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.