Fix compare_fuzzy_path_costs() to behave a bit more sanely. The original

coding would ignore startup cost differences of less than 1% of the
estimated total cost; which was OK for normal planning but highly not OK
if a very small LIMIT was applied afterwards, so that startup cost becomes
the name of the game.  Instead, compare startup and total costs fuzzily
but independently.  This changes the plan selected for two queries in the
regression tests; adjust expected-output files for resulting changes in
row order.  Per reports from Dawid Kuroczko and Sam Mason.

6 files changed, 1494 insertions, 1513 deletions

diff --git a/src/backend/optimizer/util/pathnode.c b/src/backend/optimizer/util/pathnode.c
index 2f10fbe1939..8f55c2d98f1 100644
--- a/src/backend/optimizer/util/pathnode.c
+++ b/src/backend/optimizer/util/pathnode.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/optimizer/util/pathnode.c,v 1.111.4.1 2005/07/15 17:09:49 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/optimizer/util/pathnode.c,v 1.111.4.2 2005/07/22 19:12:33 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -98,60 +98,41 @@ compare_path_costs(Path *path1, Path *path2, CostSelector criterion)
 static int
 compare_fuzzy_path_costs(Path *path1, Path *path2, CostSelector criterion)
 {
-	Cost		fuzz;
-
 	/*
-	 * The fuzz factor is set at one percent of the smaller total_cost,
-	 * but not less than 0.01 cost units (just in case total cost is
-	 * zero).
+	 * We use a fuzz factor of 1% of the smaller cost.
 	 *
 	 * XXX does this percentage need to be user-configurable?
 	 */
-	fuzz = Min(path1->total_cost, path2->total_cost) * 0.01;
-	fuzz = Max(fuzz, 0.01);
-
 	if (criterion == STARTUP_COST)
 	{
-		if (Abs(path1->startup_cost - path2->startup_cost) > fuzz)
-		{
-			if (path1->startup_cost < path2->startup_cost)
-				return -1;
-			else
-				return +1;
-		}
+		if (path1->startup_cost > path2->startup_cost * 1.01)
+			return +1;
+		if (path2->startup_cost > path1->startup_cost * 1.01)
+			return -1;
 
 		/*
 		 * If paths have the same startup cost (not at all unlikely),
 		 * order them by total cost.
 		 */
-		if (Abs(path1->total_cost - path2->total_cost) > fuzz)
-		{
-			if (path1->total_cost < path2->total_cost)
-				return -1;
-			else
-				return +1;
-		}
+		if (path1->total_cost > path2->total_cost * 1.01)
+			return +1;
+		if (path2->total_cost > path1->total_cost * 1.01)
+			return -1;
 	}
 	else
 	{
-		if (Abs(path1->total_cost - path2->total_cost) > fuzz)
-		{
-			if (path1->total_cost < path2->total_cost)
-				return -1;
-			else
-				return +1;
-		}
+		if (path1->total_cost > path2->total_cost * 1.01)
+			return +1;
+		if (path2->total_cost > path1->total_cost * 1.01)
+			return -1;
 
 		/*
 		 * If paths have the same total cost, order them by startup cost.
