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;

const double pi=acos(-1);

int main(){
    double a,b,c;
    cin>>a>>b>>c;
    c*=pi/180;
    double l=sqrt(a*a+b*b-2*a*b*cos(c));
    double h=b*sin(c);
    double s=a*h/2;
    printf("%.10f\n%.10f\n%.10f\n",s,l+a+b,h);
}