Eliminate a lot of list-management overhead within join_search_one_level

by adding a requirement that build_join_rel add new join RelOptInfos to the
appropriate list immediately at creation.  Per report from Robert Haas,
the list_concat_unique_ptr() calls that this change eliminates were taking
the lion's share of the runtime in larger join problems.  This doesn't do
anything to fix the fundamental combinatorial explosion in large join
problems, but it should push out the threshold of pain a bit further.

Note: because this changes the order in which joinrel lists are built,
it might result in changes in selected plans in cases where different
alternatives have exactly the same costs.  There is one example in the
regression tests.

1 files changed, 770 insertions, 770 deletions

diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 0dc3e56960..fed424cb33 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -662,895 +662,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 1 | -1
-     | 1 | 4 | one   | 2 |  2 | 1 | -1
-     | 1 | 4 | one   | 3 | -3 | 1 | -1
-     | 1 | 4 | one   | 2 |  4 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 0 |    | 1 | -1
-     | 1 | 4 | one   |   |    | 1 | -1
-     | 1 | 4 | one   |   |  0 | 1 | -1
+     | 1 | 4 | one   | 1 | -1 | 2 |  2
+     | 1 | 4 | one   | 1 | -1 | 3 | -3
+     | 1 | 4 | one   | 1 | -1 | 2 |  4
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 0 |   
+     | 1 | 4 | one   | 1 | -1 |   |   
+     | 1 | 4 | one   | 1 | -1 |   |  0
      | 2 | 3 | two   | 1 | -1 | 1 | -1
-     | 2 | 3 | two   | 2 |  2 | 1 | -1
-     | 2 | 3 | two   | 3 | -3 | 1 | -1
-     | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 0 |    | 1 | -1
-     | 2 | 3 | two   |   |    | 1 | -1
-     | 2 | 3 | two   |   |  0 | 1 | -1
+     | 2 | 3 | two   | 1 | -1 | 2 |  2
+     | 2 | 3 | two   | 1 | -1 | 3 | -3
+     | 2 | 3 | two   | 1 | -1 | 2 |  4
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 0 |   
+     | 2 | 3 | two   | 1 | -1 |   |   
+     | 2 | 3 | two   | 1 | -1 |   |  0
      | 3 | 2 | three | 1 | -1 | 1 | -1
-     | 3 | 2 | three | 2 |  2 | 1 | -1
-     | 3 | 2 | three | 3 | -3 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 0 |    | 1 | -1
-     | 3 | 2 | three |   |    | 1 | -1
-     | 3 | 2 | three |   |  0 | 1 | -1
+     | 3 | 2 | three | 1 | -1 | 2 |  2
+     | 3 | 2 | three | 1 | -1 | 3 | -3
+     | 3 | 2 | three | 1 | -1 | 2 |  4
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 0 |   
+     | 3 | 2 | three | 1 | -1 |   |   
+     | 3 | 2 | three | 1 | -1 |   |  0
      | 4 | 1 | four  | 1 | -1 | 1 | -1
-     | 4 | 1 | four  | 2 |  2 | 1 | -1
-     | 4 | 1 | four  | 3 | -3 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 0 |    | 1 | -1
-     | 4 | 1 | four  |   |    | 1 | -1
-     | 4 | 1 | four  |   |  0 | 1 | -1
+     | 4 | 1 | four  | 1 | -1 | 2 |  2
+     | 4 | 1 | four  | 1 | -1 | 3 | -3
+     | 4 | 1 | four  | 1 | -1 | 2 |  4
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 0 |   
+     | 4 | 1 | four  | 1 | -1 |   |   
+     | 4 | 1 | four  | 1 | -1 |   |  0
      | 5 | 0 | five  | 1 | -1 | 1 | -1
-     | 5 | 0 | five  | 2 |  2 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 0 |    | 1 | -1
-     | 5 | 0 | five  |   |    | 1 | -1
-     | 5 | 0 | five  |   |  0 | 1 | -1
+     | 5 | 0 | five  | 1 | -1 | 2 |  2
+     | 5 | 0 | five  | 1 | -1 | 3 | -3
+     | 5 | 0 | five  | 1 | -1 | 2 |  4
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 0 |   
+     | 5 | 0 | five  | 1 | -1 |   |   
+     | 5 | 0 | five  | 1 | -1 |   |  0
      | 6 | 6 | six   | 1 | -1 | 1 | -1
-     | 6 | 6 | six   | 2 |  2 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 2 |  4 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 0 |    | 1 | -1
-     | 6 | 6 | six   |   |    | 1 | -1
-     | 6 | 6 | six   |   |  0 | 1 | -1
+     | 6 | 6 | six   | 1 | -1 | 2 |  2
+     | 6 | 6 | six   | 1 | -1 | 3 | -3
+     | 6 | 6 | six   | 1 | -1 | 2 |  4
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 0 |   
+     | 6 | 6 | six   | 1 | -1 |   |   
+     | 6 | 6 | six   | 1 | -1 |   |  0
      | 7 | 7 | seven | 1 | -1 | 1 | -1
-     | 7 | 7 | seven | 2 |  2 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 2 |  4 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 0 |    | 1 | -1
-     | 7 | 7 | seven |   |    | 1 | -1
-     | 7 | 7 | seven |   |  0 | 1 | -1
+     | 7 | 7 | seven | 1 | -1 | 2 |  2
+     | 7 | 7 | seven | 1 | -1 | 3 | -3
+     | 7 | 7 | seven | 1 | -1 | 2 |  4
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 0 |   
+     | 7 | 7 | seven | 1 | -1 |   |   
+     | 7 | 7 | seven | 1 | -1 |   |  0
      | 8 | 8 | eight | 1 | -1 | 1 | -1
-     | 8 | 8 | eight | 2 |  2 | 1 | -1
-     | 8 | 8 | eight | 3 | -3 | 1 | -1
-     | 8 | 8 | eight | 2 |  4 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 0 |    | 1 | -1
-     | 8 | 8 | eight |   |    | 1 | -1
-     | 8 | 8 | eight |   |  0 | 1 | -1
+     | 8 | 8 | eight | 1 | -1 | 2 |  2
+     | 8 | 8 | eight | 1 | -1 | 3 | -3
+     | 8 | 8 | eight | 1 | -1 | 2 |  4
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 0 |   
+     | 8 | 8 | eight | 1 | -1 |   |   
+     | 8 | 8 | eight | 1 | -1 |   |  0
      | 0 |   | zero  | 1 | -1 | 1 | -1
-     | 0 |   | zero  | 2 |  2 | 1 | -1
-     | 0 |   | zero  | 3 | -3 | 1 | -1
-     | 0 |   | zero  | 2 |  4 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 0 |    | 1 | -1
-     | 0 |   | zero  |   |    | 1 | -1
-     | 0 |   | zero  |   |  0 | 1 | -1
+     | 0 |   | zero  | 1 | -1 | 2 |  2
+     | 0 |   | zero  | 1 | -1 | 3 | -3
+     | 0 |   | zero  | 1 | -1 | 2 |  4
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 0 |   
+     | 0 |   | zero  | 1 | -1 |   |   
+     | 0 |   | zero  | 1 | -1 |   |  0
      |   |   | null  | 1 | -1 | 1 | -1
-     |   |   | null  | 2 |  2 | 1 | -1
-     |   |   | null  | 3 | -3 | 1 | -1
-     |   |   | null  | 2 |  4 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 0 |    | 1 | -1
-     |   |   | null  |   |    | 1 | -1
-     |   |   | null  |   |  0 | 1 | -1
+     |   |   | null  | 1 | -1 | 2 |  2
+     |   |   | null  | 1 | -1 | 3 | -3
+     |   |   | null  | 1 | -1 | 2 |  4
+     |   |   | null  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 0 |   
+     |   |   | null  | 1 | -1 |   |   
+     |   |   | null  | 1 | -1 |   |  0
      |   | 0 | zero  | 1 | -1 | 1 | -1
-     |   | 0 | zero  | 2 |  2 | 1 | -1
-     |   | 0 | zero  | 3 | -3 | 1 | -1
-     |   | 0 | zero  | 2 |  4 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 0 |    | 1 | -1
-     |   | 0 | zero  |   |    | 1 | -1
-     |   | 0 | zero  |   |  0 | 1 | -1
