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