python3 -c "from fractions import Fraction as F
L=6
def mul(a,b):
 c=[F(0)]*L
 for i in range(L):
  for j in range(L-i):
   c[i+j]+=a[i]*b[j]
 return c
def pexp(a):
 e=[F(0)]*L
 e[0]=F(1)
 for n in range(1,L):
  s=F(0)
  for k in range(1,n+1):
   s+=a[k]*e[n-k]
  e[n]=s/n
 return e
def pinv(a):
 b=[F(0)]*L
 b[0]=1/a[0]
 for n in range(1,L):
  s=F(0)
  for k in range(1,n+1):
   s+=a[k]*b[n-k]
  b[n]=-s/a[0]
 return b
def soft(z):
 e=[pexp(z[i]) for i in range(4)]
 d=[sum(e[i][n] for i in range(4)) for n in range(L)]
 q=pinv(d)
 return [mul(e[i],q) for i in range(4)]
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(12):
 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=soft(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=soft(Z)
print(U[2][5])
print(U[2])
print(V[2][5])"