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 <math.h>
#include <stdio.h>
using namespace std;

int main(){
 double a,b,C;
 cin >> a >> b >> C;
 double S,L,h;
 C = M_PI*C/180;

 S = a*b*sin(C)/2;
 L = a+b+sqrt(a*a+b*b-2*a*b*cos(C));
 h = 2*S/a;
 printf("%.5f\n",S);
 printf("%.5f\n",L);
 printf("%.5f\n",h);
}