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;
    cin >> a >> b >> C;
    double S,L,h;
    double pi=M_PI;
    S=0.50*a*b*sin(C/180.0*pi);
    L=a+b+sqrt(a*a+b*b-2*a*b*cos(C/180.0*pi));
    h=2*S/a;
    printf("%.12lf\n%.12lf\n%.12lf\n",S,L,h);
    return 0;
}