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:
#1C
from math import acos, pi, sin

"""We can find the circumcentre of the polygon which will be the intersection of 

the perpendicular bisectors of the line segments. Using this, we can find the circumradius, R .

Now, R = s/(2*sin(pi/n)) for a regular polygon, where s is side length and n is no. of sides.

Since it is given that n<= 100, we iterate over 1 to 100 to find the smallest value of n that

gives a near-integer value of s. This will be our polygon.

Then, we find the area using the following formula:
    area= 0.5*n*R*R*sin(2*pi/n).
"""
#Fucntion to calculate the edges of the "triangle"
def f(x, y):
    return sum((i - j) ** 2 for i, j in zip(x, y))
#Function to calculate the angles
def g(a, b, c): return acos((b + c - a) / (2 * (b * c) ** 0.5)) / pi
#Function to calculate the hypotenuse
def h(x, n): return 0.01 < (x * n) % 1 < 0.99
#Now, we take the input: 3 lines that contain the coordinates of the pillars
#These pillars are part of a polygon-shaped arena
#If the triangle formed by them has the smallest possible area,
#then the arena's size will also be the smallest possible.
x, y, z = (tuple(map(float, input().split())) for i in range(3))
# a, b, c - the edges of the triangle
a, b, c = f(x, y), f(x, z), f(y, z)
# A, B, C - the angles of the triangle
A, B = g(a, b, c), g(b, a, c)
# r - the polygon circumradius
r, n = a / (8 * sin(A * pi) ** 2), 3
#Now, we find the proper number of pillars
while h(A, n) or h(B, n): n += 1
#And we print the area of the coresponding polygon
print(round(n * r * sin(2 * pi / n),8))