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 PYTHON):

Solution:
import math
a, b, deg = map(float, raw_input().split(" "))

c = math.sqrt(a**2 + b**2 - 2*a*b*math.cos(math.radians(deg)))
L = a + b + c
s = (a + b + c) / 2.0
S = math.sqrt(s*(s-a)*(s-b)*(s-c))
h = 2 * S / a

print(str(S) + " " + str(L) + " " + str(h))