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(float, input().split())
t = math.radians(T)
h = b * math.sin(t)
s = h * a / 2
c = ((a - b * math.cos(t)) ** 2 + h ** 2) ** 0.5
l = a + b + c
print(s, l, h)