We start out with the trivial tree

                         [{}, {}, {[[], []]}, [[], []]]

                 There are still non-empty or non-clone leaves

                             Let's pick , [[], []]

         Vertex , [[], []], has two pairs of children from his two wives

         From the first wife, he had the pair, {[[3], []], [[-2], []]}

         From the second wife, he had the pair, {[[], [3]], [[], [-2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    155, 845

                   and their respective gcd with, 1000,  are

                                      5, 5



                   The cardinalites from the second wife are

                                    400, 600

                   and their respective gcd with, 1000,  are

                                    200, 200

     The second wife won!, we pick, as legal heirs, {[[], [3]], [[], [-2]]}

                          Let's examine the new-comers

          [[], [3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

          [[], [-2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                             Let's pick , [[], [3]]

        Vertex , [[], [3]], has two pairs of children from his two wives

        From the first wife, he had the pair, {[[-2], [3]], [[3], [3]]}

      From the second wife, he had the pair, {[[], [3, 3]], [[], [-2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    333, 67

                   and their respective gcd with, 1000,  are

                                      1, 1



                   The cardinalites from the second wife are

                                    160, 240

                   and their respective gcd with, 1000,  are

                                     40, 40

  The second wife won!, we pick, as legal heirs, {[[], [3, 3]], [[], [-2, 3]]}

                          Let's examine the new-comers

         [[], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[], [-2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                            Let's pick , [[], [-2]]

        Vertex , [[], [-2]], has two pairs of children from his two wives

       From the first wife, he had the pair, {[[3], [-2]], [[-2], [-2]]}

     From the second wife, he had the pair, {[[], [3, -2]], [[], [-2, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    88, 512

                   and their respective gcd with, 1000,  are

                                      8, 8



                   The cardinalites from the second wife are

                                    300, 300

                   and their respective gcd with, 1000,  are

                                    100, 100

 The second wife won!, we pick, as legal heirs, {[[], [3, -2]], [[], [-2, -2]]}

                          Let's examine the new-comers

        [[], [3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[], [-2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                           Let's pick , [[], [3, 3]]

       Vertex , [[], [3, 3]], has two pairs of children from his two wives

     From the first wife, he had the pair, {[[-2], [3, 3]], [[3], [3, 3]]}

   From the second wife, he had the pair, {[[], [-2, 3, 3]], [[], [3, 3, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    130, 30

                   and their respective gcd with, 1000,  are

                                     10, 10



                   The cardinalites from the second wife are

                                     86, 74

                   and their respective gcd with, 1000,  are

                                      2, 2

 The first wife won!, we pick, as legal heirs, {[[-2], [3, 3]], [[3], [3, 3]]}

                          Let's examine the new-comers

        [[-2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[3], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                          Let's pick , [[-2], [3, 3]]

      Vertex , [[-2], [3, 3]], has two pairs of children from his two wives

 From the first wife, he had the pair, {[[-2, -2], [3, 3]], [[-2, 3], [3, 3]]}

 From the second wife, he had the pair, {[[-2], [3, 3, 3]], [[-2], [-2, 3, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    110, 20

                   and their respective gcd with, 1000,  are

                                     10, 20



                   The cardinalites from the second wife are

                                     61, 69

                   and their respective gcd with, 1000,  are

                                      1, 1

The first wife won!, we pick, as legal heirs,

    {[[-2, -2], [3, 3]], [[-2, 3], [3, 3]]}

                          Let's examine the new-comers

      [[-2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[-2, 3], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                           Let's pick , [[3], [3, 3]]

      Vertex , [[3], [3, 3]], has two pairs of children from his two wives

  From the first wife, he had the pair, {[[3, -2], [3, 3]], [[3, 3], [3, 3]]}

  From the second wife, he had the pair, {[[3], [-2, 3, 3]], [[3], [3, 3, 3]]}

                 One of the sons from the first wife is a clone

                           namely , [[3, 3], [3, 3]]

            so we pick the legal children of, [[3], [3, 3]],  to be

                     {[[3, -2], [3, 3]], [[3, 3], [3, 3]]}

                          Let's examine the new-comers

      [[3, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

           [[3, 3], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                        Let's pick , [[-2, -2], [3, 3]]

    Vertex , [[-2, -2], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, 3], [3, 3]], [[-2, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, -2], [3, 3, 3]], [[-2, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                        namely , [[-2, -2, -2], [3, 3]]

         so we pick the legal children of, [[-2, -2], [3, 3]],  to be

                {[[-2, -2, 3], [3, 3]], [[-2, -2, -2], [3, 3]]}

                          Let's examine the new-comers

    [[-2, -2, 3], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[-2, -2, -2], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[-2, -2, 3], [3, 3]]

  Vertex , [[-2, -2, 3], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, 3, 3], [3, 3]], [[-2, -2, 3, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, -2, 3], [3, 3, 3]], [[-2, -2, 3], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2, -2, 3, 3], [3, 3]]

        so we pick the legal children of, [[-2, -2, 3], [3, 3]],  to be

             {[[-2, -2, 3, 3], [3, 3]], [[-2, -2, 3, -2], [3, 3]]}

                          Let's examine the new-comers

       [[-2, -2, 3, 3], [3, 3]],  is a clone, so it is a permanent leaf,

  [[-2, -2, 3, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[-2, 3], [3, 3]]

    Vertex , [[-2, 3], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, 3], [3, 3]], [[-2, 3, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, 3], [3, 3, 3]], [[-2, 3], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                         namely , [[-2, 3, 3], [3, 3]]

          so we pick the legal children of, [[-2, 3], [3, 3]],  to be

                 {[[-2, 3, 3], [3, 3]], [[-2, 3, -2], [3, 3]]}

                          Let's examine the new-comers

         [[-2, 3, 3], [3, 3]],  is a clone, so it is a permanent leaf,

    [[-2, 3, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[-2, -2, 3, -2], [3, 3]]

 Vertex , [[-2, -2, 3, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, 3, -2, 3], [3, 3]], [[-2, -2, 3, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, -2, 3, -2], [3, 3, 3]], [[-2, -2, 3, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                     namely , [[-2, -2, 3, -2, 3], [3, 3]]

      so we pick the legal children of, [[-2, -2, 3, -2], [3, 3]],  to be

         {[[-2, -2, 3, -2, 3], [3, 3]], [[-2, -2, 3, -2, -2], [3, 3]]}

                          Let's examine the new-comers

     [[-2, -2, 3, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

[[-2, -2, 3, -2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[-2, 3, -2], [3, 3]]

  Vertex , [[-2, 3, -2], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, 3], [3, 3]], [[-2, 3, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, 3, -2], [3, 3, 3]], [[-2, 3, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2, 3, -2, 3], [3, 3]]

        so we pick the legal children of, [[-2, 3, -2], [3, 3]],  to be

             {[[-2, 3, -2, 3], [3, 3]], [[-2, 3, -2, -2], [3, 3]]}

                          Let's examine the new-comers

       [[-2, 3, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

  [[-2, 3, -2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[3, -2], [3, 3]]

    Vertex , [[3, -2], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, 3], [3, 3]], [[3, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[3, -2], [3, 3, 3]], [[3, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                         namely , [[3, -2, 3], [3, 3]]

          so we pick the legal children of, [[3, -2], [3, 3]],  to be

                 {[[3, -2, 3], [3, 3]], [[3, -2, -2], [3, 3]]}

                          Let's examine the new-comers

         [[3, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

    [[3, -2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[3, -2, -2], [3, 3]]

  Vertex , [[3, -2, -2], [3, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, 3], [3, 3]], [[3, -2, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [3, 3, 3]], [[3, -2, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[3, -2, -2, 3], [3, 3]]

        so we pick the legal children of, [[3, -2, -2], [3, 3]],  to be

             {[[3, -2, -2, 3], [3, 3]], [[3, -2, -2, -2], [3, 3]]}

                          Let's examine the new-comers

       [[3, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

  [[3, -2, -2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3, -2, -2, -2], [3, 3]]