-     | 1 | 4 | one   | 1 | -1 | 2 |  2
+     |   | 0 | zero  | 1 | -1 | 2 |  2
+     |   | 0 | zero  | 1 | -1 | 3 | -3
+     |   | 0 | zero  | 1 | -1 | 2 |  4
+     |   | 0 | zero  | 1 | -1 | 5 | -5
+     |   | 0 | zero  | 1 | -1 | 5 | -5
+     |   | 0 | zero  | 1 | -1 | 0 |   
+     |   | 0 | zero  | 1 | -1 |   |   
+     |   | 0 | zero  | 1 | -1 |   |  0
+     | 1 | 4 | one   | 2 |  2 | 1 | -1
      | 1 | 4 | one   | 2 |  2 | 2 |  2
-     | 1 | 4 | one   | 3 | -3 | 2 |  2
-     | 1 | 4 | one   | 2 |  4 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 0 |    | 2 |  2
-     | 1 | 4 | one   |   |    | 2 |  2
-     | 1 | 4 | one   |   |  0 | 2 |  2
-     | 2 | 3 | two   | 1 | -1 | 2 |  2
+     | 1 | 4 | one   | 2 |  2 | 3 | -3
+     | 1 | 4 | one   | 2 |  2 | 2 |  4
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 0 |   
+     | 1 | 4 | one   | 2 |  2 |   |   
+     | 1 | 4 | one   | 2 |  2 |   |  0
+     | 2 | 3 | two   | 2 |  2 | 1 | -1
      | 2 | 3 | two   | 2 |  2 | 2 |  2
-     | 2 | 3 | two   | 3 | -3 | 2 |  2
-     | 2 | 3 | two   | 2 |  4 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 0 |    | 2 |  2
-     | 2 | 3 | two   |   |    | 2 |  2
-     | 2 | 3 | two   |   |  0 | 2 |  2
-     | 3 | 2 | three | 1 | -1 | 2 |  2
+     | 2 | 3 | two   | 2 |  2 | 3 | -3
+     | 2 | 3 | two   | 2 |  2 | 2 |  4
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 0 |   
+     | 2 | 3 | two   | 2 |  2 |   |   
+     | 2 | 3 | two   | 2 |  2 |   |  0
+     | 3 | 2 | three | 2 |  2 | 1 | -1
      | 3 | 2 | three | 2 |  2 | 2 |  2
-     | 3 | 2 | three | 3 | -3 | 2 |  2
-     | 3 | 2 | three | 2 |  4 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 0 |    | 2 |  2
-     | 3 | 2 | three |   |    | 2 |  2
-     | 3 | 2 | three |   |  0 | 2 |  2
-     | 4 | 1 | four  | 1 | -1 | 2 |  2
+     | 3 | 2 | three | 2 |  2 | 3 | -3
+     | 3 | 2 | three | 2 |  2 | 2 |  4
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 0 |   
+     | 3 | 2 | three | 2 |  2 |   |   
+     | 3 | 2 | three | 2 |  2 |   |  0
+     | 4 | 1 | four  | 2 |  2 | 1 | -1
      | 4 | 1 | four  | 2 |  2 | 2 |  2
-     | 4 | 1 | four  | 3 | -3 | 2 |  2
-     | 4 | 1 | four  | 2 |  4 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 0 |    | 2 |  2
-     | 4 | 1 | four  |   |    | 2 |  2
-     | 4 | 1 | four  |   |  0 | 2 |  2
-     | 5 | 0 | five  | 1 | -1 | 2 |  2
+     | 4 | 1 | four  | 2 |  2 | 3 | -3
+     | 4 | 1 | four  | 2 |  2 | 2 |  4
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 0 |   
+     | 4 | 1 | four  | 2 |  2 |   |   
+     | 4 | 1 | four  | 2 |  2 |   |  0
+     | 5 | 0 | five  | 2 |  2 | 1 | -1
      | 5 | 0 | five  | 2 |  2 | 2 |  2
-     | 5 | 0 | five  | 3 | -3 | 2 |  2
-     | 5 | 0 | five  | 2 |  4 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 0 |    | 2 |  2
-     | 5 | 0 | five  |   |    | 2 |  2
-     | 5 | 0 | five  |   |  0 | 2 |  2
-     | 6 | 6 | six   | 1 | -1 | 2 |  2
+     | 5 | 0 | five  | 2 |  2 | 3 | -3
+     | 5 | 0 | five  | 2 |  2 | 2 |  4
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 0 |   
+     | 5 | 0 | five  | 2 |  2 |   |   
+     | 5 | 0 | five  | 2 |  2 |   |  0
+     | 6 | 6 | six   | 2 |  2 | 1 | -1
      | 6 | 6 | six   | 2 |  2 | 2 |  2
-     | 6 | 6 | six   | 3 | -3 | 2 |  2
-     | 6 | 6 | six   | 2 |  4 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 0 |    | 2 |  2
-     | 6 | 6 | six   |   |    | 2 |  2
-     | 6 | 6 | six   |   |  0 | 2 |  2
-     | 7 | 7 | seven | 1 | -1 | 2 |  2
+     | 6 | 6 | six   | 2 |  2 | 3 | -3
+     | 6 | 6 | six   | 2 |  2 | 2 |  4
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 0 |   
+     | 6 | 6 | six   | 2 |  2 |   |   
+     | 6 | 6 | six   | 2 |  2 |   |  0
+     | 7 | 7 | seven | 2 |  2 | 1 | -1
      | 7 | 7 | seven | 2 |  2 | 2 |  2
-     | 7 | 7 | seven | 3 | -3 | 2 |  2
-     | 7 | 7 | seven | 2 |  4 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 0 |    | 2 |  2
-     | 7 | 7 | seven |   |    | 2 |  2
-     | 7 | 7 | seven |   |  0 | 2 |  2
-     | 8 | 8 | eight | 1 | -1 | 2 |  2
+     | 7 | 7 | seven | 2 |  2 | 3 | -3
+     | 7 | 7 | seven | 2 |  2 | 2 |  4
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 0 |   
+     | 7 | 7 | seven | 2 |  2 |   |   
+     | 7 | 7 | seven | 2 |  2 |   |  0
+     | 8 | 8 | eight | 2 |  2 | 1 | -1
      | 8 | 8 | eight | 2 |  2 | 2 |  2
-     | 8 | 8 | eight | 3 | -3 | 2 |  2
-     | 8 | 8 | eight | 2 |  4 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 0 |    | 2 |  2
-     | 8 | 8 | eight |   |    | 2 |  2
-     | 8 | 8 | eight |   |  0 | 2 |  2
-     | 0 |   | zero  | 1 | -1 | 2 |  2
+     | 8 | 8 | eight | 2 |  2 | 3 | -3
+     | 8 | 8 | eight | 2 |  2 | 2 |  4
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 0 |   
+     | 8 | 8 | eight | 2 |  2 |   |   
+     | 8 | 8 | eight | 2 |  2 |   |  0
+     | 0 |   | zero  | 2 |  2 | 1 | -1
      | 0 |   | zero  | 2 |  2 | 2 |  2
-     | 0 |   | zero  | 3 | -3 | 2 |  2
-     | 0 |   | zero  | 2 |  4 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 0 |    | 2 |  2
-     | 0 |   | zero  |   |    | 2 |  2
-     | 0 |   | zero  |   |  0 | 2 |  2
-     |   |   | null  | 1 | -1 | 2 |  2
+     | 0 |   | zero  | 2 |  2 | 3 | -3
+     | 0 |   | zero  | 2 |  2 | 2 |  4
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 0 |   
+     | 0 |   | zero  | 2 |  2 |   |   
+     | 0 |   | zero  | 2 |  2 |   |  0
+     |   |   | null  | 2 |  2 | 1 | -1
      |   |   | null  | 2 |  2 | 2 |  2
-     |   |   | null  | 3 | -3 | 2 |  2
-     |   |   | null  | 2 |  4 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 0 |    | 2 |  2
-     |   |   | null  |   |    | 2 |  2
-     |   |   | null  |   |  0 | 2 |  2
-     |   | 0 | zero  | 1 | -1 | 2 |  2
+     |   |   | null  | 2 |  2 | 3 | -3
+     |   |   | null  | 2 |  2 | 2 |  4
+     |   |   | null  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 0 |   
+     |   |   | null  | 2 |  2 |   |   
+     |   |   | null  | 2 |  2 |   |  0
+     |   | 0 | zero  | 2 |  2 | 1 | -1
      |   | 0 | zero  | 2 |  2 | 2 |  2
-     |   | 0 | zero  | 3 | -3 | 2 |  2
-     |   | 0 | zero  | 2 |  4 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 0 |    | 2 |  2
-     |   | 0 | zero  |   |    | 2 |  2
-     |   | 0 | zero  |   |  0 | 2 |  2
-     | 1 | 4 | one   | 1 | -1 | 3 | -3
-     | 1 | 4 | one   | 2 |  2 | 3 | -3
+     |   | 0 | zero  | 2 |  2 | 3 | -3
+     |   | 0 | zero  | 2 |  2 | 2 |  4
+     |   | 0 | zero  | 2 |  2 | 5 | -5
+     |   | 0 | zero  | 2 |  2 | 5 | -5
+     |   | 0 | zero  | 2 |  2 | 0 |   
+     |   | 0 | zero  | 2 |  2 |   |   
+     |   | 0 | zero  | 2 |  2 |   |  0
+     | 1 | 4 | one   | 3 | -3 | 1 | -1
