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>
#include <cstdio>
using namespace std;
int main(){
    double a, b, C;
    cin >> a >> b >> C;
    C = C * M_PI / 180;
    double S, L, h;
    h = b * sin(C);
    L = a + b + sqrt(a * a + b * b - 2 * a * b * cos(C));
    S = a * h / 2;
    printf("%.5f\n%.5f\n%.5f\n", S, L, h);
}