 Vertex , [[3, -2, -2, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, -2, 3], [3, 3]], [[3, -2, -2, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[3, -2, -2, -2], [3, 3, 3]], [[3, -2, -2, -2], [-2, 3, 3]]}

           Both sons from the first wife are clones, so we pick them

       namley we pick, as children of, [[3, -2, -2, -2], [3, 3]],  to be

         {[[3, -2, -2, -2, 3], [3, 3]], [[3, -2, -2, -2, -2], [3, 3]]}

                          Let's examine the new-comers

     [[3, -2, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

     [[3, -2, -2, -2, -2], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[-2, -2, 3, -2, -2], [3, 3]]

 Vertex , [[-2, -2, 3, -2, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, 3, -2, -2, -2], [3, 3]], [[-2, -2, 3, -2, -2, 3], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, -2, 3, -2, -2], [-2, 3, 3]], [[-2, -2, 3, -2, -2], [3, 3, 3]]}

                 One of the sons from the first wife is a clone

                   namely , [[-2, -2, 3, -2, -2, 3], [3, 3]]

    so we pick the legal children of, [[-2, -2, 3, -2, -2], [3, 3]],  to be

     {[[-2, -2, 3, -2, -2, -2], [3, 3]], [[-2, -2, 3, -2, -2, 3], [3, 3]]}

                          Let's examine the new-comers

[[-2, -2, 3, -2, -2, -2], [3, 3]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

   [[-2, -2, 3, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                           Let's pick , [[], [-2, 3]]

      Vertex , [[], [-2, 3]], has two pairs of children from his two wives

    From the first wife, he had the pair, {[[3], [-2, 3]], [[-2], [-2, 3]]}

  From the second wife, he had the pair, {[[], [3, -2, 3]], [[], [-2, -2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    37, 203

                   and their respective gcd with, 1000,  are

                                      1, 1



                   The cardinalites from the second wife are

                                    120, 120

                   and their respective gcd with, 1000,  are

                                     40, 40

The second wife won!, we pick, as legal heirs,

    {[[], [3, -2, 3]], [[], [-2, -2, 3]]}

                          Let's examine the new-comers

       [[], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[], [-2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[], [3, -2, 3]]

     Vertex , [[], [3, -2, 3]], has two pairs of children from his two wives

 From the first wife, he had the pair, {[[3], [3, -2, 3]], [[-2], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[], [-2, 3, -2, 3]], [[], [3, 3, -2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    20, 100

                   and their respective gcd with, 1000,  are

                                    20, 100



                   The cardinalites from the second wife are

                                     59, 61

                   and their respective gcd with, 1000,  are

                                      1, 1

The first wife won!, we pick, as legal heirs,

    {[[3], [3, -2, 3]], [[-2], [3, -2, 3]]}

                          Let's examine the new-comers

      [[3], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[-2], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[], [-2, -2, 3]]

    Vertex , [[], [-2, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair, {[[3], [-2, -2, 3]], [[-2], [-2, -2, 3]]}

From the second wife, he had the pair,

    {[[], [-2, -2, -2, 3]], [[], [3, -2, -2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    17, 103

                   and their respective gcd with, 1000,  are

                                      1, 1



                   The cardinalites from the second wife are

                                     40, 80

                   and their respective gcd with, 1000,  are

                                     40, 40

The second wife won!, we pick, as legal heirs,

    {[[], [-2, -2, -2, 3]], [[], [3, -2, -2, 3]]}

                          Let's examine the new-comers

    [[], [-2, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

     [[], [3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [-2, -2, -2, 3]]

  Vertex , [[], [-2, -2, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [-2, -2, -2, 3]], [[-2], [-2, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[], [3, -2, -2, -2, 3]], [[], [-2, -2, -2, -2, 3]]}

        One of the sons from the second wife is a clone, so we pick them

                       namely , [[], [-2, -2, -2, -2, 3]]

        so we pick the legal children of, [[], [-2, -2, -2, 3]], to be

             {[[], [3, -2, -2, -2, 3]], [[], [-2, -2, -2, -2, 3]]}

                          Let's examine the new-comers

   [[], [3, -2, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[], [-2, -2, -2, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [3, -2, -2, 3]]

   Vertex , [[], [3, -2, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, -2, 3]], [[-2], [3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, -2, 3]], [[], [-2, 3, -2, -2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                     10, 70

                   and their respective gcd with, 1000,  are

                                     10, 10



                   The cardinalites from the second wife are

                                     50, 30

                   and their respective gcd with, 1000,  are

                                     50, 10

            It is still a tie, so now let's take gcd within the pair

                 The internal gcd of cardinalities are, 10, 10

The first wife won!, we pick, as legal heirs,

    {[[3], [3, -2, -2, 3]], [[-2], [3, -2, -2, 3]]}

                          Let's examine the new-comers

    [[3], [3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

    [[-2], [3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[3], [3, -2, -2, 3]]

  Vertex , [[3], [3, -2, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, 3], [3, -2, -2, 3]], [[3, -2], [3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[3], [3, 3, -2, -2, 3]], [[3], [-2, 3, -2, -2, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[3, 3], [3, -2, -2, 3]]

        so we pick the legal children of, [[3], [3, -2, -2, 3]],  to be

             {[[3, 3], [3, -2, -2, 3]], [[3, -2], [3, -2, -2, 3]]}

                          Let's examine the new-comers

       [[3, 3], [3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

  [[3, -2], [3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3, -2], [3, -2, -2, 3]]

 Vertex , [[3, -2], [3, -2, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, 3], [3, -2, -2, 3]], [[3, -2, -2], [3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[3, -2], [3, 3, -2, -2, 3]], [[3, -2], [-2, 3, -2, -2, 3]]}

                 One of the sons from the first wife is a clone

                     namely , [[3, -2, 3], [3, -2, -2, 3]]

      so we pick the legal children of, [[3, -2], [3, -2, -2, 3]],  to be

         {[[3, -2, 3], [3, -2, -2, 3]], [[3, -2, -2], [3, -2, -2, 3]]}

                          Let's examine the new-comers

     [[3, -2, 3], [3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

[[3, -2, -2], [3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                      Let's pick , [[-2], [3, -2, -2, 3]]

  Vertex , [[-2], [3, -2, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [3, -2, -2, 3]], [[-2, -2], [3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[-2], [-2, 3, -2, -2, 3]], [[-2], [3, 3, -2, -2, 3]]}

        One of the sons from the second wife is a clone, so we pick them

                       namely , [[-2], [3, 3, -2, -2, 3]]

        so we pick the legal children of, [[-2], [3, -2, -2, 3]], to be

            {[[-2], [-2, 3, -2, -2, 3]], [[-2], [3, 3, -2, -2, 3]]}

                          Let's examine the new-comers

  [[-2], [-2, 3, -2, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[-2], [3, 3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                    Let's pick , [[-2], [-2, 3, -2, -2, 3]]

 Vertex , [[-2], [-2, 3, -2, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [-2, 3, -2, -2, 3]], [[-2, -2], [-2, 3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[-2], [3, -2, 3, -2, -2, 3]], [[-2], [-2, -2, 3, -2, -2, 3]]}

           Both sons from the second wife are clones, so we pick them

      namley we pick, as children of, [[-2], [-2, 3, -2, -2, 3]],  to be

        {[[-2], [3, -2, 3, -2, -2, 3]], [[-2], [-2, -2, 3, -2, -2, 3]]}

                          Let's examine the new-comers

     [[-2], [3, -2, 3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

    [[-2], [-2, -2, 3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                         Let's pick , [[3], [3, -2, 3]]

