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
data = map(float, raw_input().split(" "))

rad = data[2]*math.pi/180

h = data[1]*math.sin(rad)
s = data[0]*h/2
l = data[0]+data[1]+math.sqrt((data[0]-data[1]*math.cos(rad))**2+h**2)

print "%f\n%f\n%f" % (s,l,h)