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 <cmath>
using namespace std;
using ll = long long;

double pi = 3.14159265359;

int main()
{
    double a, b, c;
    cin >> a >> b >> c;
    c = pi * c / 180.0;
    printf("%lf\n%lf\n%lf\n", a / 2 * b * sin(c), a + b + sqrt(a * a + b * b - 2 * a * b * cos(c)), b * sin(c));
}