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, t = map(int, input().split())
t = math.radians(t)
h = b * math.sin(t)
s = a * h / 2
c = math.sqrt(a **2 + b **2 - 2 * a * b * math.cos(t))
l = a + b + c
print(s)
print(l)
print(h)