 		 */
-		if (Abs(path1->startup_cost - path2->startup_cost) > fuzz)
-		{
-			if (path1->startup_cost < path2->startup_cost)
-				return -1;
-			else
-				return +1;
-		}
+		if (path1->startup_cost > path2->startup_cost * 1.01)
+			return +1;
+		if (path2->startup_cost > path1->startup_cost * 1.01)
+			return -1;
 	}
 	return 0;
 }
diff --git a/src/test/regress/expected/geometry.out b/src/test/regress/expected/geometry.out
index 7afbb1a2e2c..bdb4aa54778 100644
--- a/src/test/regress/expected/geometry.out
+++ b/src/test/regress/expected/geometry.out
@@ -258,24 +258,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,-0),(-0.2,-0.2)
-        | (0.08,-0),(0,-0.56)
-        | (0.0651176557644,0),(0,-0.0483449262493)
-        | (-0,0.0828402366864),(-0.201183431953,0)
-        | (0.2,0),(0,0)
         | (-0.1,-0.1),(-0.3,-0.3)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (0.3,0),(0.1,0)
         | (-0.25,-0.25),(-0.25,-0.35)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (0.3,0.05),(0.25,0)
         | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.08,-0),(0,-0.56)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.26,-0.7),(0.1,-0.82)
         | (0.12,-0.84),(0.12,-0.84)
+        | (0.0651176557644,0),(0,-0.0483449262493)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
         | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (-0,0.0828402366864),(-0.201183431953,0)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
+        | (0.2,0),(0,0)
+        | (0.3,0),(0.1,0)
+        | (0.3,0.05),(0.25,0)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/geometry_1.out b/src/test/regress/expected/geometry_1.out
index 06ca449fc4d..2a61b34a7ad 100644
--- a/src/test/regress/expected/geometry_1.out
+++ b/src/test/regress/expected/geometry_1.out
@@ -258,24 +258,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,0),(-0.2,-0.2)
-        | (0.08,0),(0,-0.56)
-        | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0,0.0828402366864),(-0.201183431953,0)
-        | (0.2,0),(0,0)
         | (-0.1,-0.1),(-0.3,-0.3)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (0.3,0),(0.1,0)
         | (-0.25,-0.25),(-0.25,-0.35)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (0.3,0.05),(0.25,0)
         | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.08,0),(0,-0.56)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.26,-0.7),(0.1,-0.82)
         | (0.12,-0.84),(0.12,-0.84)
+        | (0.0651176557644,0),(0,-0.0483449262493)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
         | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (0,0.0828402366864),(-0.201183431953,0)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
+        | (0.2,0),(0,0)
+        | (0.3,0),(0.1,0)
+        | (0.3,0.05),(0.25,0)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/geometry_2.out b/src/test/regress/expected/geometry_2.out
index a5ff53d6f4b..af3ee408404 100644
--- a/src/test/regress/expected/geometry_2.out
+++ b/src/test/regress/expected/geometry_2.out
@@ -258,24 +258,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (0,-0),(-0.2,-0.2)
-        | (0.08,-0),(0,-0.56)
-        | (0.0651176557644,0),(0,-0.0483449262493)
-        | (-0,0.0828402366864),(-0.201183431953,0)
-        | (0.2,0),(0,0)
         | (-0.1,-0.1),(-0.3,-0.3)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (0.3,0),(0.1,0)
         | (-0.25,-0.25),(-0.25,-0.35)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (0.3,0.05),(0.25,0)
         | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.08,-0),(0,-0.56)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.26,-0.7),(0.1,-0.82)
         | (0.12,-0.84),(0.12,-0.84)
+        | (0.0651176557644,0),(0,-0.0483449262493)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
         | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
+        | (-0,0.0828402366864),(-0.201183431953,0)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
+        | (0.2,0),(0,0)
+        | (0.3,0),(0.1,0)
+        | (0.3,0.05),(0.25,0)
         | (0.3,0),(0.3,0)
 (20 rows)
 
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 83f6939945c..4540b8fdbc4 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -660,895 +660,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 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   | 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 | 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  | 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  | 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   | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 1 | -1 | 2 |  2
+     | 2 | 3 | two   | 1 | -1 | 2 |  2
+     | 3 | 2 | three | 1 | -1 | 2 |  2
+     | 4 | 1 | four  | 1 | -1 | 2 |  2
+     | 5 | 0 | five  | 1 | -1 | 2 |  2
+     | 6 | 6 | six   | 1 | -1 | 2 |  2
+     | 7 | 7 | seven | 1 | -1 | 2 |  2
+     | 8 | 8 | eight | 1 | -1 | 2 |  2
+     | 0 |   | zero  | 1 | -1 | 2 |  2
+     |   |   | null  | 1 | -1 | 2 |  2
      |   | 0 | zero  | 1 | -1 | 2 |  2
+     | 1 | 4 | one   | 1 | -1 | 3 | -3
+     | 2 | 3 | two   | 1 | -1 | 3 | -3
+     | 3 | 2 | three | 1 | -1 | 3 | -3
+     | 4 | 1 | four  | 1 | -1 | 3 | -3
+     | 5 | 0 | five  | 1 | -1 | 3 | -3
+     | 6 | 6 | six   | 1 | -1 | 3 | -3
+     | 7 | 7 | seven | 1 | -1 | 3 | -3
+     | 8 | 8 | eight | 1 | -1 | 3 | -3
+     | 0 |   | zero  | 1 | -1 | 3 | -3
+     |   |   | null  | 1 | -1 | 3 | -3
      |   | 0 | zero  | 1 | -1 | 3 | -3
+     | 1 | 4 | one   | 1 | -1 | 2 |  4
+     | 2 | 3 | two   | 1 | -1 | 2 |  4
+     | 3 | 2 | three | 1 | -1 | 2 |  4
+     | 4 | 1 | four  | 1 | -1 | 2 |  4
+     | 5 | 0 | five  | 1 | -1 | 2 |  4
+     | 6 | 6 | six   | 1 | -1 | 2 |  4
+     | 7 | 7 | seven | 1 | -1 | 2 |  4
+     | 8 | 8 | eight | 1 | -1 | 2 |  4
+     | 0 |   | zero  | 1 | -1 | 2 |  4
+     |   |   | null  | 1 | -1 | 2 |  4
      |   | 0 | zero  | 1 | -1 | 2 |  4
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 5 | -5
      |   | 0 | zero  | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 5 | -5
      |   | 0 | zero  | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 0 |   
+     | 2 | 3 | two   | 1 | -1 | 0 |   
+     | 3 | 2 | three | 1 | -1 | 0 |   
+     | 4 | 1 | four  | 1 | -1 | 0 |   
+     | 5 | 0 | five  | 1 | -1 | 0 |   
+     | 6 | 6 | six   | 1 | -1 | 0 |   
+     | 7 | 7 | seven | 1 | -1 | 0 |   
+     | 8 | 8 | eight | 1 | -1 | 0 |   
+     | 0 |   | zero  | 1 | -1 | 0 |   
+     |   |   | null  | 1 | -1 | 0 |   
      |   | 0 | zero  | 1 | -1 | 0 |   
+     | 1 | 4 | one   | 1 | -1 |   |   
+     | 2 | 3 | two   | 1 | -1 |   |   
+     | 3 | 2 | three | 1 | -1 |   |   
+     | 4 | 1 | four  | 1 | -1 |   |   
+     | 5 | 0 | five  | 1 | -1 |   |   
+     | 6 | 6 | six   | 1 | -1 |   |   
+     | 7 | 7 | seven | 1 | -1 |   |   
+     | 8 | 8 | eight | 1 | -1 |   |   
+     | 0 |   | zero  | 1 | -1 |   |   
+     |   |   | null  | 1 | -1 |   |   
      |   | 0 | zero  | 1 | -1 |   |   
+     | 1 | 4 | one   | 1 | -1 |   |  0
+     | 2 | 3 | two   | 1 | -1 |   |  0
