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 sin, acos, degrees, radians, pi, modf, sqrt

if __name__ == "__main__":    
    i1 = raw_input()
    i2 = raw_input()
    i3 = raw_input()
    
    p1 = i1.split(' ')
    p2 = i2.split(' ')
    p3 = i3.split(' ')
    
    x1 = float(p1[0])
    y1 = float(p1[1])
    x2 = float(p2[0])
    y2 = float(p2[1])
    x3 = float(p3[0])
    y3 = float(p3[1])   
            
    #x0 = ((y1-y2)*(x1**2+y1**2-x3**2-y3**2)-(y1-y3)*(x1**2+y1**2-x2**2-y2**2)) / 2 / ( (y1-y3)*(x2-x1) - (y1-y2)*(x3-x1) )
    #y0 = ((x3-x1)*(x2**2+y2**2-x1**2-y1**2)-(x2-x1)*(x3**2+y3**2-x1**2-y1**2)) / 2 / ( (x2-x1)*(y1-y3) - (y1-y2)*(x3-x1) )
    #R = (abs(x1-x0)**2 + abs(y1-y0)**2) ** 0.5
    
    ptlist = []
    ptlist.append({'x':float(p1[0]), 'y':float(p1[1])})
    ptlist.append({'x':float(p2[0]), 'y':float(p2[1])})
    ptlist.append({'x':float(p3[0]), 'y':float(p3[1])})

    linelist = []
    linelist.append({'pt1':ptlist[0], 'pt2':ptlist[1], 'long':0.0, 'arc':0.0, 'angle':0.0})
    linelist.append({'pt1':ptlist[0], 'pt2':ptlist[2], 'long':0.0, 'arc':0.0, 'angle':0.0})
    linelist.append({'pt1':ptlist[1], 'pt2':ptlist[2], 'long':0.0, 'arc':0.0, 'angle':0.0})
    
    for l in linelist:
        l['long'] = sqrt(abs(l['pt1']['x'] - l['pt2']['x'])**2
                    +abs(l['pt1']['y'] - l['pt2']['y'])**2)
        
    a = linelist[0]['long']
    b = linelist[1]['long']
    c = linelist[2]['long']
    
    p = (a+b+c) / 2.0
    S = sqrt(p * (p-a) * (p-b) * (p-c))
    R = (a*b*c)/(4.0*S)
    
    #test
    #print a
    #print b
    #print c
    #print R
    #exit()    
    
    for l in linelist:
        if l['long'] > 2*R*0.9999:
            l['arc'] = pi
        else:
            l['arc'] = acos((R**2 + R**2 - l['long']**2)/(R**2 + R**2))
        #l['arc'] = acos((R**2 + R**2 - l['long']**2)/(R**2 + R**2))
        l['angle'] = degrees(l['arc'])

    mina = min(linelist[0]['angle'], linelist[1]['angle'], linelist[2]['angle'])
    maxa = max(linelist[0]['angle'], linelist[1]['angle'], linelist[2]['angle'])
    
    a1 = linelist[0]['angle']
    a2 = linelist[1]['angle']
    a3 = linelist[2]['angle']
    
    #test
    #print a1
    #print a2
    #print a3
    #exit()
    
    if a1+a2+a3 < 357.0:
        temp = a1
        a1 = mina
        a2 = maxa - mina
        a3 = 360.0 - maxa    
    
    angle = 1.0
    
    x = 3.5
    end = mina + 0.0005
    while x < end:
        aa1 = a1 / x
        aa2 = a2 / x
        aa3 = a3 / x
        
        aa1 = modf(aa1)[0]
        aa2 = modf(aa2)[0]
        aa3 = modf(aa3)[0]
        
        if aa1 < 0.01 and aa2 < 0.01 and aa3 < 0.01:
            #print str(x)+' a1:'+str(aa1)+' a2:'+str(aa2)+' a3:'+str(aa3)
            angle = x

        x += 0.0004
        
    #print angle
    #exit()
        
    x = angle - 0.001
    end = angle + 0.001
    while x < end:
        aa1 = a1 / x
        aa2 = a2 / x
        aa3 = a3 / x
        
        aa1 = modf(aa1)[0]
        aa2 = modf(aa2)[0]
        aa3 = modf(aa3)[0]
        
        if aa1 < 0.0001 and aa2 < 0.0001 and aa3 < 0.0001:
            angle = x

        x += 0.0000001
        
    #test 3.87096
    #x = 3.5
    #end = mina + 0.01
    #while x < end:
        #aa1 = a1 / x
        #aa2 = a2 / x
        #aa3 = a3 / x
        
        #aa1 = modf(aa1)[0]
        #aa2 = modf(aa2)[0]
        #aa3 = modf(aa3)[0]
        
        #if aa1 < 0.001 and aa2 < 0.001 and aa3 < 0.001:
            #angle = x

        #x += 0.00001      

    #print angle

    if angle > mina*0.99:
        angle = mina
        
    if angle == 1.0:
        angle = mina
        
    if modf(angle)[0] > 0.98:
        angle = round(angle)
    
    polyarea = (round(360.0/angle)/2) * (R**2) * sin(radians(angle))
    #print mina
    #print angle
    print polyarea