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, d = map(float, input().split())
h = b * math.sin(d*math.pi/180)
s = a * h / 2
l = math.sqrt(a**2 + b**2 - 2*a*b*math.cos(d*math.pi/180)) + a + b
print(s)
print(l)
print(h)