    Vertex , [[3], [3, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, 3], [3, -2, 3]], [[3, -2], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[3], [3, 3, -2, 3]], [[3], [-2, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                         namely , [[3, 3], [3, -2, 3]]

          so we pick the legal children of, [[3], [3, -2, 3]],  to be

                 {[[3, 3], [3, -2, 3]], [[3, -2], [3, -2, 3]]}

                          Let's examine the new-comers

         [[3, 3], [3, -2, 3]],  is a clone, so it is a permanent leaf,

    [[3, -2], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[3, -2], [3, -2, 3]]

  Vertex , [[3, -2], [3, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, 3], [3, -2, 3]], [[3, -2, -2], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[3, -2], [3, 3, -2, 3]], [[3, -2], [-2, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[3, -2, 3], [3, -2, 3]]

        so we pick the legal children of, [[3, -2], [3, -2, 3]],  to be

             {[[3, -2, 3], [3, -2, 3]], [[3, -2, -2], [3, -2, 3]]}

                          Let's examine the new-comers

       [[3, -2, 3], [3, -2, 3]],  is a clone, so it is a permanent leaf,

  [[3, -2, -2], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3, -2, -2], [3, -2, 3]]

 Vertex , [[3, -2, -2], [3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, -2], [3, -2, 3]], [[3, -2, -2, 3], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [-2, 3, -2, 3]], [[3, -2, -2], [3, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                     namely , [[3, -2, -2, 3], [3, -2, 3]]

      so we pick the legal children of, [[3, -2, -2], [3, -2, 3]],  to be

         {[[3, -2, -2, -2], [3, -2, 3]], [[3, -2, -2, 3], [3, -2, 3]]}

                          Let's examine the new-comers

[[3, -2, -2, -2], [3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

     [[3, -2, -2, 3], [3, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[3, -2, -2, -2], [3, -2, 3]]

 Vertex , [[3, -2, -2, -2], [3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, -2, 3], [3, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[3, -2, -2, -2], [3, 3, -2, 3]], [[3, -2, -2, -2], [-2, 3, -2, 3]]}

           Both sons from the first wife are clones, so we pick them

     namley we pick, as children of, [[3, -2, -2, -2], [3, -2, 3]],  to be

     {[[3, -2, -2, -2, 3], [3, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, 3]]}

                          Let's examine the new-comers

   [[3, -2, -2, -2, 3], [3, -2, 3]],  is a clone, so it is a permanent leaf,

   [[3, -2, -2, -2, -2], [3, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                        Let's pick , [[-2], [3, -2, 3]]

    Vertex , [[-2], [3, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2], [3, -2, 3]], [[-2, 3], [3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2], [3, 3, -2, 3]], [[-2], [-2, 3, -2, 3]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                     90, 10

                   and their respective gcd with, 1000,  are

                                     10, 10



                   The cardinalites from the second wife are

                                     50, 50

                   and their respective gcd with, 1000,  are

                                     50, 50

The second wife won!, we pick, as legal heirs,

    {[[-2], [3, 3, -2, 3]], [[-2], [-2, 3, -2, 3]]}

                          Let's examine the new-comers

    [[-2], [3, 3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

    [[-2], [-2, 3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[], [3, -2, -2, -2, 3]]

 Vertex , [[], [3, -2, -2, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, -2, -2, 3]], [[-2], [3, -2, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[], [-2, 3, -2, -2, -2, 3]], [[], [3, 3, -2, -2, -2, 3]]}

           Both sons from the second wife are clones, so we pick them

       namley we pick, as children of, [[], [3, -2, -2, -2, 3]],  to be

          {[[], [-2, 3, -2, -2, -2, 3]], [[], [3, 3, -2, -2, -2, 3]]}

                          Let's examine the new-comers

     [[], [-2, 3, -2, -2, -2, 3]],  is a clone, so it is a permanent leaf,

      [[], [3, 3, -2, -2, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[3, -2, -2], [3, -2, -2, 3]]

 Vertex , [[3, -2, -2], [3, -2, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, 3], [3, -2, -2, 3]], [[3, -2, -2, -2], [3, -2, -2, 3]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [3, 3, -2, -2, 3]], [[3, -2, -2], [-2, 3, -2, -2, 3]]}

                 One of the sons from the first wife is a clone

                   namely , [[3, -2, -2, 3], [3, -2, -2, 3]]

    so we pick the legal children of, [[3, -2, -2], [3, -2, -2, 3]],  to be

     {[[3, -2, -2, 3], [3, -2, -2, 3]], [[3, -2, -2, -2], [3, -2, -2, 3]]}

                          Let's examine the new-comers

   [[3, -2, -2, 3], [3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

[[3, -2, -2, -2], [3, -2, -2, 3]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                 Let's pick , [[3, -2, -2, -2], [3, -2, -2, 3]]

 Vertex , [[3, -2, -2, -2], [3, -2, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {

    [[3, -2, -2, -2, 3], [3, -2, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, -2, 3]]

    }

From the second wife, he had the pair, {

    [[3, -2, -2, -2], [3, 3, -2, -2, 3]], [[3, -2, -2, -2], [-2, 3, -2, -2, 3]]

    }

           Both sons from the first wife are clones, so we pick them

   namley we pick, as children of, [[3, -2, -2, -2], [3, -2, -2, 3]],  to be

 {[[3, -2, -2, -2, 3], [3, -2, -2, 3]], [[3, -2, -2, -2, -2], [3, -2, -2, 3]]}

                          Let's examine the new-comers

 [[3, -2, -2, -2, 3], [3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

 [[3, -2, -2, -2, -2], [3, -2, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                 Let's pick , [[-2, -2, 3, -2, -2, -2], [3, 3]]

 Vertex , [[-2, -2, 3, -2, -2, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {

    [[-2, -2, 3, -2, -2, -2, -2], [3, 3]], [[-2, -2, 3, -2, -2, -2, 3], [3, 3]]

    }

From the second wife, he had the pair, {

    [[-2, -2, 3, -2, -2, -2], [3, 3, 3]], [[-2, -2, 3, -2, -2, -2], [-2, 3, 3]]

    }

           Both sons from the first wife are clones, so we pick them

   namley we pick, as children of, [[-2, -2, 3, -2, -2, -2], [3, 3]],  to be

 {[[-2, -2, 3, -2, -2, -2, -2], [3, 3]], [[-2, -2, 3, -2, -2, -2, 3], [3, 3]]}

                          Let's examine the new-comers

 [[-2, -2, 3, -2, -2, -2, -2], [3, 3]],  is a clone, so it is a permanent leaf,

 [[-2, -2, 3, -2, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[-2, 3, -2, -2], [3, 3]]

 Vertex , [[-2, 3, -2, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, -2, -2], [3, 3]], [[-2, 3, -2, -2, 3], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, 3, -2, -2], [3, 3, 3]], [[-2, 3, -2, -2], [-2, 3, 3]]}

                 One of the sons from the first wife is a clone

                     namely , [[-2, 3, -2, -2, 3], [3, 3]]

      so we pick the legal children of, [[-2, 3, -2, -2], [3, 3]],  to be

         {[[-2, 3, -2, -2, -2], [3, 3]], [[-2, 3, -2, -2, 3], [3, 3]]}

                          Let's examine the new-comers

[[-2, 3, -2, -2, -2], [3, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

     [[-2, 3, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[-2, 3, -2, -2, -2], [3, 3]]

 Vertex , [[-2, 3, -2, -2, -2], [3, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, -2, -2, 3], [3, 3]], [[-2, 3, -2, -2, -2, -2], [3, 3]]}

From the second wife, he had the pair,

    {[[-2, 3, -2, -2, -2], [3, 3, 3]], [[-2, 3, -2, -2, -2], [-2, 3, 3]]}

           Both sons from the first wife are clones, so we pick them

     namley we pick, as children of, [[-2, 3, -2, -2, -2], [3, 3]],  to be

     {[[-2, 3, -2, -2, -2, 3], [3, 3]], [[-2, 3, -2, -2, -2, -2], [3, 3]]}

                          Let's examine the new-comers

   [[-2, 3, -2, -2, -2, 3], [3, 3]],  is a clone, so it is a permanent leaf,

   [[-2, 3, -2, -2, -2, -2], [3, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[-2], [3, 3, -2, 3]]

