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<cmath>
#include<cstdio>
using namespace std;

int main(){
  double a, b, c, rad, pi = 3.14159265358979;
  cin >> a >> b >> c;
  rad = pi/180 *c;
  printf("%.7f %.7f %.7f", a*b*sin(rad)/2, a+b+sqrt(a*a+b*b-2*a*b*cos(rad)), b*sin(rad));

  return 0;
}