+     | 1 | 4 | one   | 3 | -3 | 2 |  2
      | 1 | 4 | one   | 3 | -3 | 3 | -3
-     | 1 | 4 | one   | 2 |  4 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 0 |    | 3 | -3
-     | 1 | 4 | one   |   |    | 3 | -3
-     | 1 | 4 | one   |   |  0 | 3 | -3
-     | 2 | 3 | two   | 1 | -1 | 3 | -3
-     | 2 | 3 | two   | 2 |  2 | 3 | -3
+     | 1 | 4 | one   | 3 | -3 | 2 |  4
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 0 |   
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+     | 1 | 4 | one   | 3 | -3 |   |  0
+     | 2 | 3 | two   | 3 | -3 | 1 | -1
+     | 2 | 3 | two   | 3 | -3 | 2 |  2
      | 2 | 3 | two   | 3 | -3 | 3 | -3
-     | 2 | 3 | two   | 2 |  4 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 0 |    | 3 | -3
-     | 2 | 3 | two   |   |    | 3 | -3
-     | 2 | 3 | two   |   |  0 | 3 | -3
-     | 3 | 2 | three | 1 | -1 | 3 | -3
-     | 3 | 2 | three | 2 |  2 | 3 | -3
+     | 2 | 3 | two   | 3 | -3 | 2 |  4
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 0 |   
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+     | 2 | 3 | two   | 3 | -3 |   |  0
+     | 3 | 2 | three | 3 | -3 | 1 | -1
+     | 3 | 2 | three | 3 | -3 | 2 |  2
      | 3 | 2 | three | 3 | -3 | 3 | -3
-     | 3 | 2 | three | 2 |  4 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 0 |    | 3 | -3
-     | 3 | 2 | three |   |    | 3 | -3
-     | 3 | 2 | three |   |  0 | 3 | -3
-     | 4 | 1 | four  | 1 | -1 | 3 | -3
-     | 4 | 1 | four  | 2 |  2 | 3 | -3
+     | 3 | 2 | three | 3 | -3 | 2 |  4
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 0 |   
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+     | 3 | 2 | three | 3 | -3 |   |  0
+     | 4 | 1 | four  | 3 | -3 | 1 | -1
+     | 4 | 1 | four  | 3 | -3 | 2 |  2
      | 4 | 1 | four  | 3 | -3 | 3 | -3
-     | 4 | 1 | four  | 2 |  4 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 0 |    | 3 | -3
-     | 4 | 1 | four  |   |    | 3 | -3
-     | 4 | 1 | four  |   |  0 | 3 | -3
-     | 5 | 0 | five  | 1 | -1 | 3 | -3
-     | 5 | 0 | five  | 2 |  2 | 3 | -3
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+     | 5 | 0 | five  | 3 | -3 | 1 | -1
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      | 5 | 0 | five  | 3 | -3 | 3 | -3
-     | 5 | 0 | five  | 2 |  4 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 0 |    | 3 | -3
-     | 5 | 0 | five  |   |    | 3 | -3
-     | 5 | 0 | five  |   |  0 | 3 | -3
-     | 6 | 6 | six   | 1 | -1 | 3 | -3
-     | 6 | 6 | six   | 2 |  2 | 3 | -3
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+     | 5 | 0 | five  | 3 | -3 |   |  0
+     | 6 | 6 | six   | 3 | -3 | 1 | -1
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      | 6 | 6 | six   | 3 | -3 | 3 | -3
-     | 6 | 6 | six   | 2 |  4 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 0 |    | 3 | -3
-     | 6 | 6 | six   |   |    | 3 | -3
-     | 6 | 6 | six   |   |  0 | 3 | -3
-     | 7 | 7 | seven | 1 | -1 | 3 | -3
-     | 7 | 7 | seven | 2 |  2 | 3 | -3
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+     | 7 | 7 | seven | 3 | -3 | 1 | -1
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      | 7 | 7 | seven | 3 | -3 | 3 | -3
-     | 7 | 7 | seven | 2 |  4 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 0 |    | 3 | -3
-     | 7 | 7 | seven |   |    | 3 | -3
-     | 7 | 7 | seven |   |  0 | 3 | -3
-     | 8 | 8 | eight | 1 | -1 | 3 | -3
-     | 8 | 8 | eight | 2 |  2 | 3 | -3
+     | 7 | 7 | seven | 3 | -3 | 2 |  4
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 0 |   
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+     | 7 | 7 | seven | 3 | -3 |   |  0
+     | 8 | 8 | eight | 3 | -3 | 1 | -1
+     | 8 | 8 | eight | 3 | -3 | 2 |  2
      | 8 | 8 | eight | 3 | -3 | 3 | -3
-     | 8 | 8 | eight | 2 |  4 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 0 |    | 3 | -3
-     | 8 | 8 | eight |   |    | 3 | -3
-     | 8 | 8 | eight |   |  0 | 3 | -3
-     | 0 |   | zero  | 1 | -1 | 3 | -3
-     | 0 |   | zero  | 2 |  2 | 3 | -3
+     | 8 | 8 | eight | 3 | -3 | 2 |  4
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 0 |   
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+     | 8 | 8 | eight | 3 | -3 |   |  0
+     | 0 |   | zero  | 3 | -3 | 1 | -1
+     | 0 |   | zero  | 3 | -3 | 2 |  2
      | 0 |   | zero  | 3 | -3 | 3 | -3
-     | 0 |   | zero  | 2 |  4 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 0 |    | 3 | -3
-     | 0 |   | zero  |   |    | 3 | -3
-     | 0 |   | zero  |   |  0 | 3 | -3
-     |   |   | null  | 1 | -1 | 3 | -3
-     |   |   | null  | 2 |  2 | 3 | -3
+     | 0 |   | zero  | 3 | -3 | 2 |  4
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 0 |   
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+     | 0 |   | zero  | 3 | -3 |   |  0
+     |   |   | null  | 3 | -3 | 1 | -1
+     |   |   | null  | 3 | -3 | 2 |  2
      |   |   | null  | 3 | -3 | 3 | -3
-     |   |   | null  | 2 |  4 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 0 |    | 3 | -3
-     |   |   | null  |   |    | 3 | -3
-     |   |   | null  |   |  0 | 3 | -3
-     |   | 0 | zero  | 1 | -1 | 3 | -3
-     |   | 0 | zero  | 2 |  2 | 3 | -3
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+     |   |   | null  | 3 | -3 | 5 | -5
+     |   |   | null  | 3 | -3 | 5 | -5
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+     |   | 0 | zero  | 3 | -3 | 1 | -1
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      |   | 0 | zero  | 3 | -3 | 3 | -3
-     |   | 0 | zero  | 2 |  4 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 0 |    | 3 | -3
-     |   | 0 | zero  |   |    | 3 | -3
-     |   | 0 | zero  |   |  0 | 3 | -3
-     | 1 | 4 | one   | 1 | -1 | 2 |  4
-     | 1 | 4 | one   | 2 |  2 | 2 |  4
-     | 1 | 4 | one   | 3 | -3 | 2 |  4
+     |   | 0 | zero  | 3 | -3 | 2 |  4
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+     |   | 0 | zero  | 3 | -3 | 5 | -5
+     |   | 0 | zero  | 3 | -3 | 0 |   
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+     | 1 | 4 | one   | 2 |  4 | 1 | -1
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      | 1 | 4 | one   | 2 |  4 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 0 |    | 2 |  4
-     | 1 | 4 | one   |   |    | 2 |  4
-     | 1 | 4 | one   |   |  0 | 2 |  4
-     | 2 | 3 | two   | 1 | -1 | 2 |  4
-     | 2 | 3 | two   | 2 |  2 | 2 |  4
-     | 2 | 3 | two   | 3 | -3 | 2 |  4
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 0 |   
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      | 2 | 3 | two   | 2 |  4 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 0 |    | 2 |  4
-     | 2 | 3 | two   |   |    | 2 |  4
-     | 2 | 3 | two   |   |  0 | 2 |  4