  Vertex , [[-2], [3, 3, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [3, 3, -2, 3]], [[-2, -2], [3, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2], [-2, 3, 3, -2, 3]], [[-2], [3, 3, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2, -2], [3, 3, -2, 3]]

        so we pick the legal children of, [[-2], [3, 3, -2, 3]],  to be

             {[[-2, 3], [3, 3, -2, 3]], [[-2, -2], [3, 3, -2, 3]]}

                          Let's examine the new-comers

   [[-2, 3], [3, 3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[-2, -2], [3, 3, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[-2, 3], [3, 3, -2, 3]]

 Vertex , [[-2, 3], [3, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, 3], [3, 3, -2, 3]], [[-2, 3, -2], [3, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2, 3], [3, 3, 3, -2, 3]], [[-2, 3], [-2, 3, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                      namely , [[-2, 3, 3], [3, 3, -2, 3]]

      so we pick the legal children of, [[-2, 3], [3, 3, -2, 3]],  to be

          {[[-2, 3, 3], [3, 3, -2, 3]], [[-2, 3, -2], [3, 3, -2, 3]]}

                          Let's examine the new-comers

      [[-2, 3, 3], [3, 3, -2, 3]],  is a clone, so it is a permanent leaf,

 [[-2, 3, -2], [3, 3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                   Let's pick , [[-2, 3, -2], [3, 3, -2, 3]]

 Vertex , [[-2, 3, -2], [3, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, 3], [3, 3, -2, 3]], [[-2, 3, -2, -2], [3, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2, 3, -2], [3, 3, 3, -2, 3]], [[-2, 3, -2], [-2, 3, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                    namely , [[-2, 3, -2, 3], [3, 3, -2, 3]]

    so we pick the legal children of, [[-2, 3, -2], [3, 3, -2, 3]],  to be

      {[[-2, 3, -2, 3], [3, 3, -2, 3]], [[-2, 3, -2, -2], [3, 3, -2, 3]]}

                          Let's examine the new-comers

    [[-2, 3, -2, 3], [3, 3, -2, 3]],  is a clone, so it is a permanent leaf,

[[-2, 3, -2, -2], [3, 3, -2, 3]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                 Let's pick , [[-2, 3, -2, -2], [3, 3, -2, 3]]

 Vertex , [[-2, 3, -2, -2], [3, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, -2, -2], [3, 3, -2, 3]], [[-2, 3, -2, -2, 3], [3, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2, 3, -2, -2], [-2, 3, 3, -2, 3]], [[-2, 3, -2, -2], [3, 3, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                  namely , [[-2, 3, -2, -2, 3], [3, 3, -2, 3]]

  so we pick the legal children of, [[-2, 3, -2, -2], [3, 3, -2, 3]],  to be

  {[[-2, 3, -2, -2, -2], [3, 3, -2, 3]], [[-2, 3, -2, -2, 3], [3, 3, -2, 3]]}

                          Let's examine the new-comers

[[-2, 3, -2, -2, -2], [3, 3, -2, 3]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

  [[-2, 3, -2, -2, 3], [3, 3, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

               Let's pick , [[-2, 3, -2, -2, -2], [3, 3, -2, 3]]

 Vertex , [[-2, 3, -2, -2, -2], [3, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {[[-2, 3, -2, -2, -2, 3], [3, 3, -2, 3]],

    [[-2, 3, -2, -2, -2, -2], [3, 3, -2, 3]]}

From the second wife, he had the pair, {

    [[-2, 3, -2, -2, -2], [3, 3, 3, -2, 3]],

    [[-2, 3, -2, -2, -2], [-2, 3, 3, -2, 3]]}

           Both sons from the first wife are clones, so we pick them

 namley we pick, as children of, [[-2, 3, -2, -2, -2], [3, 3, -2, 3]],  to be

{[[-2, 3, -2, -2, -2, 3], [3, 3, -2, 3]],

    [[-2, 3, -2, -2, -2, -2], [3, 3, -2, 3]]}

                          Let's examine the new-comers

[[-2, 3, -2, -2, -2, 3], [3, 3, -2, 3]],

     is a clone, so it is a permanent leaf,

[[-2, 3, -2, -2, -2, -2], [3, 3, -2, 3]],

     is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                      Let's pick , [[-2], [-2, 3, -2, 3]]

  Vertex , [[-2], [-2, 3, -2, 3]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [-2, 3, -2, 3]], [[-2, -2], [-2, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2], [3, -2, 3, -2, 3]], [[-2], [-2, -2, 3, -2, 3]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2, 3], [-2, 3, -2, 3]]

       so we pick the legal children of, [[-2], [-2, 3, -2, 3]],  to be

            {[[-2, 3], [-2, 3, -2, 3]], [[-2, -2], [-2, 3, -2, 3]]}

                          Let's examine the new-comers

       [[-2, 3], [-2, 3, -2, 3]],  is a clone, so it is a permanent leaf,

  [[-2, -2], [-2, 3, -2, 3]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                    Let's pick , [[-2, -2], [-2, 3, -2, 3]]

 Vertex , [[-2, -2], [-2, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, 3], [-2, 3, -2, 3]], [[-2, -2, -2], [-2, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2, -2], [3, -2, 3, -2, 3]], [[-2, -2], [-2, -2, 3, -2, 3]]}

        One of the sons from the second wife is a clone, so we pick them

                     namely , [[-2, -2], [3, -2, 3, -2, 3]]

      so we pick the legal children of, [[-2, -2], [-2, 3, -2, 3]], to be

        {[[-2, -2], [3, -2, 3, -2, 3]], [[-2, -2], [-2, -2, 3, -2, 3]]}

                          Let's examine the new-comers

     [[-2, -2], [3, -2, 3, -2, 3]],  is a clone, so it is a permanent leaf,

[[-2, -2], [-2, -2, 3, -2, 3]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                  Let's pick , [[-2, -2], [-2, -2, 3, -2, 3]]

 Vertex , [[-2, -2], [-2, -2, 3, -2, 3]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2, -2], [-2, -2, 3, -2, 3]], [[-2, -2, 3], [-2, -2, 3, -2, 3]]}

From the second wife, he had the pair,

    {[[-2, -2], [-2, -2, -2, 3, -2, 3]], [[-2, -2], [3, -2, -2, 3, -2, 3]]}

           Both sons from the second wife are clones, so we pick them

    namley we pick, as children of, [[-2, -2], [-2, -2, 3, -2, 3]],  to be

    {[[-2, -2], [-2, -2, -2, 3, -2, 3]], [[-2, -2], [3, -2, -2, 3, -2, 3]]}

                          Let's examine the new-comers

  [[-2, -2], [-2, -2, -2, 3, -2, 3]],  is a clone, so it is a permanent leaf,

   [[-2, -2], [3, -2, -2, 3, -2, 3]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                           Let's pick , [[], [3, -2]]

      Vertex , [[], [3, -2]], has two pairs of children from his two wives

    From the first wife, he had the pair, {[[3], [3, -2]], [[-2], [3, -2]]}

  From the second wife, he had the pair, {[[], [3, 3, -2]], [[], [-2, 3, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    42, 258

                   and their respective gcd with, 1000,  are

                                      2, 2



                   The cardinalites from the second wife are

                                    130, 170

                   and their respective gcd with, 1000,  are

                                     10, 10

The second wife won!, we pick, as legal heirs,

    {[[], [3, 3, -2]], [[], [-2, 3, -2]]}

                          Let's examine the new-comers

       [[], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[], [-2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[], [3, 3, -2]]

