Taxicab Geometry

Time limit1sMemory limit128 MB

Summary

Given radius R, compute and print the area of a Euclidean circle and a taxicab-metric circle.

Level: Easy1 of 10
Topics: Math, Geometry, Implementation
Solved: No attempts yet

Problem

In the 19th century, German mathematician Hermann Minkowski introduced taxicab geometry, a form of non-Euclidean geometry.

In taxicab geometry, the distance between two points T1(x1, y1) and T2(x2, y2) is defined as follows.

D(T1, T2) = |x1 - x2| + |y1 - y2|

Except for the distance between two points, all other definitions are the same as in Euclidean geometry. Therefore, a circle in taxicab geometry is also defined as follows.

Circle: the set of all points in a plane that are at a constant distance from a fixed point

Given a radius R, write a program that computes the area of a circle in Euclidean geometry and the area of a circle in taxicab geometry.

Input

The first line contains the radius R. R is a natural number not greater than 10,000.

Output

On the first line, print the area of a circle with radius R in Euclidean geometry.

On the second line, print the area of a circle with radius R in taxicab geometry.

An absolute or relative error up to 0.0001 is accepted.

Hint

References:

Euclidean geometry: Korean Wikipedia, English Wikipedia, Wolfram MathWorld
Non-Euclidean geometry: Korean Wikipedia, English Wikipedia, Wolfram MathWorld
Taxicab geometry: Korean Wikipedia, English Wikipedia, Wolfram MathWorld

Examples3

Example 1
Input
```
1
```
Expected output
```
3.141593
2.000000
```
Example 2
Input
```
21
```
Expected output
```
1385.442360
882.000000
```
Example 3
Input
```
42
```
Expected output
```
5541.769441
3528.000000
```