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;
    scanf("%lf %lf %lf",&a,&b,&c);
    printf("%.7f\n",a*b*sin(M_PI*c/180)/2);
    printf("%.7f\n",a+b+sqrt(pow(a,2)+pow(b,2)-2*a*b*cos(M_PI*c/180)));
    printf("%.7f\n",b*sin(M_PI*c/180));
}