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 asin, modf, sin, atan2
from decimal import *

class point:
	"""New and useful point"""
	x, y = 0.0, 0.0
	
	def __init__(self, x, y):
		self.x = x
		self.y = y
		
	@classmethod
	def from_list(cls, list):
		return point(list[0], list[1])
		
	def write(self):
		print self.x, self.y

class line:
	"""New and useful line"""
	a, b, c = 0.0, 0.0, 0.0
	
	def __init__(self, a, b, c):
		self.a = a
		self.b = b
		self.c = c
	
	@classmethod
	def between_points(cls, p, q):
		return line(q.y - p.y, p.x - q.x, q.x * p.y - q.y * p.x)
		
	def write(self):
		print self.a, self.b, self.c

class vector:
	"""New and useful vector"""
	x, y = 0.0, 0.0
		
	def __init__(self, x = 0.0, y = 0.0):
		self.x = x
		self.y = y
		
	@classmethod
	def between_points(cls, p = point(0.0, 0.0), q = None):
		if q == None:
			return vector(p.x, p.y)
		else:
			return vector(q.x - p.x, q.y - p.y)
		
	def write(self):
		print self.x, self.y
	
	def __add__(self, v):
		return vector(self.x + v.x, self.y + v.y)
		
	def __sub__(self, v):
		return vector(self.x - v.x, self.y - v.y)
		
	def length(self):
		return (self.x ** 2 + self.y ** 2) ** 0.5
		
		
def inner_product(v, u):
	return v.x * u.x + v.y * u.y
		
def cross_product(v, u):
	return v.x * u.y - v.y * u.x

def cross_lines(a, b):
	if abs(b.a * a.b - a.a * b.b) < eps:
		print "Lines are parallel!"
		return None
	else:
		return point((a.c * b.b - b.c * a.b) / (b.a * a.b - a.a * b.b), 
		(a.a * b.c - b.a * a.c) / (b.a * a.b - a.a * b.b))

def perpendicular(p, q):
	return line(q.x - p.x, q.y - p.y, (p.x ** 2 - q.x ** 2 + p.y ** 2 - q.y ** 2) / 2.0) 
		
def angle_between_vectors(v, u):
	return atan2(cross_product(v, u), inner_product(v, u))
	
points = [point.from_list(map(float, raw_input().split())) for i in range(3)]
eps = 0.000001
#for i in points:
#	i.write()
#perpendicular(points[0], points[1]).write()
#perpendicular(points[1], points[2]).write()
center = cross_lines(perpendicular(points[0], points[1]), perpendicular(points[1], points[2]))
#center.write()
v = [vector.between_points(center, x) for x in points]
#print "vectors:"
#for i in v:
#	i.write()
w = [angle_between_vectors(v[i], v[i+1]) for i in range(2)]
#print w
u = [abs(x) / (4 * asin(1)) for x in w]
#print u
res = 100
for i in range(1,101):
#	print abs((i * u[0] - round(i * u[0])) / i / u[0]), abs((i * u[1] - round(i * u[1])) / i / u[1])
	if abs((i * u[0] - round(i * u[0])) / i / u[0]) < eps and abs((i * u[1] - round(i * u[1])) / i / u[1])  < eps:
		res = i
		# print "we found ", i
		break
#print res
#m = max([res * x for x in u])
#print m
print round(v[0].length() ** 2.0 * res * sin(4.0 * asin(1.0) / res) / 2.0, 6)