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>

int main(){
    double a, b, c;
    std::cin >> a >> b >> c;
    c = c / 180.0 * M_PI;
    printf("%10.8f\n", a * b * std::sin(c) / 2 );
    printf("%10.8f\n", a + b + std::sqrt(a*a + b*b - 2*a*b*std::cos(c)));
    printf("%10.8f\n", b * sin(c));
    return 0;
}