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>

using namespace std;

int main(){
    double a, b, C, S;
    cin >> a >> b >> C;
    C = C * M_PI / 180.0;
    S = (a * b * sin(C)) / 2;
    cout << fixed << setprecision(4) << S << endl
    << a+b+sqrt(a*a+b*b-2*a*b*cos(C)) << endl << 2*S/a << endl;
}