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;

int main(){
	double a,b,c,d,e,f,S,l,h=0;
	cin>>a>>b>>c;
	e=sin(c*M_PI/180);
	f=cos(c/180*M_PI);
	S=(a*b*e)/2;
	d=sqrt(a*a+b*b-(a*b*f)*2);
	l=a+b+d;
	h=(S*2)/a;
	cout <<setprecision(12)<<S<<" "<<l<<" "<<h <<endl;
	return 0;
}