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:
#!/usr/bin/env python

import math

if __name__ == '__main__':
    a, b, C = map(float, raw_input().split())
    S = a * b * math.sin(C*math.pi/180) / 2
    L = a + b + math.sqrt(a**2 + b**2 - 2*a*b*math.cos(C*math.pi/180))
    h = b * math.sin(C*math.pi/180)

    print '{}\n{}\n{}'.format(S, L, h)