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

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