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 PYTHON3):

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

class R2:
    def __init__(self,x,y):
       self.x = x
       self.y = y

    def __add__(self,v):
        return R2(self.x+v.x,self.y+v.y) 

    def __sub__(self,v):
        return R2(self.x-v.x,self.y-v.y) 

    def __mul__(self,c):
        return R2(c*self.x,c*self.y) 

    def __rmul__(self,c):
        return R2(c*self.x,c*self.y) 

    def __truediv__(self,c):
        return R2(self.x/c,self.y/c) 

    def __str__(self):
        return '({},{}) vector in R2'.format(self.x,self.y)

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

    def unit(self):
        return self/abs(self)

    def get(self):
        return (self.x,self.y)

    def rotate(self,theta):
        """
        Rotation matrix
        |cos(theta) -sin(theta)|
        |sin(theta)  cos(theta)|
        """
        return R2( self.x*cos(theta)-self.y*sin(theta)
                  ,self.x*sin(theta)+self.y*cos(theta)
                 )
    
def area(n,r):
    """Area of convex regular n-gon with radius r"""
    return 0.5*n*r*r*sin(2*pi/n)

def find_circle(a,b,c):
    """Find the circle that going through points a,b,c in the plane. """
    #Finding the unit vector perpendicular to AB
    dir1 = (b-a).unit().rotate(pi/2)
    #Finding the unit vector perpendicular to BC
    dir2 = (c-b).unit().rotate(pi/2)
    #Finding the halfpoint of AB
    half1 = a+((b-a)/2)
    #Finding the halfpoint of BC
    half2 = b+((c-b)/2)
    #Writing these vectors as components for further use
    x1,y1 = dir1.get()
    x2,y2 = dir2.get()
    r1,s1 = half1.get()
    r2,s2 = half2.get()

    # Derivation by hand. 
    # Finding the intersection of the lines with direction dir1 going through half1
    # and dir2 through half2. This is the center of the circle through a,b,c
    x = (s1-s2+r2*(y2/x2)-r1*(y1/x1))/((y2/x2)-(y1/x1))
    y = (x-r1)*(y1/x1)+s1
    center = R2(x,y) 
    radius = abs(center-a)
    return (center, radius)


def find_polygon(a,b,c,error=1e-5):
    center, r = find_circle(a,b,c)
    # Vector from center to vertice at A, like the initial position of clock arm on clock
    init_arm = a-center  
    for n in range(3,101):
        theta = 2*pi/n
        b_found = False
        c_found = False
        for i in range(1,n):
            arm = init_arm.rotate(i*theta)
            v = center+arm # convert arm vector to vertice position
            if abs(v-b)< error:
                b_found = True 
            elif abs(v-c) < error:
                c_found = True
        if b_found and c_found:
            return (n,r)

a = [float(i) for i in input().split()]
b = [float(i) for i in input().split()]
c = [float(i) for i in input().split()]

a = R2(a[0],a[1])
b = R2(b[0],b[1])
c = R2(c[0],c[1])

n,r = find_polygon(a,b,c)
print(area(n,r))