@ControlMatrix = ( [1, 2, 0, 2], [0, 0, 2, 1] )
@perms = (
  ([1, 0, 0, 0], [1, 1, 0, 0], [1, 0, 0, 1], [1, 1, 0, 1])
  ([0, 0, 0, 1], [1, 1, 1, 1])
)