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,c,pi,S,L,h;
    cin >> a >> b >> c;
    pi = acos(-1.);
    c = c/180*pi;
    S = 0.5*a*b*sin(c);
    L=a+b+sqrt(a*a+b*b-2.0*a*b*cos(c));
    h = b*sin(c);
    printf("%.4lf\n%.4lf\n%.4lf\n",S,L,h);
    return 0;
}