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 sys
import math

N = 1000

def find_circle_center(p1, p2, p3):
    (x1, y1) = p1 
    (x2, y2) = p2 
    (x3, y3) = p3 
    # the perpendicular bisectors linear function is either 
    # A*x + B*y = B * y_mid + A * x_mid, or x = x_mid when y_1 == y_2
    # where A = x_2 - x_1 and B = y_2 - y_1
    # The rest part is just solving two linear systems
    # See: https://stackoverflow.com/questions/20677795/how-do-i-compute-the-intersection-point-of-two-lines-in-python
    
    def average(a, b): return (a + b) / 2
    # Line 1: the p1-p2 perpendicular
    x_mid1 = average(x1, x2); y_mid1 = average(y1, y2)
    if y1 == y2:
        L1 = (1, 0, -x_mid1)
    else:
        A1 = x2 - x1; B1 = y2 - y1;
        C1 = B1 * y_mid1 + A1 * x_mid1
        L1 = (A1, B1, -C1)

    x_mid2 = average(x2, x3); y_mid2 = average(y2, y3)
    if y2 == y3:
        L2 = (1, 0, -x_mid2)
    else:
        A2 = x3 - x2; B2 = y3 - y2;
        C2 = B2 * y_mid2 + A2 * x_mid2
        L2 = (A2, B2, -C2)

    xp = intersection(L1, L2) 
    if xp:
        return xp 
    print("No single Intersection point detected.")
    return False

# def line(p1, p2):
#    A = (p1[1] - p2[1])
#    B = (p2[0] - p1[0])
#    C = (p1[0]*p2[1] - p2[0]*p1[1])
#    return A, B, -C

def intersection(L1, L2):
    D  = L1[0] * L2[1] - L1[1] * L2[0]
    Dx = L1[2] * L2[1] - L1[1] * L2[2]
    Dy = L1[0] * L2[2] - L1[2] * L2[0]
    if D != 0:
        x = Dx / D
        y = Dy / D
        return -x, -y
    else:
        return False

def distance(p1, p2):
    return math.sqrt(pow((p2[0] - p1[0]), 2) +  
        pow((p2[1] - p1[1]), 2))

def near_integer(num):
    u = math.ceil(num);
    l = math.floor(num);
    return math.isclose(u, num, rel_tol=1e-04) \
        or math.isclose(l, num, rel_tol=1e-04)

def main():
    ps = []
    # fin = open('input.txt', 'r')
    # for line in fin.readlines():
    for line in sys.stdin:
        (a, b) = line.split(' ')
        ps.append((float(a), float(b)))
    center = find_circle_center(ps[0], ps[1], ps[2])
    R = distance(center, ps[0])
    
    def center_angle(line):
        # Using The Law of Sines 
        # Center_angle without the Pi part
        p1, p2 = line
        return 2 * math.asin(distance(p1, p2) / R * 0.5) / math.pi

    Theta = list(map(center_angle, [(ps[0], ps[1]), (ps[1], ps[2]), (ps[2], ps[0])]))
    # find the smallest value of n that gives a near-integer value of s
    n = 0
    for n in range(3, N+1):
        # s = 2 * R * math.sin(math.pi / n)
        div_result = [x * n / 2 for x in Theta]
        if all([near_integer(x) for x in div_result]):
            break
        else:
            continue
    if n == 0:
        print("Error: input invalid.")
        return
    area = 1 / 2 * n * R * R * math.sin(2 * math.pi / n)
    print("%.6f" % area)
    return area

def test():
    p1 = (0.0, 0.0)
    p2 = (0.5, 0.5 * math.sqrt(3))
    p3 = (1.0, 0.0)
    p4 = (1.0, 1.0)
    
    
    p5 = (71.756151, 7.532275)
    p6 = (-48.634784, 100.159986)
    p7 = (91.778633, 158.107739)
    
#test()
main()