     Vertex , [[], [3, 3, -2]], has two pairs of children from his two wives

 From the first wife, he had the pair, {[[-2], [3, 3, -2]], [[3], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[], [-2, 3, 3, -2]], [[], [3, 3, 3, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    110, 20

                   and their respective gcd with, 1000,  are

                                     10, 20



                   The cardinalites from the second wife are

                                     69, 61

                   and their respective gcd with, 1000,  are

                                      1, 1

The first wife won!, we pick, as legal heirs,

    {[[-2], [3, 3, -2]], [[3], [3, 3, -2]]}

                          Let's examine the new-comers

      [[-2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[3], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                        Let's pick , [[-2], [3, 3, -2]]

    Vertex , [[-2], [3, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [3, 3, -2]], [[-2, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[-2], [3, 3, 3, -2]], [[-2], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                        namely , [[-2, -2], [3, 3, -2]]

         so we pick the legal children of, [[-2], [3, 3, -2]],  to be

                {[[-2, 3], [3, 3, -2]], [[-2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

    [[-2, 3], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[-2, -2], [3, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                         Let's pick , [[], [-2, 3, -2]]

    Vertex , [[], [-2, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair, {[[3], [-2, 3, -2]], [[-2], [-2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [-2, -2, 3, -2]], [[], [3, -2, 3, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    22, 148

                   and their respective gcd with, 1000,  are

                                      2, 4



                   The cardinalites from the second wife are

                                    70, 100

                   and their respective gcd with, 1000,  are

                                    10, 100

The second wife won!, we pick, as legal heirs,

    {[[], [-2, -2, 3, -2]], [[], [3, -2, 3, -2]]}

                          Let's examine the new-comers

    [[], [-2, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

     [[], [3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [-2, -2, 3, -2]]

  Vertex , [[], [-2, -2, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [-2, -2, 3, -2]], [[-2], [-2, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [3, -2, -2, 3, -2]], [[], [-2, -2, -2, 3, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                       namely , [[], [-2, -2, -2, 3, -2]]

        so we pick the legal children of, [[], [-2, -2, 3, -2]], to be

             {[[], [3, -2, -2, 3, -2]], [[], [-2, -2, -2, 3, -2]]}

                          Let's examine the new-comers

   [[], [3, -2, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[], [-2, -2, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[], [3, -2, -2, 3, -2]]

 Vertex , [[], [3, -2, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, -2, 3, -2]], [[-2], [3, -2, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, -2, 3, -2]], [[], [-2, 3, -2, -2, 3, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                      namely , [[], [3, 3, -2, -2, 3, -2]]

       so we pick the legal children of, [[], [3, -2, -2, 3, -2]], to be

          {[[], [3, 3, -2, -2, 3, -2]], [[], [-2, 3, -2, -2, 3, -2]]}

                          Let's examine the new-comers

      [[], [3, 3, -2, -2, 3, -2]],  is a clone, so it is a permanent leaf,

 [[], [-2, 3, -2, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                   Let's pick , [[], [-2, 3, -2, -2, 3, -2]]

 Vertex , [[], [-2, 3, -2, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2], [-2, 3, -2, -2, 3, -2]], [[3], [-2, 3, -2, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [-2, -2, 3, -2, -2, 3, -2]], [[], [3, -2, 3, -2, -2, 3, -2]]}

           Both sons from the second wife are clones, so we pick them

     namley we pick, as children of, [[], [-2, 3, -2, -2, 3, -2]],  to be

      {[[], [-2, -2, 3, -2, -2, 3, -2]], [[], [3, -2, 3, -2, -2, 3, -2]]}

                          Let's examine the new-comers

   [[], [-2, -2, 3, -2, -2, 3, -2]],  is a clone, so it is a permanent leaf,

    [[], [3, -2, 3, -2, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                         Let's pick , [[3], [3, 3, -2]]

    Vertex , [[3], [3, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, 3], [3, 3, -2]], [[3, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[3], [3, 3, 3, -2]], [[3], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                         namely , [[3, 3], [3, 3, -2]]

          so we pick the legal children of, [[3], [3, 3, -2]],  to be

                 {[[3, 3], [3, 3, -2]], [[3, -2], [3, 3, -2]]}

                          Let's examine the new-comers

         [[3, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

    [[3, -2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[3, -2], [3, 3, -2]]

  Vertex , [[3, -2], [3, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2], [3, 3, -2]], [[3, -2, 3], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[3, -2], [3, 3, 3, -2]], [[3, -2], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                       namely , [[3, -2, 3], [3, 3, -2]]

        so we pick the legal children of, [[3, -2], [3, 3, -2]],  to be

             {[[3, -2, -2], [3, 3, -2]], [[3, -2, 3], [3, 3, -2]]}

                          Let's examine the new-comers

  [[3, -2, -2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[3, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3, -2, -2], [3, 3, -2]]

 Vertex , [[3, -2, -2], [3, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [3, 3, 3, -2]], [[3, -2, -2], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                     namely , [[3, -2, -2, 3], [3, 3, -2]]

      so we pick the legal children of, [[3, -2, -2], [3, 3, -2]],  to be

         {[[3, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

     [[3, -2, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

[[3, -2, -2, -2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                   Let's pick , [[3, -2, -2, -2], [3, 3, -2]]

 Vertex , [[3, -2, -2, -2], [3, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[3, -2, -2, -2], [3, 3, 3, -2]], [[3, -2, -2, -2], [-2, 3, 3, -2]]}

           Both sons from the first wife are clones, so we pick them

     namley we pick, as children of, [[3, -2, -2, -2], [3, 3, -2]],  to be

     {[[3, -2, -2, -2, 3], [3, 3, -2]], [[3, -2, -2, -2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

   [[3, -2, -2, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

   [[3, -2, -2, -2, -2], [3, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                          Let's pick , [[], [-2, -2]]

      Vertex , [[], [-2, -2]], has two pairs of children from his two wives

   From the first wife, he had the pair, {[[3], [-2, -2]], [[-2], [-2, -2]]}

 From the second wife, he had the pair, {[[], [3, -2, -2]], [[], [-2, -2, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    46, 254

                   and their respective gcd with, 1000,  are

                                      2, 2



                   The cardinalites from the second wife are

                                    200, 100

                   and their respective gcd with, 1000,  are

                                    200, 100

The second wife won!, we pick, as legal heirs,

    {[[], [3, -2, -2]], [[], [-2, -2, -2]]}

                          Let's examine the new-comers

      [[], [3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[], [-2, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                         Let's pick , [[], [3, -2, -2]]

    Vertex , [[], [3, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair, {[[3], [3, -2, -2]], [[-2], [3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, -2]], [[], [-2, 3, -2, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                    26, 174

                   and their respective gcd with, 1000,  are

                                      2, 2



                   The cardinalites from the second wife are

                                    110, 90

                   and their respective gcd with, 1000,  are

                                     10, 10

The second wife won!, we pick, as legal heirs,

    {[[], [3, 3, -2, -2]], [[], [-2, 3, -2, -2]]}

                          Let's examine the new-comers

     [[], [3, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

    [[], [-2, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [3, 3, -2, -2]]

   Vertex , [[], [3, 3, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, 3, -2, -2]], [[-2], [3, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [-2, 3, 3, -2, -2]], [[], [3, 3, 3, -2, -2]]}

                 One of the sons from the first wife is a clone

                        namely , [[-2], [3, 3, -2, -2]]

        so we pick the legal children of, [[], [3, 3, -2, -2]],  to be

                {[[3], [3, 3, -2, -2]], [[-2], [3, 3, -2, -2]]}

                          Let's examine the new-comers

    [[3], [3, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[-2], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[3], [3, 3, -2, -2]]

  Vertex , [[3], [3, 3, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, 3], [3, 3, -2, -2]], [[3, -2], [3, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[3], [3, 3, 3, -2, -2]], [[3], [-2, 3, 3, -2, -2]]}

                 One of the sons from the first wife is a clone

                       namely , [[3, 3], [3, 3, -2, -2]]

        so we pick the legal children of, [[3], [3, 3, -2, -2]],  to be

             {[[3, 3], [3, 3, -2, -2]], [[3, -2], [3, 3, -2, -2]]}

                          Let's examine the new-comers

       [[3, 3], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

  [[3, -2], [3, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [-2, 3, -2, -2]]

