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,d;
  cin>>a>>b>>c;
  c=c*M_PI/180;
  double x=a*b*sin(c)/2,y=sqrt(a*a+b*b-2*a*b*cos(c))+a+b,z=2*x/a;
  printf("%.5f\n%.5f\n%.5f\n",x,y,z);
}