-     | 3 | 2 | three | 1 | -1 | 2 |  4
-     | 3 | 2 | three | 2 |  2 | 2 |  4
-     | 3 | 2 | three | 3 | -3 | 2 |  4
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 0 |   
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+     | 3 | 2 | three | 2 |  4 | 1 | -1
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      | 3 | 2 | three | 2 |  4 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 0 |    | 2 |  4
-     | 3 | 2 | three |   |    | 2 |  4
-     | 3 | 2 | three |   |  0 | 2 |  4
-     | 4 | 1 | four  | 1 | -1 | 2 |  4
-     | 4 | 1 | four  | 2 |  2 | 2 |  4
-     | 4 | 1 | four  | 3 | -3 | 2 |  4
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 0 |   
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+     | 4 | 1 | four  | 2 |  4 | 1 | -1
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+     | 4 | 1 | four  | 2 |  4 | 3 | -3
      | 4 | 1 | four  | 2 |  4 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 0 |    | 2 |  4
-     | 4 | 1 | four  |   |    | 2 |  4
-     | 4 | 1 | four  |   |  0 | 2 |  4
-     | 5 | 0 | five  | 1 | -1 | 2 |  4
-     | 5 | 0 | five  | 2 |  2 | 2 |  4
-     | 5 | 0 | five  | 3 | -3 | 2 |  4
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 0 |   
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+     | 4 | 1 | four  | 2 |  4 |   |  0
+     | 5 | 0 | five  | 2 |  4 | 1 | -1
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+     | 5 | 0 | five  | 2 |  4 | 3 | -3
      | 5 | 0 | five  | 2 |  4 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 0 |    | 2 |  4
-     | 5 | 0 | five  |   |    | 2 |  4
-     | 5 | 0 | five  |   |  0 | 2 |  4
-     | 6 | 6 | six   | 1 | -1 | 2 |  4
-     | 6 | 6 | six   | 2 |  2 | 2 |  4
-     | 6 | 6 | six   | 3 | -3 | 2 |  4
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 0 |   
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+     | 5 | 0 | five  | 2 |  4 |   |  0
+     | 6 | 6 | six   | 2 |  4 | 1 | -1
+     | 6 | 6 | six   | 2 |  4 | 2 |  2
+     | 6 | 6 | six   | 2 |  4 | 3 | -3
      | 6 | 6 | six   | 2 |  4 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 0 |    | 2 |  4
-     | 6 | 6 | six   |   |    | 2 |  4
-     | 6 | 6 | six   |   |  0 | 2 |  4
-     | 7 | 7 | seven | 1 | -1 | 2 |  4
-     | 7 | 7 | seven | 2 |  2 | 2 |  4
-     | 7 | 7 | seven | 3 | -3 | 2 |  4
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 0 |   
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+     | 6 | 6 | six   | 2 |  4 |   |  0
+     | 7 | 7 | seven | 2 |  4 | 1 | -1
+     | 7 | 7 | seven | 2 |  4 | 2 |  2
+     | 7 | 7 | seven | 2 |  4 | 3 | -3
      | 7 | 7 | seven | 2 |  4 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 0 |    | 2 |  4
-     | 7 | 7 | seven |   |    | 2 |  4
-     | 7 | 7 | seven |   |  0 | 2 |  4
-     | 8 | 8 | eight | 1 | -1 | 2 |  4
-     | 8 | 8 | eight | 2 |  2 | 2 |  4
-     | 8 | 8 | eight | 3 | -3 | 2 |  4
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 0 |   
+     | 7 | 7 | seven | 2 |  4 |   |   
+     | 7 | 7 | seven | 2 |  4 |   |  0
+     | 8 | 8 | eight | 2 |  4 | 1 | -1
+     | 8 | 8 | eight | 2 |  4 | 2 |  2
+     | 8 | 8 | eight | 2 |  4 | 3 | -3
      | 8 | 8 | eight | 2 |  4 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 0 |    | 2 |  4
-     | 8 | 8 | eight |   |    | 2 |  4
-     | 8 | 8 | eight |   |  0 | 2 |  4
-     | 0 |   | zero  | 1 | -1 | 2 |  4
-     | 0 |   | zero  | 2 |  2 | 2 |  4
-     | 0 |   | zero  | 3 | -3 | 2 |  4
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 0 |   
+     | 8 | 8 | eight | 2 |  4 |   |   
+     | 8 | 8 | eight | 2 |  4 |   |  0
+     | 0 |   | zero  | 2 |  4 | 1 | -1
+     | 0 |   | zero  | 2 |  4 | 2 |  2
+     | 0 |   | zero  | 2 |  4 | 3 | -3
      | 0 |   | zero  | 2 |  4 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 0 |    | 2 |  4
-     | 0 |   | zero  |   |    | 2 |  4
-     | 0 |   | zero  |   |  0 | 2 |  4
-     |   |   | null  | 1 | -1 | 2 |  4
-     |   |   | null  | 2 |  2 | 2 |  4
-     |   |   | null  | 3 | -3 | 2 |  4
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 0 |   
+     | 0 |   | zero  | 2 |  4 |   |   
+     | 0 |   | zero  | 2 |  4 |   |  0
+     |   |   | null  | 2 |  4 | 1 | -1
+     |   |   | null  | 2 |  4 | 2 |  2
+     |   |   | null  | 2 |  4 | 3 | -3
      |   |   | null  | 2 |  4 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 0 |    | 2 |  4
-     |   |   | null  |   |    | 2 |  4
-     |   |   | null  |   |  0 | 2 |  4
-     |   | 0 | zero  | 1 | -1 | 2 |  4
-     |   | 0 | zero  | 2 |  2 | 2 |  4
-     |   | 0 | zero  | 3 | -3 | 2 |  4
+     |   |   | null  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 0 |   
+     |   |   | null  | 2 |  4 |   |   
+     |   |   | null  | 2 |  4 |   |  0
+     |   | 0 | zero  | 2 |  4 | 1 | -1
+     |   | 0 | zero  | 2 |  4 | 2 |  2
+     |   | 0 | zero  | 2 |  4 | 3 | -3
      |   | 0 | zero  | 2 |  4 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 0 |    | 2 |  4
-     |   | 0 | zero  |   |    | 2 |  4
-     |   | 0 | zero  |   |  0 | 2 |  4
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     |   | 0 | zero  | 2 |  4 | 5 | -5
+     |   | 0 | zero  | 2 |  4 | 5 | -5
+     |   | 0 | zero  | 2 |  4 | 0 |   
+     |   | 0 | zero  | 2 |  4 |   |   
+     |   | 0 | zero  | 2 |  4 |   |  0
+     | 1 | 4 | one   | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 5 | -5 | 2 |  4
      | 1 | 4 | one   | 5 | -5 | 5 | -5
      | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 0 |    | 5 | -5
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 1 | 4 | one   |   |  0 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |  0
+     | 2 | 3 | two   | 5 | -5 | 1 | -1
+     | 2 | 3 | two   | 5 | -5 | 2 |  2
+     | 2 | 3 | two   | 5 | -5 | 3 | -3
+     | 2 | 3 | two   | 5 | -5 | 2 |  4
      | 2 | 3 | two   | 5 | -5 | 5 | -5
      | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 0 |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 2 | 3 | two   |   |  0 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 0 |   
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+     | 2 | 3 | two   | 5 | -5 |   |  0
+     | 3 | 2 | three | 5 | -5 | 1 | -1
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+     | 3 | 2 | three | 5 | -5 | 3 | -3
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      | 3 | 2 | three | 5 | -5 | 5 | -5
      | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 0 |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 3 | 2 | three |   |  0 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 0 |   
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+     | 4 | 1 | four  | 5 | -5 | 1 | -1
