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 math

def compute_triangle_side(p1, p2, p3):
    l1 = ((p2[0] - p3[0])**2 + (p2[1] - p3[1])**2)**(1/2)
    l2 = ((p1[0] - p3[0])**2 + (p1[1] - p3[1])**2)**(1/2)
    l3 = ((p1[0] - p2[0])**2 + (p1[1] - p2[1])**2)**(1/2)

    return (l1, l2, l3)

def compute_circumscribed_circle_radius(l1, l2, l3):
    p = (l1 + l2 + l3) / 2 # half_perimeter for heron
    area = (p * (p - l1) * (p - l2) * (p - l3))**(1 / 2) # area using heron formula
    radius = (l1 * l2 * l3) / (4 * area)

    return radius

def round_float(float_value):
    return math.floor(float_value)

def compute_min_number_of_vertices(radius):
    for n in range(3, 101):
        # area of regular polygon using number of sides and radius of cc
        area = (1/2) * n * radius * radius * math.sin((2 * math.pi) / n)
        print(area)
        if area - round_area(area) <= 0.0001:
            print(n)
            return "{0:.6f}".format(area)

    return ((1/2) * 100 * radius * radius * math.sin((2 * math.pi) / 100))

def compute_side_length(radius):
    min_area = -1
    for n in range(3, 101):
        side_length = 2 * radius * math.sin(math.pi / n)
        print(side_length)
        if side_length - round_float(side_length) <= 0.001:
            return n
    return 100

# def find_min_n(radius, l1, l2, l3):
#     (angle1, angle2, angle3) = compute_angles_to_O(radius, l1, l2, l3)
#     print(angle1, angle2, angle3)
#     for n in range(3, 101):
#         min_section = 2 * math.pi / n
#         print(min_section)
#         angle1_check = False
#         angle2_check = False
#         angle3_check = False
#         for p in range(1, n + 1):
#             curr_angle = p * min_section
#             if curr_angle - angle1 <= 0.0001:
#                 angle1_check = True
#             if curr_angle - angle2 <= 0.0001:
#                 angle2_check = True
#             if curr_angle - angle3 <= 0.0001:
#                 angle3_check = True
#         if angle1_check and angle2_check and angle3_check:
#             return n
#     return 100

# def find_min_n(radius, l1, l2, l3):
#     (angle1, angle2, angle3) = compute_angles_to_O(radius, l1, l2, l3)
#     for n in range(3, 101):
#         min_section = 2 * math.pi / n
#         r1 = angle1 / min_section
#         r2 = angle2 / min_section
#         r3 = angle3 / min_section
#         if r1 - round(r1) <= 0.0001 and r2 - round(r2) <= 0.0001 and r3 - round(r3) <= 0.0001:
#             return n

def compute_gcd(a1, a2):
    if a1 < a2:
        return compute_gcd(a2, a1)

    if abs(a2) < 0.001:
        return a1
    else:
        return compute_gcd(a2, a1 - math.floor(a1 / a2) * a2)

def find_min_n(radius, l1, l2, l3):
    angle1 = math.acos((l2 * l2 + l3 * l3 - l1 * l1) / (2 * l2 * l3))
    angle2 = math.acos((l1 * l1 + l3 * l3 - l2 * l2) / (2 * l1 * l3))
    angle3 = math.acos((l1 * l1 + l2 * l2 - l3 * l3) / (2 * l1 * l2))

    return round(math.pi / compute_gcd(angle2, compute_gcd(angle1, angle3)))

# consider O the center of circumscribed circle, we compute AOC, BOC, AOB
# A, B, C are the given points p1, p2, p3
# R is the radius
def compute_angles_to_O(R, l1, l2, l3):
    angle1 = math.acos((2 * R * R - l1 * l1) / (2 * R * R))
    angle2 = math.acos((2 * R * R - l2 * l2) / (2 * R * R))
    angle3 = math.acos((2 * R * R - l3 * l3) / (2 * R * R))
    return (angle1, angle2, angle3)

if __name__ == "__main__":
    p1 = input().split(" ")
    p1x = float(p1[0])
    p1y = float(p1[1])
    p2 = input().split(" ")
    p2x = float(p2[0])
    p2y = float(p2[1])
    p3 = input().split(" ")
    p3x = float(p3[0])
    p3y = float(p3[1])
    
    (l1, l2, l3) = compute_triangle_side((p1x, p1y), (p2x, p2y), (p3x, p3y))
    radius = compute_circumscribed_circle_radius(l1, l2, l3)
    min_n = find_min_n(radius, l1, l2, l3)
    # print(min_n)
    area = (1/2) * min_n * radius * radius * math.sin((2 * math.pi) / min_n)
    print(area)