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 <cstdio>
#define _USE_MATH_DEFINES
#include <cmath>
#define rad(r) (r * M_PI / 180)
int main() {
	double a, b, C, S;
	scanf("%lf %lf %lf", &a, &b, &C);
	S = 0.5 * a * b * sin(rad(C));
	printf("%f\n", S);
	printf("%f\n", a + b + sqrt(a*a + b*b - 2 * a*b*cos(rad(C))));
	printf("%f\n", 2 * S / a);
}