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(int,input().split())
t=math.radians(C)
S=a*b*math.sin(t)/2
c=math.sqrt(a*a+b*b-2*a*b*math.cos(t))
L=a+b+c
h=2*S/a
print(f'{S:.8f}')
print(f'{L:.8f}')
print(f'{h:.8f}')