lattice size: 7
    whole sequence: [1, 2, 3, 4, 5, 6]
     half sequence: [1, 2, 3]
lattice size: 8
    whole sequence: [1, 3, 5, 7]
     half sequence: [1, 3]
lattice size: 12
    whole sequence: [1, 7, 5, 11]
     half sequence: [1, 5]
