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:
from math import sqrt, sin, cos, pi

a, b, C = map(int, input().split())
C *= pi / 180
print(a * b * sin(C) / 2)
print(sqrt(a**2 + b**2 - a * b * cos(C) * 2) + a + b)
print(b * sin(C))