Problem: Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.

In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.

Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.

You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.

Input

The input file consists of three lines, each of them contains a pair of numbers –– coordinates of the pillar. Any coordinate doesn't exceed 1000 by absolute value, and is given with at most six digits after decimal point.

Output

Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It's guaranteed that the number of angles in the optimal polygon is not larger than 100.

Examples

Input

0.000000 0.000000
1.000000 1.000000
0.000000 1.000000


Output

1.00000000

Solution (in PYTHON):

Solution:
from math import sqrt, acos, pi, sin

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

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)

    def __mul__(self, other):
        # Multiply by number
        return Point(self.x * other, self.y * other)

    def __str__(self):
        return "{%.2f, %.2f}" % (self.x, self.y, )

    def __abs__(self):
        return sqrt(self.x ** 2 + self.y ** 2)

class Line:
    '''
    Build line from coefficients A, B, C of its equation "Ax + By + C = 0"
    '''
    def __init__(self, a, b, c):
        self.a = a
        self.b = b
        self.c = c

    '''
    Build line from two points on it
    '''
    @staticmethod
    def from_points(p1, p2):
        a = p1.y - p2.y
        b = p2.x - p1.x

        return Line._from_vector_and_point((a, b, ), p1)

    '''
    Build line from direction vector and point on the line
    '''
    @staticmethod
    def _from_vector_and_point((vx, vy, ), p):
        return Line(vx, vy, - vx * p.x - vy * p.y)

    '''
    Returns vertor perpendicular to the given one (s.t. their dot product is zero)
    '''
    @staticmethod
    def _perp_vector(a, b):
        if b == 0:
            return 0.0, 1.0
        else:
            b_new = - 1.0 * a / b

            return 1.0, b_new

    '''
    Returns a line perpendicular to the current one that goes through point `p`
    '''
    def get_perp(self, p):
        a_new, b_new = self._perp_vector(self.a, self.b)

        return Line._from_vector_and_point((a_new, b_new, ), p)

    '''
    Returns the determinant of following matrix:
    [ `a00` `a01` ]
    [ `a10` `a11` ]
    '''
    @staticmethod
    def _det(a00, a01, a10, a11):
        return a00 * a11 - a01 * a10

    '''
    Returns the intersection point between the current line and `other`
    '''
    def intersect_with(self, other):
        delta = self._det(self.a, self.b, other.a, other.b)

        if delta == 0.0:
            raise Exception("ne peresekayutsia")

        x = - self._det(self.c, self.b, other.c, other.b) / delta
        y = - self._det(self.a, self.c, other.a, other.c) / delta

        return Point(x, y)

    def __str__(self):
        return "%.2fx + %.2fy + %.2f == 0" % (self.a, self.b, self.c, )

def midpoint(p1, p2):
    return (p1 + p2) * 0.5

# Returns radian measure of angle AOB, measured clockwise
def angle(a, o, b):
    oa = a - o
    ob = b - o

    cos_phi = 1.0 * oa.dot(ob) / abs(oa) / abs(ob)

    if cos_phi < -1.0:
        cos_phi = -1.0
    elif cos_phi > 1.0:
        cos_phi = 1.0

    phi = acos(cos_phi)

    if oa.y * ob.x - oa.x * ob.y < 0: # `ob` is counterclockwise to `oa`
        return 2.0 * pi - phi
    else:
        return phi

# Returns where it is possible for a `num-sides`-sided regular polygon to have some vertices at angles `alpha` and
# `beta` between each other
def regular_polygon_possible(num_vertices, alpha, beta):
    if alpha > beta:
        alpha, beta = beta, alpha

    enc = 0

    for i in xrange(1, num_vertices):
        for phi in (alpha, beta, ):
            if abs(phi - i * 2.0 * pi / num_vertices) < 2.0 * pi / 4500:
                enc += 1

    return enc == 2

def regular_polygon_area(r_big, num_vertices):
    return num_vertices / 2.0 * r_big ** 2 * sin(2.0 * pi / num_vertices)

ps = []

for i in [1, 2, 3]:
    x, y = map(float, raw_input().split(' '))

    ps.append(Point(x, y))

l1 = Line.from_points(ps[0], ps[1])
l2 = Line.from_points(ps[1], ps[2])

m1 = midpoint(ps[0], ps[1])
m2 = midpoint(ps[1], ps[2])

center = l1.get_perp(m1).intersect_with(l2.get_perp(m2))

alpha = angle(ps[0], center, ps[1])
beta =  angle(ps[0], center, ps[2])

num_vertices = None

for i in xrange(3, 100 + 1):
    if regular_polygon_possible(i, alpha, beta):
        num_vertices = i
        break

# print center

# print num_vertices

# print abs(ps[0] - center)

print regular_polygon_area(abs(ps[0] - center), num_vertices)