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Description

You have 8 circles of equal size and you want to pack them inside a square. You want to minimize the size of the square. The following figure illustrates the minimum way of packing 8 circles inside a square:

The Problem:
Given the radius, r, find the area of the minimum square into which 8 circles of that radius can be packed.

Input

There is one input line, it consists of a positive real number (between 0.001 and 1000, inclusive) denoting the radius, r.

Output

Print the area of the minimum square where 8 circles of radius r can be packed. Print 5 digits after the decimal. Your output is considered correct if it is within ±0.00001 of the judge’s output.

Samples

Input Copy
0.1
Output
0.34383

Source

UCF2019 PRACTICE
Problem Information

 Time Limit: 1000MS (C/C++,Others×2) Memory Limit: 128MB (C/C++,Others×2) Special Judge: No AC/Submit: 10 / 28 Tags:
Contests involved

 1037. UCF 2019 Practice