLEM STATEMENT

Consider a N-level pyramid built of unit cubes. An example for N=3 can be seen in the image below.





Formally, a pyramid of size N has N levels, where the i-th level (counting from the top) contains 
an i by i grid of unit cubes.



You have K cubes. First, you select a suitable pyramid size as follows: If K is exactly the number 
of cubes necessary to build a pyramid of size N for some N, you pick that size. Otherwise, you 
pick the smallest pyramid size you can not build.



Now you start building the pyramid in a systematic bottom-up way. First you build the complete 
bottom level, then you build the level above that, etc. When building a level, also proceed in a 
systematic way, starting the next row only when the previous one is full.



For example, for 21 cubes you should get the following incomplete pyramid:





Given an int K specifying the number of cubes you have, return the surface area of the possibly 
incomplete pyramid you will build according to the instructions above.


DEFINITION
Class:PyramidOfCubes
Method:surface
Parameters:int
Returns:double
Method signature:double surface(int K)


NOTES
-The returned value must be accurate to within a relative or absolute value of 1E-9.
-The bottom sides of the cubes on the bottommost level are a part of the surface.


CONSTRAINTS
-K will be between 1 and 1,000,000,000, inclusive.


EXAMPLES

0)
14

Returns: 42.0

The first example from the problem statement.

1)
21

Returns: 58.0

The second example from the problem statement.

2)
1

Returns: 6.0

A single cube.

3)
2

Returns: 10.0

Two cubes next to each other.

4)
451234

Returns: 47498.0

Quite a lot of cubes.

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 unauthorized use or reproduction of this information without the prior written consent of 
 TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.
 
  This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.