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:
# coding=utf-8
from math import sin, pi, sqrt, cos


def main():
    a, b, CinDeg = map(int, raw_input().split())
    CinRad = pi * CinDeg / 180
    S = 0.5 * a * b * sin(CinRad)
    c = sqrt(a ** 2 + b ** 2 - 2 * a * b * cos(CinRad))
    L = a + b + c
    h = S / (0.5 * a)
    print S
    print L
    print h

if __name__ == '__main__':
    main()