Maintains contexts for:
 64->6:    0n, ud, 1n, 2nh, 2nv, 3n
 64->6->5: 0n, ud+1n, 2nh, 2nv, 3n
 64->6->3: 0n, ud+1n+2nh, 2nv+3n

Where ud = up/down,
      1n = single neighbour
      2nh = two horizontal neighbours
      2nv = two vertical neighbours
      3n = three neighbours
      0n = no neighbours