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