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
a,b,C = map(float,input().split(' '))
S = a*b*math.sin(math.radians(C)) / 2.0
c = math.sqrt(a**2+b**2-2*a*b*math.cos(math.radians(C)))
h = 2*S/a
print(S)
print(a+b+c)
print(h)