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      | 4 | 1 | four  | 5 | -5 | 5 | -5
      | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 0 |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 4 | 1 | four  |   |  0 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
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      | 5 | 0 | five  | 5 | -5 | 5 | -5
      | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 0 |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 5 | 0 | five  |   |  0 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
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+     | 6 | 6 | six   | 5 | -5 | 1 | -1
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      | 6 | 6 | six   | 5 | -5 | 5 | -5
      | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 0 |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 6 | 6 | six   |   |  0 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
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+     | 7 | 7 | seven | 5 | -5 | 1 | -1
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      | 7 | 7 | seven | 5 | -5 | 5 | -5
      | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 0 |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 7 | 7 | seven |   |  0 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
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+     | 8 | 8 | eight | 5 | -5 | 1 | -1
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      | 8 | 8 | eight | 5 | -5 | 5 | -5
      | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 0 |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 8 | 8 | eight |   |  0 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
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      | 0 |   | zero  | 5 | -5 | 5 | -5
      | 0 |   | zero  | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 0 |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     | 0 |   | zero  |   |  0 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
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      |   |   | null  | 5 | -5 | 5 | -5
      |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 0 |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   |   | null  |   |  0 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
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      |   | 0 | zero  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 0 |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     |   | 0 | zero  |   |  0 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
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      | 1 | 4 | one   | 5 | -5 | 5 | -5
      | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 0 |    | 5 | -5
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 1 | 4 | one   |   |  0 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
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      | 2 | 3 | two   | 5 | -5 | 5 | -5
      | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 0 |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 2 | 3 | two   |   |  0 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
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      | 3 | 2 | three | 5 | -5 | 5 | -5
      | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 0 |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 3 | 2 | three |   |  0 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 0 |   
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      | 4 | 1 | four  | 5 | -5 | 5 | -5
      | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 0 |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 4 | 1 | four  |   |  0 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
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      | 5 | 0 | five  | 5 | -5 | 5 | -5
      | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 0 |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 5 | 0 | five  |   |  0 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 0 |   
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+     | 6 | 6 | six   | 5 | -5 | 1 | -1
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      | 6 | 6 | six   | 5 | -5 | 5 | -5
      | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 0 |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 6 | 6 | six   |   |  0 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 0 |   
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+     | 6 | 6 | six   | 5 | -5 |   |  0
+     | 7 | 7 | seven | 5 | -5 | 1 | -1
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
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      | 7 | 7 | seven | 5 | -5 | 5 | -5
      | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 0 |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 7 | 7 | seven |   |  0 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 0 |   
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+     | 7 | 7 | seven | 5 | -5 |   |  0
+     | 8 | 8 | eight | 5 | -5 | 1 | -1
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
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+     | 8 | 8 | eight | 5 | -5 | 2 |  4
      | 8 | 8 | eight | 5 | -5 | 5 | -5
      | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 0 |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 8 | 8 | eight |   |  0 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 0 |   
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+     | 8 | 8 | eight | 5 | -5 |   |  0
+     | 0 |   | zero  | 5 | -5 | 1 | -1
+     | 0 |   | zero  | 5 | -5 | 2 |  2
+     | 0 |   | zero  | 5 | -5 | 3 | -3
+     | 0 |   | zero  | 5 | -5 | 2 |  4
      | 0 |   | zero  | 5 | -5 | 5 | -5
      | 0 |   | zero  | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 0 |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     | 0 |   | zero  |   |  0 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 0 |   
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+     |   |   | null  | 5 | -5 | 2 |  4
      |   |   | null  | 5 | -5 | 5 | -5
      |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 0 |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   |   | null  |   |  0 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
+     |   |   | null  | 5 | -5 | 0 |   
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+     |   |   | null  | 5 | -5 |   |  0
+     |   | 0 | zero  | 5 | -5 | 1 | -1
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+     |   | 0 | zero  | 5 | -5 | 2 |  4
      |   | 0 | zero  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 0 |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     |   | 0 | zero  |   |  0 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 0 |   
