# N3 is the list of GAP IDs (Crystcat IDs) of
# indecomposable lattice of rank 3
# whose flabby class [M_G]^fl is not invertivle.
# N4 (resp. N31) is the list of GAP IDs (Crystcat IDs) of
# indecomposable (resp. decomposable) lattice of rank 4
# whose flabby class [M_G]^fl is not invertivle.
# I4 is the list of GAP IDs (Crystcat IDs) of
# indecomposable lattice of rank 3
# whose flabby class [M_G]^fl is invertivle but not zero.
# For GAP ID (Crystcat ID), see http://www.ams.org/books/memo/1176/ (Chapter 3).

N3:=
[ [ 3, 3, 1, 3 ], [ 3, 3, 3, 3 ], [ 3, 3, 3, 4 ], [ 3, 4, 3, 2 ], 
  [ 3, 4, 4, 2 ], [ 3, 4, 6, 3 ], [ 3, 4, 7, 2 ], [ 3, 7, 1, 2 ], 
  [ 3, 7, 2, 2 ], [ 3, 7, 2, 3 ], [ 3, 7, 3, 2 ], [ 3, 7, 3, 3 ], 
  [ 3, 7, 4, 2 ], [ 3, 7, 5, 2 ], [ 3, 7, 5, 3 ] ];
N31:=
[ [ 4, 4, 3, 6 ], [ 4, 4, 4, 4 ], [ 4, 4, 4, 6 ], [ 4, 5, 1, 9 ], 
  [ 4, 5, 2, 4 ], [ 4, 5, 2, 7 ], [ 4, 6, 1, 4 ], [ 4, 6, 1, 8 ], 
  [ 4, 6, 2, 4 ], [ 4, 6, 2, 8 ], [ 4, 6, 2, 9 ], [ 4, 6, 3, 3 ], 
  [ 4, 6, 3, 6 ], [ 4, 7, 3, 2 ], [ 4, 7, 4, 3 ], [ 4, 7, 5, 2 ], 
  [ 4, 7, 7, 2 ], [ 4, 12, 2, 4 ], [ 4, 12, 3, 7 ], [ 4, 12, 4, 6 ], 
  [ 4, 12, 4, 8 ], [ 4, 12, 4, 9 ], [ 4, 12, 5, 6 ], [ 4, 12, 5, 7 ], 
  [ 4, 13, 1, 3 ], [ 4, 13, 2, 4 ], [ 4, 13, 3, 4 ], [ 4, 13, 4, 3 ], 
  [ 4, 13, 5, 3 ], [ 4, 13, 6, 3 ], [ 4, 13, 7, 6 ], [ 4, 13, 7, 7 ], 
  [ 4, 13, 7, 8 ], [ 4, 13, 8, 3 ], [ 4, 13, 8, 4 ], [ 4, 13, 9, 3 ], 
  [ 4, 13, 10, 3 ], [ 4, 24, 1, 5 ], [ 4, 24, 2, 3 ], [ 4, 24, 2, 5 ], 
  [ 4, 24, 3, 5 ], [ 4, 24, 4, 3 ], [ 4, 24, 4, 5 ], [ 4, 24, 5, 3 ], 
  [ 4, 24, 5, 5 ], [ 4, 25, 1, 2 ], [ 4, 25, 1, 4 ], [ 4, 25, 2, 4 ], 
  [ 4, 25, 3, 2 ], [ 4, 25, 3, 4 ], [ 4, 25, 4, 4 ], [ 4, 25, 5, 2 ], 
  [ 4, 25, 5, 4 ], [ 4, 25, 6, 2 ], [ 4, 25, 6, 4 ], [ 4, 25, 7, 2 ], 
  [ 4, 25, 7, 4 ], [ 4, 25, 8, 2 ], [ 4, 25, 8, 4 ], [ 4, 25, 9, 4 ], 
  [ 4, 25, 10, 2 ], [ 4, 25, 10, 4 ], [ 4, 25, 11, 2 ], [ 4, 25, 11, 4 ] ];
N4:=
[ [ 4, 5, 1, 12 ], [ 4, 5, 2, 5 ], [ 4, 5, 2, 8 ], [ 4, 5, 2, 9 ], 
  [ 4, 6, 1, 6 ], [ 4, 6, 1, 11 ], [ 4, 6, 2, 6 ], [ 4, 6, 2, 10 ], 
  [ 4, 6, 2, 12 ], [ 4, 6, 3, 4 ], [ 4, 6, 3, 7 ], [ 4, 6, 3, 8 ], 
  [ 4, 12, 2, 5 ], [ 4, 12, 2, 6 ], [ 4, 12, 3, 11 ], [ 4, 12, 4, 10 ], 
  [ 4, 12, 4, 11 ], [ 4, 12, 4, 12 ], [ 4, 12, 5, 8 ], [ 4, 12, 5, 9 ], 
  [ 4, 12, 5, 10 ], [ 4, 12, 5, 11 ], [ 4, 13, 1, 5 ], [ 4, 13, 2, 5 ], 
  [ 4, 13, 3, 5 ], [ 4, 13, 4, 5 ], [ 4, 13, 5, 4 ], [ 4, 13, 5, 5 ], 
