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 <cmath>
#include <cstdio>

using namespace std;

int main() {
    double a, b, c;
    cin >> a >> b >> c;
    c *= (M_PI/180);
    printf("%.10lf\n", (1.0/2.0)*a*b*sin(c));
    printf("%.10lf\n", a+b+sqrt(a*a+b*b-2*a*b*cos(c)));
    printf("%.10lf\n", b*sin(c));
    return 0;
}