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
#include <cstdio>
#include <stdlib.h>
#include <cmath>
using namespace std;
int main() {
	int a, b, C;
	scanf("%d %d %d", &a, &b, &C);
	double S, L, h;
	h = b * sin(C * M_PI / 180);
	S = a * h / 2;
	L = a + b + sqrt(pow(a, 2.0) + pow(b, 2.0) - 2 * a * b * cos(C * M_PI / 180));
	printf("%f\n%f\n%f\n", S, L, h);
}
