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:
import math
a, b, C = map(float, input().split())
rad_C = C*math.pi/180
c2 =a**2 + b**2 -2*a*b*math.cos(rad_C)
S = 0.5*a*b*math.sin(rad_C)
L = a + b + math.sqrt(c2)
h = 2*S/a
print(S)
print(L)
print(h)