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 PI = 3.14159265359;
	double a,b,C,S,L,h;

	cin >> a >> b >> C;

	h = b*sin(C/180.0*PI);
	S = a*h/2.0;
	L = sqrt(pow(h,2.0)+pow(a-b*cos(C/180.0*PI),2.0))+a+b;

	printf("%.08lf %.08lf %.08lf",S,L,h);

	return 0;
}