-     | 1 | 4 | one   | 2 |  2 | 0 |   
-     | 1 | 4 | one   | 3 | -3 | 0 |   
-     | 1 | 4 | one   | 2 |  4 | 0 |   
-     | 1 | 4 | one   | 5 | -5 | 0 |   
-     | 1 | 4 | one   | 5 | -5 | 0 |   
+     |   | 0 | zero  | 5 | -5 | 0 |   
+     |   | 0 | zero  | 5 | -5 |   |   
+     |   | 0 | zero  | 5 | -5 |   |  0
+     | 1 | 4 | one   | 0 |    | 1 | -1
+     | 1 | 4 | one   | 0 |    | 2 |  2
+     | 1 | 4 | one   | 0 |    | 3 | -3
+     | 1 | 4 | one   | 0 |    | 2 |  4
+     | 1 | 4 | one   | 0 |    | 5 | -5
+     | 1 | 4 | one   | 0 |    | 5 | -5
      | 1 | 4 | one   | 0 |    | 0 |   
-     | 1 | 4 | one   |   |    | 0 |   
-     | 1 | 4 | one   |   |  0 | 0 |   
-     | 2 | 3 | two   | 1 | -1 | 0 |   
-     | 2 | 3 | two   | 2 |  2 | 0 |   
-     | 2 | 3 | two   | 3 | -3 | 0 |   
-     | 2 | 3 | two   | 2 |  4 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 0 |    |   |   
+     | 1 | 4 | one   | 0 |    |   |  0
+     | 2 | 3 | two   | 0 |    | 1 | -1
+     | 2 | 3 | two   | 0 |    | 2 |  2
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+     | 2 | 3 | two   | 0 |    | 2 |  4
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+     | 2 | 3 | two   | 0 |    | 5 | -5
      | 2 | 3 | two   | 0 |    | 0 |   
-     | 2 | 3 | two   |   |    | 0 |   
-     | 2 | 3 | two   |   |  0 | 0 |   
-     | 3 | 2 | three | 1 | -1 | 0 |   
-     | 3 | 2 | three | 2 |  2 | 0 |   
-     | 3 | 2 | three | 3 | -3 | 0 |   
-     | 3 | 2 | three | 2 |  4 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
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+     | 2 | 3 | two   | 0 |    |   |  0
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+     | 3 | 2 | three | 0 |    | 5 | -5
      | 3 | 2 | three | 0 |    | 0 |   
-     | 3 | 2 | three |   |    | 0 |   
-     | 3 | 2 | three |   |  0 | 0 |   
-     | 4 | 1 | four  | 1 | -1 | 0 |   
-     | 4 | 1 | four  | 2 |  2 | 0 |   
-     | 4 | 1 | four  | 3 | -3 | 0 |   
-     | 4 | 1 | four  | 2 |  4 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
+     | 3 | 2 | three | 0 |    |   |   
+     | 3 | 2 | three | 0 |    |   |  0
+     | 4 | 1 | four  | 0 |    | 1 | -1
+     | 4 | 1 | four  | 0 |    | 2 |  2
+     | 4 | 1 | four  | 0 |    | 3 | -3
+     | 4 | 1 | four  | 0 |    | 2 |  4
+     | 4 | 1 | four  | 0 |    | 5 | -5
+     | 4 | 1 | four  | 0 |    | 5 | -5
      | 4 | 1 | four  | 0 |    | 0 |   
-     | 4 | 1 | four  |   |    | 0 |   
-     | 4 | 1 | four  |   |  0 | 0 |   
-     | 5 | 0 | five  | 1 | -1 | 0 |   
-     | 5 | 0 | five  | 2 |  2 | 0 |   
-     | 5 | 0 | five  | 3 | -3 | 0 |   
-     | 5 | 0 | five  | 2 |  4 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
+     | 4 | 1 | four  | 0 |    |   |   
+     | 4 | 1 | four  | 0 |    |   |  0
+     | 5 | 0 | five  | 0 |    | 1 | -1
+     | 5 | 0 | five  | 0 |    | 2 |  2
+     | 5 | 0 | five  | 0 |    | 3 | -3
+     | 5 | 0 | five  | 0 |    | 2 |  4
+     | 5 | 0 | five  | 0 |    | 5 | -5
+     | 5 | 0 | five  | 0 |    | 5 | -5
      | 5 | 0 | five  | 0 |    | 0 |   
-     | 5 | 0 | five  |   |    | 0 |   
-     | 5 | 0 | five  |   |  0 | 0 |   
-     | 6 | 6 | six   | 1 | -1 | 0 |   
-     | 6 | 6 | six   | 2 |  2 | 0 |   
-     | 6 | 6 | six   | 3 | -3 | 0 |   
-     | 6 | 6 | six   | 2 |  4 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
+     | 5 | 0 | five  | 0 |    |   |   
+     | 5 | 0 | five  | 0 |    |   |  0
+     | 6 | 6 | six   | 0 |    | 1 | -1
+     | 6 | 6 | six   | 0 |    | 2 |  2
+     | 6 | 6 | six   | 0 |    | 3 | -3
+     | 6 | 6 | six   | 0 |    | 2 |  4
+     | 6 | 6 | six   | 0 |    | 5 | -5
+     | 6 | 6 | six   | 0 |    | 5 | -5
      | 6 | 6 | six   | 0 |    | 0 |   
-     | 6 | 6 | six   |   |    | 0 |   
-     | 6 | 6 | six   |   |  0 | 0 |   
-     | 7 | 7 | seven | 1 | -1 | 0 |   
-     | 7 | 7 | seven | 2 |  2 | 0 |   
-     | 7 | 7 | seven | 3 | -3 | 0 |   
-     | 7 | 7 | seven | 2 |  4 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
+     | 6 | 6 | six   | 0 |    |   |   
+     | 6 | 6 | six   | 0 |    |   |  0
+     | 7 | 7 | seven | 0 |    | 1 | -1
+     | 7 | 7 | seven | 0 |    | 2 |  2
+     | 7 | 7 | seven | 0 |    | 3 | -3
+     | 7 | 7 | seven | 0 |    | 2 |  4
+     | 7 | 7 | seven | 0 |    | 5 | -5
+     | 7 | 7 | seven | 0 |    | 5 | -5
      | 7 | 7 | seven | 0 |    | 0 |   
-     | 7 | 7 | seven |   |    | 0 |   
-     | 7 | 7 | seven |   |  0 | 0 |   
-     | 8 | 8 | eight | 1 | -1 | 0 |   
-     | 8 | 8 | eight | 2 |  2 | 0 |   
-     | 8 | 8 | eight | 3 | -3 | 0 |   
-     | 8 | 8 | eight | 2 |  4 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
+     | 7 | 7 | seven | 0 |    |   |   
+     | 7 | 7 | seven | 0 |    |   |  0
+     | 8 | 8 | eight | 0 |    | 1 | -1
+     | 8 | 8 | eight | 0 |    | 2 |  2
+     | 8 | 8 | eight | 0 |    | 3 | -3
+     | 8 | 8 | eight | 0 |    | 2 |  4
+     | 8 | 8 | eight | 0 |    | 5 | -5
+     | 8 | 8 | eight | 0 |    | 5 | -5
      | 8 | 8 | eight | 0 |    | 0 |   
-     | 8 | 8 | eight |   |    | 0 |   
-     | 8 | 8 | eight |   |  0 | 0 |   
-     | 0 |   | zero  | 1 | -1 | 0 |   
-     | 0 |   | zero  | 2 |  2 | 0 |   
-     | 0 |   | zero  | 3 | -3 | 0 |   
-     | 0 |   | zero  | 2 |  4 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
+     | 8 | 8 | eight | 0 |    |   |   
+     | 8 | 8 | eight | 0 |    |   |  0
+     | 0 |   | zero  | 0 |    | 1 | -1
+     | 0 |   | zero  | 0 |    | 2 |  2
+     | 0 |   | zero  | 0 |    | 3 | -3
+     | 0 |   | zero  | 0 |    | 2 |  4
+     | 0 |   | zero  | 0 |    | 5 | -5
+     | 0 |   | zero  | 0 |    | 5 | -5
      | 0 |   | zero  | 0 |    | 0 |   
-     | 0 |   | zero  |   |    | 0 |   
-     | 0 |   | zero  |   |  0 | 0 |   
-     |   |   | null  | 1 | -1 | 0 |   
-     |   |   | null  | 2 |  2 | 0 |   
-     |   |   | null  | 3 | -3 | 0 |   
-     |   |   | null  | 2 |  4 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
+     | 0 |   | zero  | 0 |    |   |   
+     | 0 |   | zero  | 0 |    |   |  0
+     |   |   | null  | 0 |    | 1 | -1
+     |   |   | null  | 0 |    | 2 |  2
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+     |   |   | null  | 0 |    | 2 |  4
+     |   |   | null  | 0 |    | 5 | -5
+     |   |   | null  | 0 |    | 5 | -5
      |   |   | null  | 0 |    | 0 |   
-     |   |   | null  |   |    | 0 |   
-     |   |   | null  |   |  0 | 0 |   
-     |   | 0 | zero  | 1 | -1 | 0 |   
-     |   | 0 | zero  | 2 |  2 | 0 |   
-     |   | 0 | zero  | 3 | -3 | 0 |   
-     |   | 0 | zero  | 2 |  4 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
+     |   |   | null  | 0 |    |   |   
