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())
c=math.sqrt(a*a + b*b - 2*a*b*math.cos(math.radians(C)))
s=(a+b+c)/2
S=math.sqrt(s*(s-a)*(s-b)*(s-c))
L=a+b+c
h=2*S/a
print(f"{S:.5f}\n{L:.5f}\n{h:.5f}")