+     | 3 | 2 | three | 1 | -1 |   |  0
+     | 4 | 1 | four  | 1 | -1 |   |  0
+     | 5 | 0 | five  | 1 | -1 |   |  0
+     | 6 | 6 | six   | 1 | -1 |   |  0
+     | 7 | 7 | seven | 1 | -1 |   |  0
+     | 8 | 8 | eight | 1 | -1 |   |  0
+     | 0 |   | zero  | 1 | -1 |   |  0
+     |   |   | null  | 1 | -1 |   |  0
      |   | 0 | zero  | 1 | -1 |   |  0
      | 1 | 4 | one   | 2 |  2 | 1 | -1
-     | 1 | 4 | one   | 2 |  2 | 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   | 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 | 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  | 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  | 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   | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 2 |  2 | 2 |  2
+     | 2 | 3 | two   | 2 |  2 | 2 |  2
+     | 3 | 2 | three | 2 |  2 | 2 |  2
+     | 4 | 1 | four  | 2 |  2 | 2 |  2
+     | 5 | 0 | five  | 2 |  2 | 2 |  2
+     | 6 | 6 | six   | 2 |  2 | 2 |  2
+     | 7 | 7 | seven | 2 |  2 | 2 |  2
+     | 8 | 8 | eight | 2 |  2 | 2 |  2
+     | 0 |   | zero  | 2 |  2 | 2 |  2
+     |   |   | null  | 2 |  2 | 2 |  2
      |   | 0 | zero  | 2 |  2 | 2 |  2
+     | 1 | 4 | one   | 2 |  2 | 3 | -3
+     | 2 | 3 | two   | 2 |  2 | 3 | -3
+     | 3 | 2 | three | 2 |  2 | 3 | -3
+     | 4 | 1 | four  | 2 |  2 | 3 | -3
+     | 5 | 0 | five  | 2 |  2 | 3 | -3
+     | 6 | 6 | six   | 2 |  2 | 3 | -3
+     | 7 | 7 | seven | 2 |  2 | 3 | -3
+     | 8 | 8 | eight | 2 |  2 | 3 | -3
+     | 0 |   | zero  | 2 |  2 | 3 | -3
+     |   |   | null  | 2 |  2 | 3 | -3
      |   | 0 | zero  | 2 |  2 | 3 | -3
+     | 1 | 4 | one   | 2 |  2 | 2 |  4
+     | 2 | 3 | two   | 2 |  2 | 2 |  4
+     | 3 | 2 | three | 2 |  2 | 2 |  4
+     | 4 | 1 | four  | 2 |  2 | 2 |  4
+     | 5 | 0 | five  | 2 |  2 | 2 |  4
+     | 6 | 6 | six   | 2 |  2 | 2 |  4
+     | 7 | 7 | seven | 2 |  2 | 2 |  4
+     | 8 | 8 | eight | 2 |  2 | 2 |  4
+     | 0 |   | zero  | 2 |  2 | 2 |  4
+     |   |   | null  | 2 |  2 | 2 |  4
      |   | 0 | zero  | 2 |  2 | 2 |  4
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 5 | -5
      |   | 0 | zero  | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 5 | -5
      |   | 0 | zero  | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 0 |   
+     | 2 | 3 | two   | 2 |  2 | 0 |   
+     | 3 | 2 | three | 2 |  2 | 0 |   
+     | 4 | 1 | four  | 2 |  2 | 0 |   
+     | 5 | 0 | five  | 2 |  2 | 0 |   
+     | 6 | 6 | six   | 2 |  2 | 0 |   
+     | 7 | 7 | seven | 2 |  2 | 0 |   
+     | 8 | 8 | eight | 2 |  2 | 0 |   
+     | 0 |   | zero  | 2 |  2 | 0 |   
+     |   |   | null  | 2 |  2 | 0 |   
      |   | 0 | zero  | 2 |  2 | 0 |   
+     | 1 | 4 | one   | 2 |  2 |   |   
+     | 2 | 3 | two   | 2 |  2 |   |   
+     | 3 | 2 | three | 2 |  2 |   |   
+     | 4 | 1 | four  | 2 |  2 |   |   
+     | 5 | 0 | five  | 2 |  2 |   |   
+     | 6 | 6 | six   | 2 |  2 |   |   
+     | 7 | 7 | seven | 2 |  2 |   |   
+     | 8 | 8 | eight | 2 |  2 |   |   
+     | 0 |   | zero  | 2 |  2 |   |   
+     |   |   | null  | 2 |  2 |   |   
      |   | 0 | zero  | 2 |  2 |   |   
+     | 1 | 4 | one   | 2 |  2 |   |  0
+     | 2 | 3 | two   | 2 |  2 |   |  0
+     | 3 | 2 | three | 2 |  2 |   |  0
+     | 4 | 1 | four  | 2 |  2 |   |  0
+     | 5 | 0 | five  | 2 |  2 |   |  0
+     | 6 | 6 | six   | 2 |  2 |   |  0
+     | 7 | 7 | seven | 2 |  2 |   |  0
+     | 8 | 8 | eight | 2 |  2 |   |  0
+     | 0 |   | zero  | 2 |  2 |   |  0
+     |   |   | null  | 2 |  2 |   |  0
