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 <math.h>
#include <stdio.h>
using namespace std;

int main() {
	double a, b, c, d, s, l, h;
	cin >> a >> b >> c;
	c = c * M_PI / 180;
	d = sqrt(a * a + b * b - 2 * a * b * cos(c));
	l = a + b + d;
	s = 1.0 / 2.0 * a * b * sin(c);
	h = s * 2 / a;
	printf("%.6f\n%.6f\n%.6f\n", s, l, h);
}