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())

sinc = math.sin(c*math.pi/180)
cosc = math.cos(c*math.pi/180)
c = math.sqrt(a**2+b**2-2*a*b*cosc)
s = a*b*sinc/2.0

print(s)
print(a+b+c)
print(s/a*2.0)