  Vertex , [[], [-2, 3, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [-2, 3, -2, -2]], [[-2], [-2, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [3, -2, 3, -2, -2]], [[], [-2, -2, 3, -2, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                       namely , [[], [-2, -2, 3, -2, -2]]

        so we pick the legal children of, [[], [-2, 3, -2, -2]], to be

             {[[], [3, -2, 3, -2, -2]], [[], [-2, -2, 3, -2, -2]]}

                          Let's examine the new-comers

   [[], [3, -2, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

       [[], [-2, -2, 3, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3, -2], [3, 3, -2, -2]]

 Vertex , [[3, -2], [3, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, 3], [3, 3, -2, -2]], [[3, -2, -2], [3, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[3, -2], [3, 3, 3, -2, -2]], [[3, -2], [-2, 3, 3, -2, -2]]}

                 One of the sons from the first wife is a clone

                     namely , [[3, -2, 3], [3, 3, -2, -2]]

      so we pick the legal children of, [[3, -2], [3, 3, -2, -2]],  to be

         {[[3, -2, 3], [3, 3, -2, -2]], [[3, -2, -2], [3, 3, -2, -2]]}

                          Let's examine the new-comers

     [[3, -2, 3], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

[[3, -2, -2], [3, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[], [3, -2, 3, -2, -2]]

 Vertex , [[], [3, -2, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, 3, -2, -2]], [[-2], [3, -2, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, 3, -2, -2]], [[], [-2, 3, -2, 3, -2, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                      namely , [[], [3, 3, -2, 3, -2, -2]]

       so we pick the legal children of, [[], [3, -2, 3, -2, -2]], to be

          {[[], [3, 3, -2, 3, -2, -2]], [[], [-2, 3, -2, 3, -2, -2]]}

                          Let's examine the new-comers

      [[], [3, 3, -2, 3, -2, -2]],  is a clone, so it is a permanent leaf,

 [[], [-2, 3, -2, 3, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                   Let's pick , [[], [-2, 3, -2, 3, -2, -2]]

 Vertex , [[], [-2, 3, -2, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2], [-2, 3, -2, 3, -2, -2]], [[3], [-2, 3, -2, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [-2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, 3, -2, 3, -2, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                    namely , [[], [3, -2, 3, -2, 3, -2, -2]]

     so we pick the legal children of, [[], [-2, 3, -2, 3, -2, -2]], to be

      {[[], [-2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, 3, -2, 3, -2, -2]]}

                          Let's examine the new-comers

[[], [-2, -2, 3, -2, 3, -2, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

    [[], [3, -2, 3, -2, 3, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                 Let's pick , [[], [-2, -2, 3, -2, 3, -2, -2]]

 Vertex , [[], [-2, -2, 3, -2, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2], [-2, -2, 3, -2, 3, -2, -2]], [[3], [-2, -2, 3, -2, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[], [-2, -2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, -2, 3, -2, 3, -2, -2]]}

           Both sons from the second wife are clones, so we pick them

   namley we pick, as children of, [[], [-2, -2, 3, -2, 3, -2, -2]],  to be

  {[[], [-2, -2, -2, 3, -2, 3, -2, -2]], [[], [3, -2, -2, 3, -2, 3, -2, -2]]}

                          Let's examine the new-comers

 [[], [-2, -2, -2, 3, -2, 3, -2, -2]],  is a clone, so it is a permanent leaf,

  [[], [3, -2, -2, 3, -2, 3, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                        Let's pick , [[], [-2, -2, -2]]

    Vertex , [[], [-2, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [-2, -2, -2]], [[-2], [-2, -2, -2]]}

From the second wife, he had the pair,

    {[[], [3, -2, -2, -2]], [[], [-2, -2, -2, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                        namely , [[], [-2, -2, -2, -2]]

          so we pick the legal children of, [[], [-2, -2, -2]], to be

                {[[], [3, -2, -2, -2]], [[], [-2, -2, -2, -2]]}

                          Let's examine the new-comers

    [[], [3, -2, -2, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

        [[], [-2, -2, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [3, -2, -2, -2]]

  Vertex , [[], [3, -2, -2, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, -2, -2]], [[-2], [3, -2, -2, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, -2, -2]], [[], [-2, 3, -2, -2, -2]]}

           Both sons from the second wife are clones, so we pick them

         namley we pick, as children of, [[], [3, -2, -2, -2]],  to be

             {[[], [3, 3, -2, -2, -2]], [[], [-2, 3, -2, -2, -2]]}

                          Let's examine the new-comers

       [[], [3, 3, -2, -2, -2]],  is a clone, so it is a permanent leaf,

       [[], [-2, 3, -2, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[3, -2, -2], [3, 3, -2, -2]]

 Vertex , [[3, -2, -2], [3, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2], [3, 3, -2, -2]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [3, 3, 3, -2, -2]], [[3, -2, -2], [-2, 3, 3, -2, -2]]}

                 One of the sons from the first wife is a clone

                   namely , [[3, -2, -2, 3], [3, 3, -2, -2]]

    so we pick the legal children of, [[3, -2, -2], [3, 3, -2, -2]],  to be

     {[[3, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2], [3, 3, -2, -2]]}

                          Let's examine the new-comers

   [[3, -2, -2, 3], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

[[3, -2, -2, -2], [3, 3, -2, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                 Let's pick , [[3, -2, -2, -2], [3, 3, -2, -2]]

 Vertex , [[3, -2, -2, -2], [3, 3, -2, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {

    [[3, -2, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2, -2], [3, 3, -2, -2]]

    }

From the second wife, he had the pair, {

    [[3, -2, -2, -2], [3, 3, 3, -2, -2]], [[3, -2, -2, -2], [-2, 3, 3, -2, -2]]

    }

           Both sons from the first wife are clones, so we pick them

   namley we pick, as children of, [[3, -2, -2, -2], [3, 3, -2, -2]],  to be

 {[[3, -2, -2, -2, 3], [3, 3, -2, -2]], [[3, -2, -2, -2, -2], [3, 3, -2, -2]]}

                          Let's examine the new-comers

 [[3, -2, -2, -2, 3], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

 [[3, -2, -2, -2, -2], [3, 3, -2, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[], [3, -2, 3, -2]]

   Vertex , [[], [3, -2, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [3, -2, 3, -2]], [[-2], [3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, -2, 3, -2]], [[], [-2, 3, -2, 3, -2]]}

             Let's examine the cardinalities of these four children

                    The cardinalites from the first wife are

                                     10, 90

                   and their respective gcd with, 1000,  are

                                     10, 10



                   The cardinalites from the second wife are

                                     50, 50

                   and their respective gcd with, 1000,  are

                                     50, 50

The second wife won!, we pick, as legal heirs,

    {[[], [3, 3, -2, 3, -2]], [[], [-2, 3, -2, 3, -2]]}

                          Let's examine the new-comers

   [[], [3, 3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

   [[], [-2, 3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                      Let's pick , [[], [3, 3, -2, 3, -2]]

 Vertex , [[], [3, 3, -2, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2], [3, 3, -2, 3, -2]], [[3], [3, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [3, 3, 3, -2, 3, -2]], [[], [-2, 3, 3, -2, 3, -2]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2], [3, 3, -2, 3, -2]]

       so we pick the legal children of, [[], [3, 3, -2, 3, -2]],  to be

             {[[-2], [3, 3, -2, 3, -2]], [[3], [3, 3, -2, 3, -2]]}

                          Let's examine the new-comers

       [[-2], [3, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

   [[3], [3, 3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[3], [3, 3, -2, 3, -2]]

 Vertex , [[3], [3, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2], [3, 3, -2, 3, -2]], [[3, 3], [3, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[3], [3, 3, 3, -2, 3, -2]], [[3], [-2, 3, 3, -2, 3, -2]]}

