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:
import math as m

a,b,c=input().split()
a=int(a)
b=int(b)
c=int(c)
c=m.radians(c)
S=0.5*a*b*m.sin(c)
L=a+b+m.sqrt(a*a+b*b-2*a*b*m.cos(c))
H=b*m.sin(c)
print(S)
print(L)
print(H)