Problem B. Ball of fir

Author:G. Grenkin   Time limit:1 sec
Input file:input.txt   Memory limit:256 Mb
Output file:output.txt  

Statement

Mathematicians from the Institute of New Year Research developed a mathematical model of the New Year fir-tree. In this model the fir is supposed to be a sphere with a radius of 1 meter. Modeling of a fir garland is, however, more complicated.

A fir garland is modeled with a curve located on the sphere. The curve begins at the topmost point of the sphere, ends at the bottommost point of the sphere, and makes exactly N turns around it.

Consider spherical coordinates φ (longitude) and θ (latitude). The initial value of longitude equals 0, longitude makes exactly N turns and the final value equals 0 again. The initial value of latitude equals 90°, the final value equals  − 90°. The increment of latitude is proportional to the increment of longitude.

Your program must, for a given value of N, calculate the length of the curve which models a fir garland.

Input file format

Input file contains a single integer N.

Output file format

Output file must contain a single real number — the length of the curve (in meters) with at least 3 correct digits after decimal point.

Constraints

1 ≤ N ≤ 100

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
1
5.270
2
3
12.612

0.313s 0.018s 15