Problem: You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the Ox axis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

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Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

Input

The first line contains three integers w, h, α (1 ≤ w, h ≤ 106; 0 ≤ α ≤ 180). Angle α is given in degrees.

Output

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

1 1 45


Output

0.828427125


Input

6 4 30


Output

19.668384925

Note

The second sample has been drawn on the picture above.

Solution (in PYTHON):

Solution:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import sys
import math

class Point():
    def __init__(self, x, y):
        self.x = float(x)
        self.y = float(y)

    def __repr__(self):
        return "({}, {})".format(self.x, self.y)

    def add(self, q):
        return Point(self.x + q.x, self.y + q.y)

    def minus(self, q):
        return Point(self.x - q.x, self.y - q.y)

    def multiply(self, t):
        ''' Multiplication by a scalar :t '''
        return Point(t*self.x, t*self.y)

    def divide(self, t):
        return Point(self.x/t, self.y/t)

    def scalar_product(self, q):
        return self.x * q.x + self.y * q.y

    def cross_product(self, q):
        return self.x * q.y - self.y * q.x

    def rotate(self, t):
        """ Rotates this point :t degrees where :t is given in radians """
        return Point(self.x * math.cos(t) - self.y * math.sin(t),
                     self.x * math.sin(t) + self.y * math.cos(t))

class Line():
    def __init__(self, P, Q):
        """ Receives two points that uniquely indentify the line """
        self.p = P
        self.q = Q

    def intersect(self, l2):
        """ Returns the intersection of this line with :l2 """
        a = self.q.minus(self.p)
        b = l2.q.minus(l2.p)
        c = Point(self.p.cross_product(self.q), l2.p.cross_product(l2.q))
        return Point(Point(a.x, b.x).cross_product(c),
                     Point(a.y, b.y).cross_product(c)).divide(a.cross_product(b))


class Polygon:
    def __init__(self, points):
        """ :points is a list of Point structures specified clockwise """
        self.points = points

    def area(self):
        """
        Calculates the area of the polygon if the polygon is convex
        """
        s = 0.0
        n = len(self.points)
        for i in xrange(n):
            s += self.points[i].cross_product(self.points[(i + 1) % n])

        return s / 2.0

    def clip_with_plane(self, line):
        """ 
        Removes the right side of the intersection of this polygon with
        :line and returns a polygon with an area smaller or equal to the
        original one.

        :line is an instance of the Line class. As Line is internally
        represented by points P and Q, this algorithm removes everything
        to the right of the vector with direction Q-P 
        """
        q_points = []
        p1 = line.p
        p2 = line.q

        n = len(self.points)
        for i in xrange(n):
            c = p2.minus(p1).cross_product(self.points[i].minus(p1))
            d = p2.minus(p1).cross_product(self.points[(i + 1) % n].minus(p1))

            if c >= 0:
                q_points.append(self.points[i])
            if c * d < 0:
                l2 = line.intersect(Line(self.points[i], self.points[(i + 1) % n]))
                q_points.append(l2)

        return Polygon(q_points)


if __name__ == '__main__':
    w, h, alpha = map(int, sys.stdin.readline().strip().split())
    teta = math.pi * alpha / 180

    topL = Point(-w/2.0, h/2.0)
    topR = Point(w/2.0 , h/2.0)
    botL = Point(-w/2.0, -h/2.0)
    botR = Point(w/2.0 , -h/2.0)

    topL2 = topL.rotate(teta)
    topR2 = topR.rotate(teta)
    botL2 = botL.rotate(teta)
    botR2 = botR.rotate(teta)


    p = Polygon([botL, topL, topR, botR])
    q = Polygon([botL2, topL2, topR2, botR2])

    for i in xrange(4):
        l = Line(q.points[(i + 1) % 4], q.points[i])
        p = p.clip_with_plane(l)

    print abs(p.area())