+     |   |   | null  | 0 |    |   |  0
+     |   | 0 | zero  | 0 |    | 1 | -1
+     |   | 0 | zero  | 0 |    | 2 |  2
+     |   | 0 | zero  | 0 |    | 3 | -3
+     |   | 0 | zero  | 0 |    | 2 |  4
+     |   | 0 | zero  | 0 |    | 5 | -5
+     |   | 0 | zero  | 0 |    | 5 | -5
      |   | 0 | zero  | 0 |    | 0 |   
-     |   | 0 | zero  |   |    | 0 |   
-     |   | 0 | zero  |   |  0 | 0 |   
-     | 1 | 4 | one   | 1 | -1 |   |   
-     | 1 | 4 | one   | 2 |  2 |   |   
-     | 1 | 4 | one   | 3 | -3 |   |   
-     | 1 | 4 | one   | 2 |  4 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 1 | 4 | one   | 0 |    |   |   
+     |   | 0 | zero  | 0 |    |   |   
+     |   | 0 | zero  | 0 |    |   |  0
+     | 1 | 4 | one   |   |    | 1 | -1
+     | 1 | 4 | one   |   |    | 2 |  2
+     | 1 | 4 | one   |   |    | 3 | -3
+     | 1 | 4 | one   |   |    | 2 |  4
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 0 |   
      | 1 | 4 | one   |   |    |   |   
-     | 1 | 4 | one   |   |  0 |   |   
-     | 2 | 3 | two   | 1 | -1 |   |   
-     | 2 | 3 | two   | 2 |  2 |   |   
-     | 2 | 3 | two   | 3 | -3 |   |   
-     | 2 | 3 | two   | 2 |  4 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 0 |    |   |   
+     | 1 | 4 | one   |   |    |   |  0
+     | 2 | 3 | two   |   |    | 1 | -1
+     | 2 | 3 | two   |   |    | 2 |  2
+     | 2 | 3 | two   |   |    | 3 | -3
+     | 2 | 3 | two   |   |    | 2 |  4
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 0 |   
      | 2 | 3 | two   |   |    |   |   
-     | 2 | 3 | two   |   |  0 |   |   
-     | 3 | 2 | three | 1 | -1 |   |   
-     | 3 | 2 | three | 2 |  2 |   |   
-     | 3 | 2 | three | 3 | -3 |   |   
-     | 3 | 2 | three | 2 |  4 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 0 |    |   |   
+     | 2 | 3 | two   |   |    |   |  0
+     | 3 | 2 | three |   |    | 1 | -1
+     | 3 | 2 | three |   |    | 2 |  2
+     | 3 | 2 | three |   |    | 3 | -3
+     | 3 | 2 | three |   |    | 2 |  4
+     | 3 | 2 | three |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 0 |   
      | 3 | 2 | three |   |    |   |   
-     | 3 | 2 | three |   |  0 |   |   
-     | 4 | 1 | four  | 1 | -1 |   |   
-     | 4 | 1 | four  | 2 |  2 |   |   
-     | 4 | 1 | four  | 3 | -3 |   |   
-     | 4 | 1 | four  | 2 |  4 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 0 |    |   |   
+     | 3 | 2 | three |   |    |   |  0
+     | 4 | 1 | four  |   |    | 1 | -1
+     | 4 | 1 | four  |   |    | 2 |  2
+     | 4 | 1 | four  |   |    | 3 | -3
+     | 4 | 1 | four  |   |    | 2 |  4
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 0 |   
      | 4 | 1 | four  |   |    |   |   
-     | 4 | 1 | four  |   |  0 |   |   
-     | 5 | 0 | five  | 1 | -1 |   |   
-     | 5 | 0 | five  | 2 |  2 |   |   
-     | 5 | 0 | five  | 3 | -3 |   |   
-     | 5 | 0 | five  | 2 |  4 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 0 |    |   |   
+     | 4 | 1 | four  |   |    |   |  0
+     | 5 | 0 | five  |   |    | 1 | -1
+     | 5 | 0 | five  |   |    | 2 |  2
+     | 5 | 0 | five  |   |    | 3 | -3
+     | 5 | 0 | five  |   |    | 2 |  4
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 0 |   
      | 5 | 0 | five  |   |    |   |   
-     | 5 | 0 | five  |   |  0 |   |   
-     | 6 | 6 | six   | 1 | -1 |   |   
-     | 6 | 6 | six   | 2 |  2 |   |   
-     | 6 | 6 | six   | 3 | -3 |   |   
-     | 6 | 6 | six   | 2 |  4 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 0 |    |   |   
+     | 5 | 0 | five  |   |    |   |  0
+     | 6 | 6 | six   |   |    | 1 | -1
+     | 6 | 6 | six   |   |    | 2 |  2
+     | 6 | 6 | six   |   |    | 3 | -3
+     | 6 | 6 | six   |   |    | 2 |  4
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 0 |   
      | 6 | 6 | six   |   |    |   |   
-     | 6 | 6 | six   |   |  0 |   |   
-     | 7 | 7 | seven | 1 | -1 |   |   
-     | 7 | 7 | seven | 2 |  2 |   |   
-     | 7 | 7 | seven | 3 | -3 |   |   
-     | 7 | 7 | seven | 2 |  4 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 0 |    |   |   
+     | 6 | 6 | six   |   |    |   |  0
+     | 7 | 7 | seven |   |    | 1 | -1
+     | 7 | 7 | seven |   |    | 2 |  2
+     | 7 | 7 | seven |   |    | 3 | -3
+     | 7 | 7 | seven |   |    | 2 |  4
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 0 |   
      | 7 | 7 | seven |   |    |   |   
-     | 7 | 7 | seven |   |  0 |   |   
-     | 8 | 8 | eight | 1 | -1 |   |   
-     | 8 | 8 | eight | 2 |  2 |   |   
-     | 8 | 8 | eight | 3 | -3 |   |   
-     | 8 | 8 | eight | 2 |  4 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 8 | 8 | eight | 0 |    |   |   
+     | 7 | 7 | seven |   |    |   |  0
+     | 8 | 8 | eight |   |    | 1 | -1
+     | 8 | 8 | eight |   |    | 2 |  2
+     | 8 | 8 | eight |   |    | 3 | -3
+     | 8 | 8 | eight |   |    | 2 |  4
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 0 |   
      | 8 | 8 | eight |   |    |   |   
-     | 8 | 8 | eight |   |  0 |   |   
-     | 0 |   | zero  | 1 | -1 |   |   
-     | 0 |   | zero  | 2 |  2 |   |   
-     | 0 |   | zero  | 3 | -3 |   |   
-     | 0 |   | zero  | 2 |  4 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 0 |    |   |   
+     | 8 | 8 | eight |   |    |   |  0
+     | 0 |   | zero  |   |    | 1 | -1
+     | 0 |   | zero  |   |    | 2 |  2
+     | 0 |   | zero  |   |    | 3 | -3
+     | 0 |   | zero  |   |    | 2 |  4
+     | 0 |   | zero  |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 0 |   
      | 0 |   | zero  |   |    |   |   
-     | 0 |   | zero  |   |  0 |   |   
-     |   |   | null  | 1 | -1 |   |   
-     |   |   | null  | 2 |  2 |   |   
-     |   |   | null  | 3 | -3 |   |   
-     |   |   | null  | 2 |  4 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 0 |    |   |   
+     | 0 |   | zero  |   |    |   |  0
+     |   |   | null  |   |    | 1 | -1
+     |   |   | null  |   |    | 2 |  2
+     |   |   | null  |   |    | 3 | -3
+     |   |   | null  |   |    | 2 |  4
+     |   |   | null  |   |    | 5 | -5
+     |   |   | null  |   |    | 5 | -5
+     |   |   | null  |   |    | 0 |   
      |   |   | null  |   |    |   |   
-     |   |   | null  |   |  0 |   |   
-     |   | 0 | zero  | 1 | -1 |   |   
-     |   | 0 | zero  | 2 |  2 |   |   
-     |   | 0 | zero  | 3 | -3 |   |   
-     |   | 0 | zero  | 2 |  4 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     |   | 0 | zero  | 0 |    |   |   
+     |   |   | null  |   |    |   |  0
+     |   | 0 | zero  |   |    | 1 | -1
+     |   | 0 | zero  |   |    | 2 |  2
+     |   | 0 | zero  |   |    | 3 | -3
+     |   | 0 | zero  |   |    | 2 |  4
+     |   | 0 | zero  |   |    | 5 | -5