      |   | 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   | 3 | -3 | 2 |  4
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 0 |   
-     | 1 | 4 | one   | 3 | -3 |   |   
-     | 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   | 3 | -3 | 2 |  4
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 0 |   
-     | 2 | 3 | two   | 3 | -3 |   |   
-     | 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 | 3 | -3 | 2 |  4
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 0 |   
-     | 3 | 2 | three | 3 | -3 |   |   
-     | 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  | 3 | -3 | 2 |  4
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 0 |   
-     | 4 | 1 | four  | 3 | -3 |   |   
-     | 4 | 1 | four  | 3 | -3 |   |  0
      | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 2 |  2
-     | 5 | 0 | five  | 3 | -3 | 3 | -3
-     | 5 | 0 | five  | 3 | -3 | 2 |  4
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 0 |   
-     | 5 | 0 | five  | 3 | -3 |   |   
-     | 5 | 0 | five  | 3 | -3 |   |  0
      | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 2 |  2
-     | 6 | 6 | six   | 3 | -3 | 3 | -3
-     | 6 | 6 | six   | 3 | -3 | 2 |  4
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 0 |   
-     | 6 | 6 | six   | 3 | -3 |   |   
-     | 6 | 6 | six   | 3 | -3 |   |  0
      | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 2 |  2
-     | 7 | 7 | seven | 3 | -3 | 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 |   
-     | 7 | 7 | seven | 3 | -3 |   |   
-     | 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 | 3 | -3 | 2 |  4
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 0 |   
-     | 8 | 8 | eight | 3 | -3 |   |   
-     | 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  | 3 | -3 | 2 |  4
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 0 |   
-     | 0 |   | zero  | 3 | -3 |   |   
-     | 0 |   | zero  | 3 | -3 |   |  0
      |   |   | null  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 2 |  2
-     |   |   | null  | 3 | -3 | 3 | -3
-     |   |   | null  | 3 | -3 | 2 |  4
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 0 |   
-     |   |   | null  | 3 | -3 |   |   
-     |   |   | null  | 3 | -3 |   |  0
      |   | 0 | zero  | 3 | -3 | 1 | -1
+     | 1 | 4 | one   | 3 | -3 | 2 |  2
+     | 2 | 3 | two   | 3 | -3 | 2 |  2
+     | 3 | 2 | three | 3 | -3 | 2 |  2
+     | 4 | 1 | four  | 3 | -3 | 2 |  2
+     | 5 | 0 | five  | 3 | -3 | 2 |  2
+     | 6 | 6 | six   | 3 | -3 | 2 |  2
+     | 7 | 7 | seven | 3 | -3 | 2 |  2
+     | 8 | 8 | eight | 3 | -3 | 2 |  2
+     | 0 |   | zero  | 3 | -3 | 2 |  2
+     |   |   | null  | 3 | -3 | 2 |  2
      |   | 0 | zero  | 3 | -3 | 2 |  2
+     | 1 | 4 | one   | 3 | -3 | 3 | -3
+     | 2 | 3 | two   | 3 | -3 | 3 | -3
+     | 3 | 2 | three | 3 | -3 | 3 | -3
+     | 4 | 1 | four  | 3 | -3 | 3 | -3
+     | 5 | 0 | five  | 3 | -3 | 3 | -3
+     | 6 | 6 | six   | 3 | -3 | 3 | -3
+     | 7 | 7 | seven | 3 | -3 | 3 | -3
+     | 8 | 8 | eight | 3 | -3 | 3 | -3
+     | 0 |   | zero  | 3 | -3 | 3 | -3
+     |   |   | null  | 3 | -3 | 3 | -3
      |   | 0 | zero  | 3 | -3 | 3 | -3
+     | 1 | 4 | one   | 3 | -3 | 2 |  4
+     | 2 | 3 | two   | 3 | -3 | 2 |  4
+     | 3 | 2 | three | 3 | -3 | 2 |  4
+     | 4 | 1 | four  | 3 | -3 | 2 |  4
+     | 5 | 0 | five  | 3 | -3 | 2 |  4
+     | 6 | 6 | six   | 3 | -3 | 2 |  4
+     | 7 | 7 | seven | 3 | -3 | 2 |  4
+     | 8 | 8 | eight | 3 | -3 | 2 |  4
+     | 0 |   | zero  | 3 | -3 | 2 |  4
