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,t;
    cin >> a >> b >> t;
    t = t / 180.0 * M_PI;
    double L = a+b+sqrt((a-b*cos(t))*(a-b*cos(t))+b*b*sin(t)*sin(t));
    printf("%.8f\n%.8f\n%.8f\n",1.0/2.0*a*b*sin(t),L,b*sin(t));
}