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<iostream>
#include<stdio.h>
#include<math.h>
using namespace std;
int main(){
  double a,b,C;
  double S,L,h;
  cin >> a >> b >> C ;
  C=C/180*M_PI;
  S=(a*b*sin(C))/2;
  L=a+b+sqrt(a*a+b*b-2*a*b*cos(C));
  h=b*sin(C);
  printf("%.8f\n%.8f\n%.8f\n",S,L,h);
}