+     |   | 0 | zero  |   |    | 5 | -5
+     |   | 0 | zero  |   |    | 0 |   
      |   | 0 | zero  |   |    |   |   
-     |   | 0 | zero  |   |  0 |   |   
-     | 1 | 4 | one   | 1 | -1 |   |  0
-     | 1 | 4 | one   | 2 |  2 |   |  0
-     | 1 | 4 | one   | 3 | -3 |   |  0
-     | 1 | 4 | one   | 2 |  4 |   |  0
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 1 | 4 | one   | 0 |    |   |  0
-     | 1 | 4 | one   |   |    |   |  0
+     |   | 0 | zero  |   |    |   |  0
+     | 1 | 4 | one   |   |  0 | 1 | -1
+     | 1 | 4 | one   |   |  0 | 2 |  2
+     | 1 | 4 | one   |   |  0 | 3 | -3
+     | 1 | 4 | one   |   |  0 | 2 |  4
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 0 |   
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      | 1 | 4 | one   |   |  0 |   |  0
-     | 2 | 3 | two   | 1 | -1 |   |  0
-     | 2 | 3 | two   | 2 |  2 |   |  0
-     | 2 | 3 | two   | 3 | -3 |   |  0
-     | 2 | 3 | two   | 2 |  4 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 0 |    |   |  0
-     | 2 | 3 | two   |   |    |   |  0
+     | 2 | 3 | two   |   |  0 | 1 | -1
+     | 2 | 3 | two   |   |  0 | 2 |  2
+     | 2 | 3 | two   |   |  0 | 3 | -3
+     | 2 | 3 | two   |   |  0 | 2 |  4
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 0 |   
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      | 2 | 3 | two   |   |  0 |   |  0
-     | 3 | 2 | three | 1 | -1 |   |  0
-     | 3 | 2 | three | 2 |  2 |   |  0
-     | 3 | 2 | three | 3 | -3 |   |  0
-     | 3 | 2 | three | 2 |  4 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 3 | 2 | three | 0 |    |   |  0
-     | 3 | 2 | three |   |    |   |  0
+     | 3 | 2 | three |   |  0 | 1 | -1
+     | 3 | 2 | three |   |  0 | 2 |  2
+     | 3 | 2 | three |   |  0 | 3 | -3
+     | 3 | 2 | three |   |  0 | 2 |  4
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 0 |   
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      | 3 | 2 | three |   |  0 |   |  0
-     | 4 | 1 | four  | 1 | -1 |   |  0
-     | 4 | 1 | four  | 2 |  2 |   |  0
-     | 4 | 1 | four  | 3 | -3 |   |  0
-     | 4 | 1 | four  | 2 |  4 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 4 | 1 | four  | 0 |    |   |  0
-     | 4 | 1 | four  |   |    |   |  0
+     | 4 | 1 | four  |   |  0 | 1 | -1
+     | 4 | 1 | four  |   |  0 | 2 |  2
+     | 4 | 1 | four  |   |  0 | 3 | -3
+     | 4 | 1 | four  |   |  0 | 2 |  4
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 0 |   
+     | 4 | 1 | four  |   |  0 |   |   
      | 4 | 1 | four  |   |  0 |   |  0
-     | 5 | 0 | five  | 1 | -1 |   |  0
-     | 5 | 0 | five  | 2 |  2 |   |  0
-     | 5 | 0 | five  | 3 | -3 |   |  0
-     | 5 | 0 | five  | 2 |  4 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 0 |    |   |  0
-     | 5 | 0 | five  |   |    |   |  0
+     | 5 | 0 | five  |   |  0 | 1 | -1
+     | 5 | 0 | five  |   |  0 | 2 |  2
+     | 5 | 0 | five  |   |  0 | 3 | -3
+     | 5 | 0 | five  |   |  0 | 2 |  4
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 0 |   
+     | 5 | 0 | five  |   |  0 |   |   
      | 5 | 0 | five  |   |  0 |   |  0
-     | 6 | 6 | six   | 1 | -1 |   |  0
-     | 6 | 6 | six   | 2 |  2 |   |  0
-     | 6 | 6 | six   | 3 | -3 |   |  0
-     | 6 | 6 | six   | 2 |  4 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 6 | 6 | six   | 0 |    |   |  0
-     | 6 | 6 | six   |   |    |   |  0
+     | 6 | 6 | six   |   |  0 | 1 | -1
+     | 6 | 6 | six   |   |  0 | 2 |  2
+     | 6 | 6 | six   |   |  0 | 3 | -3
+     | 6 | 6 | six   |   |  0 | 2 |  4
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 0 |   
+     | 6 | 6 | six   |   |  0 |   |   
      | 6 | 6 | six   |   |  0 |   |  0
-     | 7 | 7 | seven | 1 | -1 |   |  0
-     | 7 | 7 | seven | 2 |  2 |   |  0
-     | 7 | 7 | seven | 3 | -3 |   |  0
-     | 7 | 7 | seven | 2 |  4 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 7 | 7 | seven | 0 |    |   |  0
-     | 7 | 7 | seven |   |    |   |  0
+     | 7 | 7 | seven |   |  0 | 1 | -1
+     | 7 | 7 | seven |   |  0 | 2 |  2
+     | 7 | 7 | seven |   |  0 | 3 | -3
+     | 7 | 7 | seven |   |  0 | 2 |  4
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 0 |   
+     | 7 | 7 | seven |   |  0 |   |   
      | 7 | 7 | seven |   |  0 |   |  0
-     | 8 | 8 | eight | 1 | -1 |   |  0
-     | 8 | 8 | eight | 2 |  2 |   |  0
-     | 8 | 8 | eight | 3 | -3 |   |  0
-     | 8 | 8 | eight | 2 |  4 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 8 | 8 | eight | 0 |    |   |  0
-     | 8 | 8 | eight |   |    |   |  0
+     | 8 | 8 | eight |   |  0 | 1 | -1
+     | 8 | 8 | eight |   |  0 | 2 |  2
+     | 8 | 8 | eight |   |  0 | 3 | -3
+     | 8 | 8 | eight |   |  0 | 2 |  4
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 0 |   
+     | 8 | 8 | eight |   |  0 |   |   
      | 8 | 8 | eight |   |  0 |   |  0
-     | 0 |   | zero  | 1 | -1 |   |  0
-     | 0 |   | zero  | 2 |  2 |   |  0
-     | 0 |   | zero  | 3 | -3 |   |  0
-     | 0 |   | zero  | 2 |  4 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     | 0 |   | zero  | 0 |    |   |  0
-     | 0 |   | zero  |   |    |   |  0
+     | 0 |   | zero  |   |  0 | 1 | -1
+     | 0 |   | zero  |   |  0 | 2 |  2
+     | 0 |   | zero  |   |  0 | 3 | -3
+     | 0 |   | zero  |   |  0 | 2 |  4
+     | 0 |   | zero  |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 0 |   
+     | 0 |   | zero  |   |  0 |   |   
      | 0 |   | zero  |   |  0 |   |  0
-     |   |   | null  | 1 | -1 |   |  0
-     |   |   | null  | 2 |  2 |   |  0
-     |   |   | null  | 3 | -3 |   |  0
-     |   |   | null  | 2 |  4 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   |   | null  | 0 |    |   |  0
-     |   |   | null  |   |    |   |  0
+     |   |   | null  |   |  0 | 1 | -1
+     |   |   | null  |   |  0 | 2 |  2
+     |   |   | null  |   |  0 | 3 | -3
+     |   |   | null  |   |  0 | 2 |  4
+     |   |   | null  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 0 |   
+     |   |   | null  |   |  0 |   |   
      |   |   | null  |   |  0 |   |  0
-     |   | 0 | zero  | 1 | -1 |   |  0
-     |   | 0 | zero  | 2 |  2 |   |  0
-     |   | 0 | zero  | 3 | -3 |   |  0
-     |   | 0 | zero  | 2 |  4 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
-     |   | 0 | zero  | 0 |    |   |  0
-     |   | 0 | zero  |   |    |   |  0
+     |   | 0 | zero  |   |  0 | 1 | -1
+     |   | 0 | zero  |   |  0 | 2 |  2
+     |   | 0 | zero  |   |  0 | 3 | -3
+     |   | 0 | zero  |   |  0 | 2 |  4
+     |   | 0 | zero  |   |  0 | 5 | -5
+     |   | 0 | zero  |   |  0 | 5 | -5
+     |   | 0 | zero  |   |  0 | 0 |   
+     |   | 0 | zero  |   |  0 |   |   
      |   | 0 | zero  |   |  0 |   |  0
 (891 rows)