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:
# python 2.7 code for P001C
# steps:
# 1) get the center and radius
# 2) get the angle and n
# 3) get the area
#https://stackoverflow.com/questions/35176451/python-code-to-calcualte-angle-between-three-point-using-thier-3d-coordinates
#http://www.it610.com/article/5541237.htm
import math

def distance(point_a, point_b):
	x_1, y_1 = point_a
	x_2, y_2 = point_b
	dist = math.sqrt((x_1 - x_2)**2 + (y_1 - y_2)**2)
	return dist

def tri_area(l_a, l_b, l_c): #Heron's formula
	p = (l_a + l_b + l_c) / 2.0
	area = math.sqrt(p * (p-l_a) * (p-l_b) * (p-l_c))
	return area

def find_center(p_a, p_b, p_c): #find the coordinates of the center of the polygon/circumcircle
	x1, y1 = p_a
	x2, y2 = p_b
	x3, y3 = p_c

	x0 = ((y2-y1)*(y3*y3-y1*y1+x3*x3-x1*x1)-(y3-y1)*(y2*y2-y1*y1+x2*x2-x1*x1))/(2.0*((x3-x1)*(y2-y1)-(x2-x1)*(y3-y1)))
	y0 = ((x2-x1)*(x3*x3-x1*x1+y3*y3-y1*y1)-(x3-x1)*(x2*x2-x1*x1+y2*y2-y1*y1))/(2.0*((y3-y1)*(x2-x1)-(y2-y1)*(x3-x1)))
	r = math.sqrt((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0))

	return [x0, y0, r]

def center_angle(center, p_a, p_b):
	x0, y0 = center
	x1, y1 = p_a
	x2, y2 = p_b

	a = distance(p_a, p_b)
	b = distance(center, p_a)
	c = distance(center, p_b)
	cos_X = 1.0 * (b*b + c*c - a*a) / (2*b*c)
	ang = math.acos(cos_X)
	return ang

def gcd(num1, num2):
	err = 0.0001
	while abs(num1 - num2) >= err:
		if num1 > num2 + err:
			num1 -= num2
		elif num2 > num1 + err:
			num2 -= num1
	return max(num1, num2)


if __name__ == '__main__':

	err = 0.0001

	P_1 = raw_input()
	P_2 = raw_input()
	P_3 = raw_input()

	p1 = [float(x) for x in P_1.split(' ')]
	p2 = [float(x) for x in P_2.split(' ')]
	p3 = [float(x) for x in P_3.split(' ')]

	#c = find_center(p1, p2, p3)[0:2]
	r = find_center(p1, p2, p3)[2]
	dis_list = [distance(p1, p2), distance(p2, p3), distance(p3, p1)]
	l_min = min(dis_list)
	l_max = max(dis_list)
	l_mid = 0
	for x in dis_list:
		if not x == l_min and not x == l_max:
			l_mid = x

	cos_ang_min = (r*r + r*r - l_min*l_min) / (2.0 * r * r)
	cos_ang_max = (r*r + r*r - l_max*l_max) / (2.0 * r * r)
	cos_ang_mid = (r*r + r*r - l_mid*l_mid) / (2.0 * r * r)
	ang_min = math.acos(cos_ang_min)
	ang_max = math.acos(cos_ang_max)
	ang_mid = math.acos(cos_ang_mid)
	
	a0 = ang_min
	if ang_max - ang_min < err:
		a1 = a0
	else:
		a1 = ang_max - ang_min
	a2 = 2.0 * math.pi - a1 - a0
	a3 = ang_max

	g1 = gcd(gcd(a2, a0), a1)
	g2 = gcd(gcd(a3, a0), a1)

	n1 = 2.0 * math.pi / g1
	n2 = 2.0 * math.pi / g2

	if math.fmod(n2,1) < 0.01 and n2 < n1:
		n = n2
		g = g2
	else:
		n = n1
		g = g1

	# i = dis_list.index(min(dis_list))
	# p_c1 = eval('p'+str(i+1))
	# p_c2 = eval('p'+str((i+1)%3 + 1))

	#half_unit_ang = math.asin((s/2.0)/r)
	#unit_area = tri_area(r, r, s)
	#n = round(2.0 * math.pi / center_angle(c, p_c1, p_c2))

	#total_area = n * unit_area
	total_area = 0.5*n*r*r*math.sin(g)

	print total_area