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, A = map(float, input().split())

h = b*math.sin(math.radians(A))
S = a*h*0.5
L = a + b + math.sqrt(pow(a, 2) + pow(b, 2) - 2*a*b*math.cos(math.radians(A)))

print(S)
print(L)
print(h)