                 One of the sons from the first wife is a clone

                      namely , [[3, 3], [3, 3, -2, 3, -2]]

      so we pick the legal children of, [[3], [3, 3, -2, 3, -2]],  to be

          {[[3, -2], [3, 3, -2, 3, -2]], [[3, 3], [3, 3, -2, 3, -2]]}

                          Let's examine the new-comers

 [[3, -2], [3, 3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

      [[3, 3], [3, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                   Let's pick , [[3, -2], [3, 3, -2, 3, -2]]

 Vertex , [[3, -2], [3, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2], [3, 3, -2, 3, -2]], [[3, -2, 3], [3, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[3, -2], [-2, 3, 3, -2, 3, -2]], [[3, -2], [3, 3, 3, -2, 3, -2]]}

                 One of the sons from the first wife is a clone

                    namely , [[3, -2, 3], [3, 3, -2, 3, -2]]

    so we pick the legal children of, [[3, -2], [3, 3, -2, 3, -2]],  to be

      {[[3, -2, -2], [3, 3, -2, 3, -2]], [[3, -2, 3], [3, 3, -2, 3, -2]]}

                          Let's examine the new-comers

[[3, -2, -2], [3, 3, -2, 3, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

    [[3, -2, 3], [3, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                 Let's pick , [[3, -2, -2], [3, 3, -2, 3, -2]]

 Vertex , [[3, -2, -2], [3, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3, -2, -2, 3], [3, 3, -2, 3, -2]], [[3, -2, -2, -2], [3, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[3, -2, -2], [3, 3, 3, -2, 3, -2]], [[3, -2, -2], [-2, 3, 3, -2, 3, -2]]}

                 One of the sons from the first wife is a clone

                  namely , [[3, -2, -2, 3], [3, 3, -2, 3, -2]]

  so we pick the legal children of, [[3, -2, -2], [3, 3, -2, 3, -2]],  to be

  {[[3, -2, -2, 3], [3, 3, -2, 3, -2]], [[3, -2, -2, -2], [3, 3, -2, 3, -2]]}

                          Let's examine the new-comers

  [[3, -2, -2, 3], [3, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

[[3, -2, -2, -2], [3, 3, -2, 3, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

               Let's pick , [[3, -2, -2, -2], [3, 3, -2, 3, -2]]

 Vertex , [[3, -2, -2, -2], [3, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {[[3, -2, -2, -2, 3], [3, 3, -2, 3, -2]],

    [[3, -2, -2, -2, -2], [3, 3, -2, 3, -2]]}

From the second wife, he had the pair, {

    [[3, -2, -2, -2], [3, 3, 3, -2, 3, -2]],

    [[3, -2, -2, -2], [-2, 3, 3, -2, 3, -2]]}

           Both sons from the first wife are clones, so we pick them

 namley we pick, as children of, [[3, -2, -2, -2], [3, 3, -2, 3, -2]],  to be

{[[3, -2, -2, -2, 3], [3, 3, -2, 3, -2]],

    [[3, -2, -2, -2, -2], [3, 3, -2, 3, -2]]}

                          Let's examine the new-comers

[[3, -2, -2, -2, 3], [3, 3, -2, 3, -2]],

     is a clone, so it is a permanent leaf,

[[3, -2, -2, -2, -2], [3, 3, -2, 3, -2]],

     is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                     Let's pick , [[], [-2, 3, -2, 3, -2]]

 Vertex , [[], [-2, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[3], [-2, 3, -2, 3, -2]], [[-2], [-2, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[], [3, -2, 3, -2, 3, -2]], [[], [-2, -2, 3, -2, 3, -2]]}

                 One of the sons from the first wife is a clone

                       namely , [[3], [-2, 3, -2, 3, -2]]

      so we pick the legal children of, [[], [-2, 3, -2, 3, -2]],  to be

            {[[3], [-2, 3, -2, 3, -2]], [[-2], [-2, 3, -2, 3, -2]]}

                          Let's examine the new-comers

       [[3], [-2, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

  [[-2], [-2, 3, -2, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                    Let's pick , [[-2], [-2, 3, -2, 3, -2]]

 Vertex , [[-2], [-2, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, -2], [-2, 3, -2, 3, -2]], [[-2, 3], [-2, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[-2], [-2, -2, 3, -2, 3, -2]], [[-2], [3, -2, 3, -2, 3, -2]]}

        One of the sons from the second wife is a clone, so we pick them

                     namely , [[-2], [3, -2, 3, -2, 3, -2]]

      so we pick the legal children of, [[-2], [-2, 3, -2, 3, -2]], to be

        {[[-2], [-2, -2, 3, -2, 3, -2]], [[-2], [3, -2, 3, -2, 3, -2]]}

                          Let's examine the new-comers

[[-2], [-2, -2, 3, -2, 3, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

     [[-2], [3, -2, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                  Let's pick , [[-2], [-2, -2, 3, -2, 3, -2]]

 Vertex , [[-2], [-2, -2, 3, -2, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3], [-2, -2, 3, -2, 3, -2]], [[-2, -2], [-2, -2, 3, -2, 3, -2]]}

From the second wife, he had the pair,

    {[[-2], [-2, -2, -2, 3, -2, 3, -2]], [[-2], [3, -2, -2, 3, -2, 3, -2]]}

           Both sons from the second wife are clones, so we pick them

    namley we pick, as children of, [[-2], [-2, -2, 3, -2, 3, -2]],  to be

    {[[-2], [-2, -2, -2, 3, -2, 3, -2]], [[-2], [3, -2, -2, 3, -2, 3, -2]]}

                          Let's examine the new-comers

  [[-2], [-2, -2, -2, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

   [[-2], [3, -2, -2, 3, -2, 3, -2]],  is a clone, so it is a permanent leaf,

                 There are still non-empty or non-clone leaves

                       Let's pick , [[-2, 3], [3, 3, -2]]

  Vertex , [[-2, 3], [3, 3, -2]], has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, 3], [3, 3, -2]], [[-2, 3, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[-2, 3], [3, 3, 3, -2]], [[-2, 3], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                       namely , [[-2, 3, 3], [3, 3, -2]]

        so we pick the legal children of, [[-2, 3], [3, 3, -2]],  to be

             {[[-2, 3, 3], [3, 3, -2]], [[-2, 3, -2], [3, 3, -2]]}

                          Let's examine the new-comers

       [[-2, 3, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

  [[-2, 3, -2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                     Let's pick , [[-2, 3, -2], [3, 3, -2]]

 Vertex , [[-2, 3, -2], [3, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[-2, 3, -2], [-2, 3, 3, -2]], [[-2, 3, -2], [3, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                     namely , [[-2, 3, -2, 3], [3, 3, -2]]

      so we pick the legal children of, [[-2, 3, -2], [3, 3, -2]],  to be

         {[[-2, 3, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

     [[-2, 3, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

[[-2, 3, -2, -2], [3, 3, -2]],  is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                   Let's pick , [[-2, 3, -2, -2], [3, 3, -2]]

 Vertex , [[-2, 3, -2, -2], [3, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair,

    {[[-2, 3, -2, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2, -2], [3, 3, -2]]}

From the second wife, he had the pair,

    {[[-2, 3, -2, -2], [3, 3, 3, -2]], [[-2, 3, -2, -2], [-2, 3, 3, -2]]}

                 One of the sons from the first wife is a clone

                   namely , [[-2, 3, -2, -2, 3], [3, 3, -2]]

    so we pick the legal children of, [[-2, 3, -2, -2], [3, 3, -2]],  to be

     {[[-2, 3, -2, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

   [[-2, 3, -2, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

[[-2, 3, -2, -2, -2], [3, 3, -2]],

     is not a clone, so it is a new (temporay) leaf,

           eventually to have children (and become an internal vertex)

                 There are still non-empty or non-clone leaves

                 Let's pick , [[-2, 3, -2, -2, -2], [3, 3, -2]]

 Vertex , [[-2, 3, -2, -2, -2], [3, 3, -2]],

    has two pairs of children from his two wives

From the first wife, he had the pair, {

    [[-2, 3, -2, -2, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2, -2, -2], [3, 3, -2]]

    }

From the second wife, he had the pair, {

    [[-2, 3, -2, -2, -2], [3, 3, 3, -2]], [[-2, 3, -2, -2, -2], [-2, 3, 3, -2]]

    }

           Both sons from the first wife are clones, so we pick them

   namley we pick, as children of, [[-2, 3, -2, -2, -2], [3, 3, -2]],  to be

 {[[-2, 3, -2, -2, -2, 3], [3, 3, -2]], [[-2, 3, -2, -2, -2, -2], [3, 3, -2]]}

                          Let's examine the new-comers

 [[-2, 3, -2, -2, -2, 3], [3, 3, -2]],  is a clone, so it is a permanent leaf,

 [[-2, 3, -2, -2, -2, -2], [3, 3, -2]],  is a clone, so it is a permanent leaf,

               There are no more temporary leaves!, we are done.

