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:
import collections
import re
import math

class coord:
    def __init__(self, x, y):
        self.x = float(x)
        self.y = float(y)
        
    def __eq__(self, other):
        return (abs(self.x - other.x) <= 0.00001) and (abs(self.y - other.y) <= 0.00001)
    
    def length(self, other):
        return round((((self.x - other.x)**2 + (self.y - other.y)**2)**0.5), 6)

class polygon:
    def __init__(self):
        self.center = coord(0.0, 0.0)
        self.c = []
        self.Radius = 0
        self.Area = 0
    
    def addCoord(self, coord):
        self.c.append(coord)
        if len(self.c) == 1:
            pt1 = coord
        elif len(self.c) == 2:
            pt2 = coord
        elif len(self.c) == 3:
            pt3 = coord
            self.Radius =-1		# error checking 
            
            if (not self.IsPerpendicular(1, 2, 3)):				
                self.CalcCircle(1, 2, 3)
            elif (not self.IsPerpendicular(1, 3, 2)):
                self.CalcCircle(1, 3, 2)
            elif (not self.IsPerpendicular(2, 1, 3) ):
                self.CalcCircle(2, 1, 3)
            elif (not self.IsPerpendicular(2, 3, 1) ):
                self.CalcCircle(2, 3, 1)
            elif (not self.IsPerpendicular(3, 2, 1) ):
                self.CalcCircle(3, 2, 1)
            elif (not self.IsPerpendicular(3, 1, 2) ):
                self.CalcCircle(3, 1, 2)
            else: 
        #       The three pts are perpendicular to axis
        #		pt1->trace();			pt2->trace();			pt3->trace();
                self.Radius =-1
    
    def IsPerpendicular(self, n1, n2, n3):
    # Check the given point are perpendicular to x or y axis 
        pt1 = self.c[n1-1]
        pt2 = self.c[n2-1]
        pt3 = self.c[n3-1]
        yDelta_a = pt2.y - pt1.y
        xDelta_a = pt2.x - pt1.x
        yDelta_b = pt3.y - pt2.y
        xDelta_b = pt3.x - pt2.x
    # checking whether the line of the two pts are vertical
        if (abs(xDelta_a) == 0 and abs(yDelta_b) == 0):
            return False
        if (abs(yDelta_a) == 0):
            return True
        elif (abs(yDelta_b) == 0):
            return True
        elif (abs(xDelta_a) == 0):
            return True
        elif (abs(xDelta_b) == 0):
            return True
        else:
            return False
    
    def CalcCircle(self, n1, n2, n3):
        if len(self.c) >= 3:
            
            pt1 = self.c[n1-1]
            pt2 = self.c[n2-1]
            pt3 = self.c[n3-1]
            
            yDelta_a= pt2.y - pt1.y
            xDelta_a= pt2.x - pt1.x
            yDelta_b= pt3.y - pt2.y
            xDelta_b= pt3.x - pt2.x
            
            if (abs(xDelta_a) == 0 and abs(yDelta_b) == 0):
                self.center = coord(0.5*(pt2.x + pt3.x), 0.5*(pt1.y + pt2.y))
                self.Radius = self.center.length(pt1)		# calc. radius
                return self.Radius
            aSlope=yDelta_a/xDelta_a 
            bSlope=yDelta_b/xDelta_b
            if (abs(aSlope-bSlope) == 0):	# checking whether the given points are colinear. 	
                return -1

            self.center.x= (aSlope*bSlope*(pt1.y - pt3.y) + bSlope*(pt1.x + pt2.x)
                - aSlope*(pt2.x+pt3.x) )/(2* (bSlope-aSlope) )
            self.center.y = -1*(self.center.x - (pt1.x+pt2.x)/2)/aSlope +  (pt1.y+pt2.y)/2
            
            self.Radius = self.center.length(pt1)		# calc. radius
            return self.Radius
    
    def coord_range(self, bordCount):
        #point = coord()
        for bordNumber in range(1, bordCount+1, 1):
            sin0 = (self.c[0].y - self.center.y)/self.Radius;
            cos0 = (self.c[0].x - self.center.x)/self.Radius;
            x = self.center.x + (cos0*math.cos(math.pi*2*(bordNumber-1)/bordCount)-sin0*math.sin(math.pi*2*(bordNumber-1)/bordCount))*self.Radius#- self.Radius + self.c[0].x
            y = self.center.y + (sin0*math.cos(math.pi*2*(bordNumber-1)/bordCount)+cos0*math.sin(math.pi*2*(bordNumber-1)/bordCount))*self.Radius#+ self.c[0].y
            point = coord(x, y)
            #print ('coord ', bordNumber, ' angle ', 360*(bordNumber-1)/bordCount, 'calc coords: ', 'x ', x, ' y', y)
            yield point
    
    def calcCent(self):
        if len(self.c) >= 3:
            
            for bordNumber in range(3, 101, 1):
                nRes = 0
                for coordFullIndex in self.coord_range(bordNumber):
                    for coordIndex in self.c:
                        #print ('real coords: ', 'x ', coordIndex.x, 'y ', coordIndex.y) 
                        if coordIndex == coordFullIndex:
                            nRes = nRes + 1
                #print ('possible area: ', (self.Radius**2*bordNumber/2)*math.sin(math.pi*2/bordNumber))
                if nRes >= 3:
                    self.Area = (self.Radius**2*bordNumber/2)*math.sin(math.pi*2/bordNumber)
                    break
    
coordinates = []

sstorage_path = 'params'
plg = polygon()
#with open(sstorage_path) as f:
for line in range(1,4,1):
    line = input()
    match = re.findall(r'(\S+)', line)
    rate1 = float(match[0])
    rate2 = float(match[1])
    coordinates.append(coord(match[0], match[1]))
    plg.addCoord(coord(match[0], match[1]))

plg.calcCent()              
#print(plg.center.x, ' ', plg.center.y, ' ', plg.Radius, ' ', plg.Area)
print(plg.Area)
#for coord in coordinates:
    #print(coord.x, ' ', coord.y)

#f.close()