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(void){
	double a,b,c;
	double s,l,h;
	cin>>a>>b>>c;
	s=0.5*a*b*sin(M_PI*c/180);
	l=sqrt(pow(a,2)+pow(b,2)-2*a*b*cos(M_PI*c/180))+a+b;
	h=b*sin(M_PI*c/180);
	cout<<fixed;
	cout<<s<<endl;
	cout<<l<<endl;
	cout<<h<<endl;
	return 0;
}