+     |   |   | null  | 3 | -3 | 2 |  4
      |   | 0 | zero  | 3 | -3 | 2 |  4
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 4 | 1 | four  | 3 | -3 | 5 | -5
+     | 5 | 0 | five  | 3 | -3 | 5 | -5
+     | 6 | 6 | six   | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     |   |   | null  | 3 | -3 | 5 | -5
      |   | 0 | zero  | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 4 | 1 | four  | 3 | -3 | 5 | -5
+     | 5 | 0 | five  | 3 | -3 | 5 | -5
+     | 6 | 6 | six   | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     |   |   | null  | 3 | -3 | 5 | -5
      |   | 0 | zero  | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 0 |   
+     | 2 | 3 | two   | 3 | -3 | 0 |   
+     | 3 | 2 | three | 3 | -3 | 0 |   
+     | 4 | 1 | four  | 3 | -3 | 0 |   
+     | 5 | 0 | five  | 3 | -3 | 0 |   
+     | 6 | 6 | six   | 3 | -3 | 0 |   
+     | 7 | 7 | seven | 3 | -3 | 0 |   
+     | 8 | 8 | eight | 3 | -3 | 0 |   
+     | 0 |   | zero  | 3 | -3 | 0 |   
+     |   |   | null  | 3 | -3 | 0 |   
      |   | 0 | zero  | 3 | -3 | 0 |   
+     | 1 | 4 | one   | 3 | -3 |   |   
+     | 2 | 3 | two   | 3 | -3 |   |   
+     | 3 | 2 | three | 3 | -3 |   |   
+     | 4 | 1 | four  | 3 | -3 |   |   
+     | 5 | 0 | five  | 3 | -3 |   |   
+     | 6 | 6 | six   | 3 | -3 |   |   
+     | 7 | 7 | seven | 3 | -3 |   |   
+     | 8 | 8 | eight | 3 | -3 |   |   
+     | 0 |   | zero  | 3 | -3 |   |   
+     |   |   | null  | 3 | -3 |   |   
      |   | 0 | zero  | 3 | -3 |   |   
+     | 1 | 4 | one   | 3 | -3 |   |  0
+     | 2 | 3 | two   | 3 | -3 |   |  0
+     | 3 | 2 | three | 3 | -3 |   |  0
+     | 4 | 1 | four  | 3 | -3 |   |  0
+     | 5 | 0 | five  | 3 | -3 |   |  0
+     | 6 | 6 | six   | 3 | -3 |   |  0
+     | 7 | 7 | seven | 3 | -3 |   |  0
+     | 8 | 8 | eight | 3 | -3 |   |  0
+     | 0 |   | zero  | 3 | -3 |   |  0
+     |   |   | null  | 3 | -3 |   |  0
      |   | 0 | zero  | 3 | -3 |   |  0
      | 1 | 4 | one   | 2 |  4 | 1 | -1
-     | 1 | 4 | one   | 2 |  4 | 2 |  2
-     | 1 | 4 | one   | 2 |  4 | 3 | -3
-     | 1 | 4 | one   | 2 |  4 | 2 |  4
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 0 |   
-     | 1 | 4 | one   | 2 |  4 |   |   
-     | 1 | 4 | one   | 2 |  4 |   |  0
      | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 2 | 3 | two   | 2 |  4 | 2 |  2
-     | 2 | 3 | two   | 2 |  4 | 3 | -3
-     | 2 | 3 | two   | 2 |  4 | 2 |  4
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 0 |   
-     | 2 | 3 | two   | 2 |  4 |   |   
-     | 2 | 3 | two   | 2 |  4 |   |  0
      | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 2 |  2
-     | 3 | 2 | three | 2 |  4 | 3 | -3
-     | 3 | 2 | three | 2 |  4 | 2 |  4
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 0 |   
-     | 3 | 2 | three | 2 |  4 |   |   
-     | 3 | 2 | three | 2 |  4 |   |  0
      | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 2 |  2
-     | 4 | 1 | four  | 2 |  4 | 3 | -3
-     | 4 | 1 | four  | 2 |  4 | 2 |  4
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 0 |   
-     | 4 | 1 | four  | 2 |  4 |   |   
-     | 4 | 1 | four  | 2 |  4 |   |  0
      | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 2 |  2
-     | 5 | 0 | five  | 2 |  4 | 3 | -3
-     | 5 | 0 | five  | 2 |  4 | 2 |  4
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 0 |   
-     | 5 | 0 | five  | 2 |  4 |   |   
-     | 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   | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 0 |   
