## VZLA2019D - Drawing Polygrams

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

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 2Output:9.5105710 4 5

Input:40.61496

Output:

### Constraints

3 ≤ p ≤ 10^{3}

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 |