#--------Python module for OEIS sequence number A092866.------

#-------------------------------------------------------------------
#	Example of use
# >>>> A092866(6)
#	1237
#-------------------------------------------------------------------

#Three points are collinear if the determinant of the matrix of their barycentric coordinates vanishes

def A092866_coef_matrice(a1,b1,c1,a2,b2,c2):
    
    k1=b1*c2-b2*c1
    k2=a2*c1-a1*c2
    k3=a1*b2-a2*b1
    return k1,k2,k3


class A092866_InternalPoint(Exception):
    def __init__(self, value):
       self.value = value
    def __str__(self):
      return repr(self.value)
        
def A092866_Internal(x):
     if (x[0]<=0 or x[1]<=0 or x[2]<=0 or x[0]>=1 or x[1]>=1 or x[2]>=1):
         raise A092866_InternalPoint("Not inside the triangle")

#Finding the intersection coordinates between two lines

def A092866_interLines(l1,l2):

    a=A092866_coef_matrice(l1[0][0],l1[0][1],l1[0][2],l1[1][0],l1[1][1],l1[1][2])
    b=A092866_coef_matrice(l2[0][0],l2[0][1],l2[0][2],l2[1][0],l2[1][1],l2[1][2])
    m=matrix([[a[0],a[1],a[2]],[b[0],b[1],b[2]],[1,1,1]])
    y = vector([0,0,1])
    try:
        g=m.solve_right(y)
        A092866_Internal(g)
    except (ValueError, A092866_InternalPoint):
        return None
    else:
        return tuple(g)


def A092866_points_lines(n):

 # collection of points

    x=[1,0,0]
    y=[0,1,0]
    z=[0,0,1]

    x1=[((x[0]+y[0])*(i/n),(x[1]+y[1])*((n-i)/n),0) for i in range(1,n)]
    y1=[(0,(z[1]+y[1])*(i/n),(z[2]+y[2])*((n-i)/n)) for i in range(1,n)]
    z1=[((z[0]+x[0])*(i/n),0,(z[2]+x[2])*((n-i)/n)) for i in range(1,n)]
    
    a=[(tuple(x), tuple(y1[k])) for k in range(n-1)]
    b=[(tuple(y), tuple(z1[k])) for k in range(n-1)]
    c=[(tuple(z), tuple(x1[k])) for k in range(n-1)]
    
    d=[((x1[k]),(y1[l])) for k in range(n-1) for l in range(n-1)]
    e=[((x1[k]),(z1[l])) for k in range(n-1) for l in range(n-1)]
    f=[((z1[k]),(y1[l])) for k in range(n-1) for l in range(n-1)]
    
    g=[(tuple(x), tuple(y))]
    h=[(tuple(y), tuple(z))]
    i=[(tuple(z), tuple(x))]
    
    # Construction of lines
    L=(a+b+c+d+e+f+g+h+i)
    
    return L

def A092866(n):
    
    L=A092866_points_lines(n)
    
    #Finding intersections 
    q=[A092866_interLines((L[p]),L[j]) for p in range(len(L)) for j in range(p+1,len(L)) if p!=j] 
    
    #Each intersection has to be calculated once time
    f=set(q)
    f.remove(None)
    
    intersection=len(f)

    return intersection