-     | 6 | 6 | six   | 2 |  4 |   |   
-     | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 2 |  4 | 2 |  2
+     | 2 | 3 | two   | 2 |  4 | 2 |  2
+     | 3 | 2 | three | 2 |  4 | 2 |  2
+     | 4 | 1 | four  | 2 |  4 | 2 |  2
+     | 5 | 0 | five  | 2 |  4 | 2 |  2
+     | 6 | 6 | six   | 2 |  4 | 2 |  2
+     | 7 | 7 | seven | 2 |  4 | 2 |  2
+     | 8 | 8 | eight | 2 |  4 | 2 |  2
+     | 0 |   | zero  | 2 |  4 | 2 |  2
+     |   |   | null  | 2 |  4 | 2 |  2
      |   | 0 | zero  | 2 |  4 | 2 |  2
+     | 1 | 4 | one   | 2 |  4 | 3 | -3
+     | 2 | 3 | two   | 2 |  4 | 3 | -3
+     | 3 | 2 | three | 2 |  4 | 3 | -3
+     | 4 | 1 | four  | 2 |  4 | 3 | -3
+     | 5 | 0 | five  | 2 |  4 | 3 | -3
+     | 6 | 6 | six   | 2 |  4 | 3 | -3
+     | 7 | 7 | seven | 2 |  4 | 3 | -3
+     | 8 | 8 | eight | 2 |  4 | 3 | -3
+     | 0 |   | zero  | 2 |  4 | 3 | -3
+     |   |   | null  | 2 |  4 | 3 | -3
      |   | 0 | zero  | 2 |  4 | 3 | -3
+     | 1 | 4 | one   | 2 |  4 | 2 |  4
+     | 2 | 3 | two   | 2 |  4 | 2 |  4
+     | 3 | 2 | three | 2 |  4 | 2 |  4
+     | 4 | 1 | four  | 2 |  4 | 2 |  4
+     | 5 | 0 | five  | 2 |  4 | 2 |  4
+     | 6 | 6 | six   | 2 |  4 | 2 |  4
+     | 7 | 7 | seven | 2 |  4 | 2 |  4
+     | 8 | 8 | eight | 2 |  4 | 2 |  4
+     | 0 |   | zero  | 2 |  4 | 2 |  4
+     |   |   | null  | 2 |  4 | 2 |  4
      |   | 0 | zero  | 2 |  4 | 2 |  4
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 5 | -5
      |   | 0 | zero  | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 5 | -5
      |   | 0 | zero  | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 0 |   
+     | 2 | 3 | two   | 2 |  4 | 0 |   
+     | 3 | 2 | three | 2 |  4 | 0 |   
+     | 4 | 1 | four  | 2 |  4 | 0 |   
+     | 5 | 0 | five  | 2 |  4 | 0 |   
+     | 6 | 6 | six   | 2 |  4 | 0 |   
+     | 7 | 7 | seven | 2 |  4 | 0 |   
+     | 8 | 8 | eight | 2 |  4 | 0 |   
+     | 0 |   | zero  | 2 |  4 | 0 |   
+     |   |   | null  | 2 |  4 | 0 |   
      |   | 0 | zero  | 2 |  4 | 0 |   
+     | 1 | 4 | one   | 2 |  4 |   |   
+     | 2 | 3 | two   | 2 |  4 |   |   
+     | 3 | 2 | three | 2 |  4 |   |   
+     | 4 | 1 | four  | 2 |  4 |   |   
+     | 5 | 0 | five  | 2 |  4 |   |   
+     | 6 | 6 | six   | 2 |  4 |   |   
+     | 7 | 7 | seven | 2 |  4 |   |   
+     | 8 | 8 | eight | 2 |  4 |   |   
+     | 0 |   | zero  | 2 |  4 |   |   
+     |   |   | null  | 2 |  4 |   |   
      |   | 0 | zero  | 2 |  4 |   |   
+     | 1 | 4 | one   | 2 |  4 |   |  0
+     | 2 | 3 | two   | 2 |  4 |   |  0
+     | 3 | 2 | three | 2 |  4 |   |  0
+     | 4 | 1 | four  | 2 |  4 |   |  0
+     | 5 | 0 | five  | 2 |  4 |   |  0
+     | 6 | 6 | six   | 2 |  4 |   |  0
+     | 7 | 7 | seven | 2 |  4 |   |  0
+     | 8 | 8 | eight | 2 |  4 |   |  0
+     | 0 |   | zero  | 2 |  4 |   |  0
+     |   |   | null  | 2 |  4 |   |  0
      |   | 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   | 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   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |  0
      | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |  0
      | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |  0
      | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |  0
      | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |  0
      | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |  0
      | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 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  | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |  0
