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())
d = math.radians(c)
print(0.5 * a * b * (math.sin(d)))
e = math.sqrt(a*a + b*b - 2*a*b*(math.cos(d)))
print(a+b+e)
print(b * (math.sin(d)))