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:
import math

A = map(float,raw_input().strip().split())
B = map(float,raw_input().strip().split())
C = map(float,raw_input().strip().split())

def is_close(a, b, tol=1e-9):
        return abs(a-b) <= tol

def calculateDistance(x1, y1, x2, y2) :
    return math.sqrt( (x2-x1)**2 + (y2-y1)**2 )

def calculateAreaOfTriangle(a,b,c) :
    semiPerimeter = (a+b+c)/2
    return math.sqrt(semiPerimeter * (semiPerimeter - a) * (semiPerimeter - b) * (semiPerimeter -c))

def calculateRadius(sideLength, alpha) :
    return sideLength/(2*math.sin(alpha))

def calculateAngle(adjacentSide1, adjacentSide2, oppositeSide) :
    """ This function calculates the angle of a triangle using the sides of it. Uses Law Of Cosines.
    
    Arguments:
        adjacentSide1 {[int]} -- [One of the sides which has got vertice which contains this point]
        adjacentSide2 {[int]} -- [One of the sides which has got vertice which contains this point]
        oppositeSide {[int]} -- [The side opposite to the angle which needs to be calculated. This side doesn't contain the center vertex of the angle being calculated.]
    """

    angle = math.acos((adjacentSide1**2 + adjacentSide2**2 - oppositeSide**2)/(2*adjacentSide1*adjacentSide2))
    return angle

def gcd(x,y,eps = 0.001) :
    while math.fabs(x) > eps and math.fabs(y) > eps:
        if x > y :
            x = x - (math.floor(x/y)*y)
        else :
            y = y - (math.floor(y/x)*x)
    return x+y

def calculateSidesOfPolygon(A,B,C) :
    """This calculates the number of sides of an equiangular regular polygon given 3 angles of the 3 random points.
    
    Arguments:
        A {[float]} -- [1st angle in radians formed by the triangle]
        B {[float]} -- [2nd angle in radians formed by the triangle]
        C {[float]} -- [3rd angle in radians formed by the triangle]
    """
    sides = 1/(gcd((A/math.pi),gcd((B/math.pi),(C/math.pi))))
    return sides

def calculateApothem(sideLength,sides) :
    """Calculates Apothem of a regular polygon
    
    Arguments:
        circumRadius {[float]} -- Circumradius of the polygon
        sides {[int]} -- The number of sides of the polygon
    """
    return sideLength/(2*math.tan(math.pi/sides))

def calculateAreaOfPolygon(circumRadius,numberOfSides) :
    """Calculates the area of an equiangular regular n sided polygon with given circumradius
    
    Arguments:
        sides {int} -- The number of sides in the polygon
        circumRadius {float} -- The circumradius of the polygon
    """
    area = numberOfSides*0.5*((circumRadius**2) * math.sin((2*math.pi)/numberOfSides))
    return area

AB = calculateDistance(A[0],A[1],B[0],B[1])
BC = calculateDistance(B[0],B[1],C[0],C[1])
AC = calculateDistance(A[0],A[1],C[0],C[1])

sidesOfTriangle = [AB,BC,AC]
sidesOfTriangle.sort()

angleA = calculateAngle(AB,AC,BC)
angleB = calculateAngle(AB,BC,AC)
angleC = math.pi - angleA - angleB

minimumSides = round(calculateSidesOfPolygon(angleA,angleB,angleC))

areaOfTriangle = calculateAreaOfTriangle(AB,BC,AC)

circumRadius = calculateRadius(BC,angleA)

print calculateAreaOfPolygon(circumRadius,minimumSides)