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, C = map(int, raw_input().split())
S = 0.5 * a * b * math.sin(math.radians(C))
c = math.sqrt(a * a + b * b - 2 * a * b * math.cos(math.radians(C)))
print("%8f" %(S))
print("%8f" %(a + b + c))
print("%8f" %(S / a * 2))