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