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;
	cin >> a >> b >> C;
	double PI = acos(-1);
	printf("%.10f\n", a * b * sin(C * PI / 180) / 2);
	printf("%.10f\n", a + b + sqrt( a * a + b * b - 2 * a * b * cos(C * PI / 180)));
	printf("%.10f\n", b * sin(C * PI / 180));
}