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;

#define pi 3.14159265

int main(){
    double a,b,C;
    cin >> a  >> b >> C;
    double S,  L, h;
    C = C*(pi/180);
    S = a * b * sin(C)/2;
    double c = sqrt(a*a + b*b -2*a*b*cos(C));
    L  = a + b + c;
    h = 2*S/a;
    printf("%.8f\n%.8f\n%.8f\n",S,L,h);
}