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() {
	double a, b, C, c, h, PI = acos(-1);
	cin >> a >> b >> C;
	C *= PI / 180;
	h = b * sin(C);
	c = sqrt(a * a + b * b - 2 * a * b * cos(C));
	printf("%.8f\n", a * h / 2);
	printf("%.8f\n", a + b + c);
	printf("%.8f\n", h);
}