Problem: For given two sides of a triangle a and b and the angle C between them, calculate the following properties:

* S: Area of the triangle
* L: The length of the circumference of the triangle
* h: The height of the triangle with side a as a bottom edge



Input

The length of a, the length of b and the angle C are given in integers.

Output

Print S, L and h in a line respectively. The output should not contain an absolute error greater than 10-4.

Example

Input

4 3 90


Output

6.00000000
12.00000000
3.00000000

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
constexpr ll mod=1e9+7;

int main()
{
  cout<<fixed<<setprecision(20);
  double a,b,c;
  cin>>a>>b>>c;
  c=c/180*M_PI;
  cout<<0.5*a*b*sin(c)<<" ";
  cout<<a+b+sqrt(a*a+b*b-2*a*b*cos(c))<<" ";
  cout<<b*sin(c)<<endl;
}