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
#include<bits/stdc++.h>
using namespace std;

int main(){
    double a, b, c;
    cin>>a >>b >>c;
    c = c*3.1415926535/180;
    printf("%f\n", a*b*sin(c)/2);
    printf("%f\n", a+b+sqrt(a*a+b*b-2*a*b*cos(c)));
    printf("%f\n", b*sin(c));
    return 0;
}