  [ 4, 13, 6, 5 ], [ 4, 13, 7, 9 ], [ 4, 13, 7, 10 ], [ 4, 13, 7, 11 ], 
  [ 4, 13, 8, 5 ], [ 4, 13, 8, 6 ], [ 4, 13, 9, 4 ], [ 4, 13, 9, 5 ], 
  [ 4, 13, 10, 4 ], [ 4, 13, 10, 5 ], [ 4, 18, 1, 3 ], [ 4, 18, 2, 4 ], 
  [ 4, 18, 2, 5 ], [ 4, 18, 3, 5 ], [ 4, 18, 3, 6 ], [ 4, 18, 3, 7 ], 
  [ 4, 18, 4, 4 ], [ 4, 18, 4, 5 ], [ 4, 18, 5, 5 ], [ 4, 18, 5, 6 ], 
  [ 4, 18, 5, 7 ], [ 4, 19, 1, 2 ], [ 4, 19, 2, 2 ], [ 4, 19, 3, 2 ], 
  [ 4, 19, 4, 3 ], [ 4, 19, 4, 4 ], [ 4, 19, 5, 2 ], [ 4, 19, 6, 2 ], 
  [ 4, 22, 1, 1 ], [ 4, 22, 2, 1 ], [ 4, 22, 3, 1 ], [ 4, 22, 4, 1 ], 
  [ 4, 22, 5, 1 ], [ 4, 22, 5, 2 ], [ 4, 22, 6, 1 ], [ 4, 22, 7, 1 ], 
  [ 4, 22, 8, 1 ], [ 4, 22, 9, 1 ], [ 4, 22, 10, 1 ], [ 4, 22, 11, 1 ], 
  [ 4, 24, 2, 4 ], [ 4, 24, 2, 6 ], [ 4, 24, 4, 4 ], [ 4, 24, 5, 4 ], 
  [ 4, 24, 5, 6 ], [ 4, 25, 1, 3 ], [ 4, 25, 2, 3 ], [ 4, 25, 2, 5 ], 
  [ 4, 25, 3, 3 ], [ 4, 25, 4, 3 ], [ 4, 25, 5, 3 ], [ 4, 25, 5, 5 ], 
  [ 4, 25, 6, 3 ], [ 4, 25, 6, 5 ], [ 4, 25, 7, 3 ], [ 4, 25, 8, 3 ], 
  [ 4, 25, 9, 3 ], [ 4, 25, 9, 5 ], [ 4, 25, 10, 3 ], [ 4, 25, 10, 5 ], 
  [ 4, 25, 11, 3 ], [ 4, 25, 11, 5 ], [ 4, 29, 1, 1 ], [ 4, 29, 1, 2 ], 
  [ 4, 29, 2, 1 ], [ 4, 29, 3, 1 ], [ 4, 29, 3, 2 ], [ 4, 29, 3, 3 ], 
  [ 4, 29, 4, 1 ], [ 4, 29, 4, 2 ], [ 4, 29, 5, 1 ], [ 4, 29, 6, 1 ], 
  [ 4, 29, 7, 1 ], [ 4, 29, 7, 2 ], [ 4, 29, 8, 1 ], [ 4, 29, 8, 2 ], 
  [ 4, 29, 9, 1 ], [ 4, 32, 1, 2 ], [ 4, 32, 2, 2 ], [ 4, 32, 3, 2 ], 
  [ 4, 32, 4, 2 ], [ 4, 32, 5, 2 ], [ 4, 32, 5, 3 ], [ 4, 32, 6, 2 ], 
  [ 4, 32, 7, 2 ], [ 4, 32, 8, 2 ], [ 4, 32, 9, 4 ], [ 4, 32, 9, 5 ], 
  [ 4, 32, 10, 2 ], [ 4, 32, 11, 2 ], [ 4, 32, 11, 3 ], [ 4, 32, 12, 2 ], 
  [ 4, 32, 13, 3 ], [ 4, 32, 13, 4 ], [ 4, 32, 14, 3 ], [ 4, 32, 14, 4 ], 
  [ 4, 32, 15, 2 ], [ 4, 32, 16, 2 ], [ 4, 32, 16, 3 ], [ 4, 32, 17, 2 ], 
  [ 4, 32, 18, 2 ], [ 4, 32, 18, 3 ], [ 4, 32, 19, 2 ], [ 4, 32, 19, 3 ], 
  [ 4, 32, 20, 2 ], [ 4, 32, 20, 3 ], [ 4, 32, 21, 2 ], [ 4, 32, 21, 3 ], 
  [ 4, 33, 1, 1 ], [ 4, 33, 3, 1 ], [ 4, 33, 4, 1 ], [ 4, 33, 5, 1 ], 
  [ 4, 33, 6, 1 ], [ 4, 33, 7, 1 ], [ 4, 33, 8, 1 ], [ 4, 33, 9, 1 ], 
  [ 4, 33, 10, 1 ], [ 4, 33, 11, 1 ], [ 4, 33, 12, 1 ], [ 4, 33, 13, 1 ], 
  [ 4, 33, 14, 1 ], [ 4, 33, 14, 2 ], [ 4, 33, 15, 1 ], [ 4, 33, 16, 1 ] ];
I4:=
[ [ 4, 31, 1, 3 ], [ 4, 31, 1, 4 ], [ 4, 31, 2, 2 ], [ 4, 31, 4, 2 ], 
  [ 4, 31, 5, 2 ], [ 4, 31, 7, 2 ], [ 4, 33, 2, 1 ] ];