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

input = map(float, raw_input().split(" "))
a = input[0]
b = input[1]
c = math.radians(input[2])

h = math.sin(c) * b
s = a * h / 2
l = math.pow((a - math.cos(c) * b) ** 2 + h ** 2, 0.5) + a + b

print "{0:.5f}".format(s)
print "{0:.5f}".format(l)
print "{0:.5f}".format(h)