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())
c = c * math.pi / 180
h = b * math.sin(c)
d = math.sqrt(b ** 2 + a ** 2 - 2 * b * a * math.cos(c))
S = a * h / 2
print(S)
print(a + b + d)
print(h)