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,r,h,s;
    cin >> a >> b >> r;
    r = r /180.0 * M_PI;
    c = sqrt(a*a+b*b-2*a*b*cos(r));
    h = b * sin(r);
    s = a * h / 2.0;
    printf("%lf\n%lf\n%lf\n",s,a+b+c,h);
}