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 <cstdio>
#include <cmath>
using namespace std;

int main()
{
    int a, b;
    double c, C, s, l, h;
    scanf("%d%d%lf", &a, &b, &C);
    C *= M_PI/180;
    s = a*b*sin(C)/2;
    c = sqrt(a*a + b*b -2*a*b*cos(C));
    l = a+b+c;
    h = 2*s/a;
    printf("%lf\n%lf\n%lf\n", s, l, h);
    return 0;

}