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:


stdin_flag=1
if not stdin_flag:
  read_line_index=0
  testcasefilename="test.txt"
  Stestcase=open(testcasefilename).read()
  read_line_datas=Stestcase.split("\n")


def debugs(s):
  if not stdin_flag:
    print ";;;",s

#####################################
######################################

def read_line():
  global read_line_index
  if stdin_flag:
    return raw_input()
  else:
    s=read_line_datas[read_line_index]
    read_line_index+=1
    return s

def answer():
  if stdin_flag:
    return solve()
  else:
    while read_line_proceed():
      solve()
      

def read_line_proceed():
  global read_line_index
  print"##################"
  while 1:
    if read_line_index>= len (read_line_datas ):
      return False
    if read_line_datas[read_line_index]=="%%%":
      read_line_index+=1
      return True
    read_line_index+=1


def readint():
  return int (read_line() )


def readints():
  return map(int, read_line().split(" "))

def reads():
  return read_line()




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def compute(m,n,d):
  pass

def ccc((pa,pb,pc)):
  m=[pa,pb,pc,pa,pb,pc]
  d=2*sum(m[i][0]*(m[i+1][1]-m[i+2][1])  for i in xrange(3))
  return [ sum( (m[i][0]**2+m[i][1]**2)*(m[i+1+k][1-k]-m[i+2-k][1-k])/d for i in xrange(3)) for k in xrange(2) ]

def solve():
  from math import sin,atan2,pi
  m=[]
  for _ in xrange(3):
    m.append(map(float,reads().split()))
  cp=ccc(m)
  debugs(cp)
  ma=[atan2(p[0]-cp[0], p[1]-cp[1]) for p in m]
  ma=[(z-ma[0])/2/pi for z in ma]
  debugs(ma)
  for k in xrange(3,105):
    if all(abs(a*k-round(a*k))<0.1**5 for a in ma):break
  r=(p[0]-cp[0])**2+(p[1]-cp[1])**2
  debugs(k)
  print r*sin(2*pi/k)*k/2

def test():
  pass
  #debugs(ccc((0.0,0.0),(0.0,1.0),(1.0,0.0)))

test()
answer()