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
#include<cstdio>
#include<cmath>

int main(){
    double a,b,c,deg,S;
    scanf("%lf%lf%lf",&a,&b,&deg);
    S = (0.5) * a * b * sin(M_PI * deg / 180);
    c = sqrt(a * a + b * b - 2 * a * b * cos(M_PI * deg / 180));
    printf("%.8lf\n%.8lf\n%.8lf\n",S,a + b + c,2 * S / a);

    return 0;
}
