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 PYTHON3):

Solution:
from math import sin,cos,pi,sqrt
a,b,d=map(float,input().split())
S=a*b*sin(d*pi/180)/2
c=sqrt(a**2+b**2-2*a*b*cos(d*pi/180))
h=2*S/a
print(S)
print(a+b+c)
print(h)