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 <cstdio>
#include <cmath>
using namespace std;

int main() {
    double a, b, c, s , l , h;
    cin >> a >> b >> c;
    h=b*sin(c/180.0*M_PI);
    s=a*h/2.0;
    l=sqrt(pow(h,2.0)+pow(a-b*cos(c/180.0*M_PI),2.0))+a+b;
    printf("%5lf %5lf %5lf\n", s, l, h);
    return 0;
}