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 <iostream>
#include <cstdio>
#include <cmath> 
using namespace std;

int main()
{
    double a,b,sinB,c,C,S,L,h;
	cin>>a>>b>>C;
	S=0.5*a*b*sin(C*M_PI/180);
	c=sqrt(pow(a,2.0)+pow(b,2.0)-2*a*b*cos(C*M_PI/180));
	L=a+b+c;
	sinB=(2*S)/(a*c);
	h=c*sinB;
	
	printf("%10f\n%10f\n%10f\n",S,L,h);
    return 0;
}