L=[1,0,-1,0,1,0,-1,0]
E=[1]+[0]*~-len(L)
F=[]
I=[]
i=f=1
while len(F)<len(L):
F.append(f)
L[i-1]/=f
f *= i
i += 1
for i in range(len(L)):
c = E[i]/L[0]
I.append(c*F[i])
for j in range(len(L)-i):
E[i+j] -= c*L[j]
print(I)
TD1bMSwwLC0xLDAsMSwwLC0xLDBdCkU9WzFdK1swXSp+LWxlbihMKQpGPVtdCkk9W10KCmk9Zj0xCndoaWxlIGxlbihGKTxsZW4oTCk6CiAgICBGLmFwcGVuZChmKQogICAgTFtpLTFdLz1mCiAgICBmICo9IGkKICAgIGkgKz0gMQoKZm9yIGkgaW4gcmFuZ2UobGVuKEwpKToKICAgIGMgPSBFW2ldL0xbMF0KICAgIEkuYXBwZW5kKGMqRltpXSkKICAgIGZvciBqIGluIHJhbmdlKGxlbihMKS1pKToKICAgICAgICBFW2kral0gLT0gYypMW2pdCgpwcmludChJKQo=