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,deg,theta;
    cin >> a >> b >> deg;
    theta = deg / 180 * acos(-1);
    double S,L,h;
    h = b * sin(theta);
    S = a * h / 2;
    L = a + b + sqrt(pow(a,2)+pow(b,2)-2*a*b*cos(theta));
    printf("%f %f %f",S,L,h);
    return 0;
}