               Let's look which of the internal vertices, [V1,V2]

                    is such that V1V2 belongs to our language

      Internal vertex, [[-2, 3], [3, 3, -2]],  does not have this property

     Internal vertex, [[], [3, 3, -2, 3, -2]],  does not have this property

  Internal vertex, [[3, -2, -2], [3, -2, -2, 3]],  does not have this property

    Internal vertex, [[3, -2], [3, -2, -2, 3]],  does not have this property

        Internal vertex, [[], [3, 3, -2]],  does not have this property

      Internal vertex, [[-2, -2, 3], [3, 3]],  does not have this property

        Internal vertex, [[3], [3, 3, -2]],  does not have this property

  Internal vertex, [[-2, 3, -2, -2, -2], [3, 3]],  does not have this property

      Internal vertex, [[3, -2], [3, 3, -2]],  does not have this property

  Internal vertex, [[], [-2, 3, -2, 3, -2, -2]],  does not have this property

        Internal vertex, [[], [-2, 3, -2]],  does not have this property

Internal vertex, [[3, -2, -2], [3, 3, -2, 3, -2]],  does not have this property

        Internal vertex, [[3], [3, -2, 3]],  does not have this property

  Internal vertex, [[-2, 3, -2, -2], [3, 3, -2]],  does not have this property

      Internal vertex, [[], [-2, 3, -2, -2]],  does not have this property

      Internal vertex, [[3, -2], [3, -2, 3]],  does not have this property

Internal vertex, [[3, -2, -2, -2], [3, 3, -2, 3, -2]],

     does not have this property

  Internal vertex, [[-2, 3, -2], [3, 3, -2, 3]],  does not have this property

   Internal vertex, [[-2, -2], [-2, 3, -2, 3]],  does not have this property

   Internal vertex, [[-2], [-2, 3, -2, 3, -2]],  does not have this property

         Internal vertex, [[-2], [3, 3]],  does not have this property

          Internal vertex, [[], [3, 3]],  does not have this property

        Internal vertex, [[3, -2], [3, 3]],  does not have this property

    Internal vertex, [[3, -2, -2], [3, 3, -2]],  does not have this property

      Internal vertex, [[], [-2, -2, -2, 3]],  does not have this property

Internal vertex, [[], [-2, -2, 3, -2, 3, -2, -2]],  does not have this property

          Internal vertex, [[], [3, -2, 3, -2, -2]], has this property

      Internal vertex, [[3, -2, -2], [3, 3]],  does not have this property

        Internal vertex, [[], [-2, -2, 3]],  does not have this property

      Internal vertex, [[], [3, -2, -2, 3]],  does not have this property

  Internal vertex, [[3, -2, -2, -2], [3, 3, -2]],  does not have this property

      Internal vertex, [[], [3, -2, -2, -2]],  does not have this property

Internal vertex, [[-2, 3, -2, -2], [3, 3, -2, 3]],  does not have this property

      Internal vertex, [[-2], [3, 3, -2, 3]],  does not have this property

          Internal vertex, [[3], [3, 3]],  does not have this property

    Internal vertex, [[-2, 3, -2, -2], [3, 3]],  does not have this property

    Internal vertex, [[-2, 3, -2], [3, 3, -2]],  does not have this property

          Internal vertex, [[], [3, -2, -2, -2, 3]], has this property

          Internal vertex, [[], [3, -2, -2, 3, -2]], has this property

    Internal vertex, [[-2, 3], [3, 3, -2, 3]],  does not have this property

       Internal vertex, [[-2], [3, 3, -2]],  does not have this property

        Internal vertex, [[], [3, -2, 3]],  does not have this property

  Internal vertex, [[-2, -2, 3, -2, -2], [3, 3]],  does not have this property

    Internal vertex, [[-2, -2, 3, -2], [3, 3]],  does not have this property

Internal vertex, [[-2, 3, -2, -2, -2], [3, 3, -2, 3]],

     does not have this property

          Internal vertex, [[], [3, -2]],  does not have this property

           Internal vertex, [[], [-2]],  does not have this property

      Internal vertex, [[], [-2, -2, 3, -2]],  does not have this property

  Internal vertex, [[3, -2, -2, -2], [3, -2, 3]],  does not have this property

Internal vertex, [[3, -2, -2, -2], [3, 3, -2, -2]],

     does not have this property

        Internal vertex, [[], [3, -2, -2]],  does not have this property

    Internal vertex, [[3, -2, -2, -2], [3, 3]],  does not have this property

          Internal vertex, [[], [-2, 3]],  does not have this property

  Internal vertex, [[3, -2, -2], [3, 3, -2, -2]],  does not have this property

        Internal vertex, [[-2, 3], [3, 3]],  does not have this property

      Internal vertex, [[], [3, -2, 3, -2]],  does not have this property

    Internal vertex, [[3, -2], [3, 3, -2, -2]],  does not have this property

  Internal vertex, [[], [-2, 3, -2, -2, 3, -2]],  does not have this property

   Internal vertex, [[-2], [-2, 3, -2, -2, 3]],  does not have this property

    Internal vertex, [[3, -2, -2], [3, -2, 3]],  does not have this property

           Internal vertex, [[-2], [3, -2, -2, 3]], has this property

       Internal vertex, [[-2, -2], [3, 3]],  does not have this property

      Internal vertex, [[], [3, 3, -2, -2]],  does not have this property

 Internal vertex, [[-2], [-2, -2, 3, -2, 3, -2]],  does not have this property

  Internal vertex, [[3, -2], [3, 3, -2, 3, -2]],  does not have this property

      Internal vertex, [[3], [3, -2, -2, 3]],  does not have this property

 Internal vertex, [[-2, -2], [-2, -2, 3, -2, 3]],  does not have this property

       Internal vertex, [[-2], [3, -2, 3]],  does not have this property

      Internal vertex, [[-2, 3, -2], [3, 3]],  does not have this property

Internal vertex, [[-2, -2, 3, -2, -2, -2], [3, 3]],

     does not have this property

                  Internal vertex, [[], []], has this property

Internal vertex, [[-2, 3, -2, -2, -2], [3, 3, -2]],

     does not have this property

           Internal vertex, [[-2], [-2, 3, -2, 3]], has this property

       Internal vertex, [[], [-2, -2, -2]],  does not have this property

          Internal vertex, [[], [-2, 3, -2, 3, -2]], has this property

            Internal vertex, [[], [3]],  does not have this property

Internal vertex, [[3, -2, -2, -2], [3, -2, -2, 3]],

     does not have this property

      Internal vertex, [[3], [3, 3, -2, -2]],  does not have this property

    Internal vertex, [[3], [3, 3, -2, 3, -2]],  does not have this property

         Internal vertex, [[], [-2, -2]],  does not have this property

                     The whole thing took, 5.373, second.