python3 -c "from fractions import Fraction as F
L=4
def softrec(z):
 u=[[F(1,4)]*L for i in range(4)]
 for n in range(1,L):
  S=[]
  for m in range(n):
   s=F(0)
   for j in range(4):
    for k in range(1,m+2):
     s+=k*z[j][k]*u[j][m+1-k]
   S.append(s)
  for i in range(4):
   s=F(0)
   for k in range(1,n+1):
    s+=k*z[i][k]*u[i][n-k]
   for a in range(n):
    s-=u[i][a]*S[n-1-a]
   u[i][n]=s/n
 return u
M=[[0,-1,1,-2],[0,2,1,0],[0,0,2,-1],[-2,-1,2,-1]]
N=[[0,2,-1,-2],[-1,-2,-2,-2],[1,2,-2,2],[1,1,0,-1]]
U=[[F(1,4)]*L for i in range(4)]
V=[[F(1,4)]*L for i in range(4)]
for it in range(5):
 Z=[]
 for i in range(4):
  A=[sum(M[i][j]*V[j][n] for j in range(4)) for n in range(L)]
  Z.append([F(0)]+A[:-1])
 U=softrec(Z)
 Z=[]
 for j in range(4):
  B=[sum(U[i][n]*N[i][j] for i in range(4)) for n in range(L)]
  Z.append([F(0)]+B[:-1])
 V=softrec(Z)
print('V1',[V[j][1] for j in range(4)])
print('M V1',[sum(M[i][j]*V[j][1] for j in range(4)) for i in range(4)])
print('U2',[U[i][2] for i in range(4)])
a0=[F(-1,2),F(3,4),F(1,4),F(-1,2)]
a1=[sum(M[i][j]*V[j][1] for j in range(4)) for i in range(4)]
w=softrec([[F(0),a0[i],a1[i]] for i in range(4)])
print('direct2',[w[i][2] for i in range(4)])"