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 radians, sin, cos, sqrt
a, b, C = map(float, input().split())
h = b * sin(radians(C))
c = sqrt(a*a+b*b-2*a*b*cos(radians(C)))
S = a * h / 2
L = a + b + c
print(S, L, h)