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;
    S = 0.5 * a * b * sin(C * M_PI / 180.0);
    L = a + b + sqrt(a * a + b * b - 2 * a * b * cos(C * M_PI / 180.0));
    h = 2 * S / a;
    printf("%f\n%f\n%f\n", S, L, h);
    return 0;
}