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, S, L, h;
    cin >> a >> b >> c;
    double rad = c * M_PI / 180;
    
    S = 1.0/2 * a * b * sin(rad);
    L = a + b + sqrt(a*a + b*b - 2*a*b*cos(rad));
    h = b * sin(rad);
    
    printf("%.10lf\n%.10lf\n%.10lf\n", S, L, h);
}