python3 -c "from fractions import Fraction as F
L=3
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
z1=[F(-1,2),F(3,4),F(1,4),F(-1,2)]
z2=[F(-1,4),F(1,4),F(-3,8),F(-5,8)]
z=[[F(0),z1[i],z2[i]] for i in range(4)]
w=softrec(z)
for i in range(4): print(i,w[i][1],w[i][2])"