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<bits/stdc++.h>
using namespace std;
int main() {
    double a,b,c;
    cin >>a >> b >> c;
    double h = b*sin(c * M_PI /180);
    cout << fixed <<a*h / 2.0 << endl;
    cout << fixed << a+b+sqrt(pow(a-b*cos(c*M_PI/180),2) + pow(h,2))  <<endl;
    cout << fixed << h << endl;
}