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(){
    int a,b,c;
    double s,S,L,H;
    cin>>a>>b>>c;
    s=c*acos(-1)/180;
    S=a*b*sin(s)/2;
    L=a+b+sqrt(a*a+b*b-2*a*b*cos(s));
    H=S*2/a;
    printf("%lf\n %lf\n %lf\n",S,L,H);
    return 0;
}