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
#coding: UTF-8
import sys
import math

i= sys.stdin.readline()

a,b,c = map(int,i.split())

d = math.cos(math.radians(c))
c = math.sin(math.radians(c))

S = 0.5*a*b*c
L = math.sqrt(a**2+b**2-2*a*b*d)+a+b
h = S*2/a

print S,L,h