VZLA2019D - Drawing Polygrams

no tags 

Drawing stars on the last page of a notebook is a very entertaining hobby. Did you know these cute "stars" are actually called polygrams?

Given a regular polygon with p vertices, we define a polygram p/q, as the resultant polygon obtained after connecting every i-th vertex with the (i+q)-th vertex.

You may know the polygram 5/2 as pentagram

Another example is the hexagram 6/2. Given that 6 and 2 are not coprime, this polygram is composed by two 3/1 polygrams

Star polygons
Given a regular polygon with p vertices, its radius R (the distance from its center to any vertex) and a number q, can you calculate the area of the polygram p/q?

It is guaranteed that the resultant polygon will not be degenerated, i.e q ≠ p/2 and q ≠ p

Input

The first and only line of the input contains three integers p, q and r

Output

Print in a single line the area of the resultant polygram p/q with radius r. Print the answer with exactly five decimal places

Example

Input:
5 4 2

Output:
9.51057

Input:
10 4 5
Output:
40.61496

Constraints

3 ≤ p ≤ 103
1 ≤ q < p
1 ≤ r ≤ 100
q ≠ p/2 and q ≠ p



Added by:Samuel Nacache
Date:2019-10-27
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Samuel Nacache - Used for Venezuelan 2019 ICPC Local Contest