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:
#define _GLIBCXX_DEBUG
#include<bits/stdc++.h>
using namespace std;

int main(){
  int a, b, C;
  double pi, c, S, L, h;
  cin >> a >> b >> C;
  pi=acos(-1);
  S=a*b*sin(C*pi/180)/2;
  c=sqrt(pow(a,2)+pow(b,2)-2*a*b*cos(C*pi/180));
  L=a+b+c;
  h=2*S/a;
  printf("%.5f\n%.5f\n%.5f\n",S,L,h);
  return 0;
}