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, h, S, L, rad;
	cin >> a >> b >> C;
	rad = M_PI * C / 180.0;
	h = b*sin(rad);
	S = a*h/2;
	L = a + b + sqrt(a*a + b*b - 2*a*b*cos(rad));
	printf("%.8f\n%.8f\n%.8f\n", S, L, h);
	return 0;
}