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:
from __future__ import division, print_function
from sys import stdin
from math import radians, sin, cos, sqrt
a, b, degree = (float(s) for s in stdin.readline().split())
h = b * sin(radians(degree))
s = a * h / 2.0
L = sqrt(a**2 + b**2 - 2.0*a*b*cos(radians(degree))) + a + b
print('{:.4f}\n{:.4f}\n{:.4f}'.format(s, L, h))