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 <stdio.h>
using namespace std;

double a,b,C;
int main(){
	cin >> a >> b >> C;
	double S = a/2*b*sin(C/180*M_PI);
	double c = sqrt(a*a+b*b-2*a*b*cos(C/180*M_PI));
	double L = (a+b+c);
	double h = 2*S/a;
	printf("%.6f\n",S);
	printf("%.6f\n",L);
	printf("%.6f\n",h);
}