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 sys
import math

for line in sys.stdin:
    if len(line)>1:
        a, b, r = line.strip('\n').split()
        a, b, r = float(a), float(b), math.radians(float(r))
        
        h = b * math.sin(r)
        c = (a**2 + b**2 - 2*a*b*math.cos(r))**0.5
        l = a + b + c
        s = a * h / 2
        print s
        print l
        print h