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 <iomanip>
#include <cmath>
using namespace std;
#define M_PI acos(-1)

int main(){
	int a,b,c;
	cin >> a >> b >> c;
	cout << fixed << setprecision(8) << a*b*sin(M_PI / 180 * c)/2 << endl << a + b + sqrt(a*a+b*b-2*b*a*cos(M_PI/180*c)) << endl << b * sin(M_PI/180*c)<< endl;
}