      |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
+     | 2 | 3 | two   | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 5 | 0 | five  | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 0 |   | zero  | 5 | -5 | 2 |  2
+     |   |   | null  | 5 | -5 | 2 |  2
      |   | 0 | zero  | 5 | -5 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 2 | 3 | two   | 5 | -5 | 3 | -3
+     | 3 | 2 | three | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 5 | 0 | five  | 5 | -5 | 3 | -3
+     | 6 | 6 | six   | 5 | -5 | 3 | -3
+     | 7 | 7 | seven | 5 | -5 | 3 | -3
+     | 8 | 8 | eight | 5 | -5 | 3 | -3
+     | 0 |   | zero  | 5 | -5 | 3 | -3
+     |   |   | null  | 5 | -5 | 3 | -3
      |   | 0 | zero  | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 5 | -5 | 2 |  4
+     | 2 | 3 | two   | 5 | -5 | 2 |  4
+     | 3 | 2 | three | 5 | -5 | 2 |  4
+     | 4 | 1 | four  | 5 | -5 | 2 |  4
+     | 5 | 0 | five  | 5 | -5 | 2 |  4
+     | 6 | 6 | six   | 5 | -5 | 2 |  4
+     | 7 | 7 | seven | 5 | -5 | 2 |  4
+     | 8 | 8 | eight | 5 | -5 | 2 |  4
+     | 0 |   | zero  | 5 | -5 | 2 |  4
+     |   |   | null  | 5 | -5 | 2 |  4
      |   | 0 | zero  | 5 | -5 | 2 |  4
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 0 |   
+     | 2 | 3 | two   | 5 | -5 | 0 |   
+     | 3 | 2 | three | 5 | -5 | 0 |   
+     | 4 | 1 | four  | 5 | -5 | 0 |   
+     | 5 | 0 | five  | 5 | -5 | 0 |   
+     | 6 | 6 | six   | 5 | -5 | 0 |   
+     | 7 | 7 | seven | 5 | -5 | 0 |   
+     | 8 | 8 | eight | 5 | -5 | 0 |   
+     | 0 |   | zero  | 5 | -5 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
      |   | 0 | zero  | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     |   |   | null  | 5 | -5 |   |   
      |   | 0 | zero  | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |  0
+     | 2 | 3 | two   | 5 | -5 |   |  0
+     | 3 | 2 | three | 5 | -5 |   |  0
+     | 4 | 1 | four  | 5 | -5 |   |  0
+     | 5 | 0 | five  | 5 | -5 |   |  0
+     | 6 | 6 | six   | 5 | -5 |   |  0
+     | 7 | 7 | seven | 5 | -5 |   |  0
+     | 8 | 8 | eight | 5 | -5 |   |  0
+     | 0 |   | zero  | 5 | -5 |   |  0
+     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 |   |  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   | 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   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |  0
      | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |  0
      | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |  0
      | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |  0
      | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |  0
      | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |  0
      | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 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  | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |  0
      |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
+     | 2 | 3 | two   | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 5 | 0 | five  | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 0 |   | zero  | 5 | -5 | 2 |  2
+     |   |   | null  | 5 | -5 | 2 |  2
      |   | 0 | zero  | 5 | -5 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 2 | 3 | two   | 5 | -5 | 3 | -3
+     | 3 | 2 | three | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 5 | 0 | five  | 5 | -5 | 3 | -3
+     | 6 | 6 | six   | 5 | -5 | 3 | -3
+     | 7 | 7 | seven | 5 | -5 | 3 | -3
+     | 8 | 8 | eight | 5 | -5 | 3 | -3
+     | 0 |   | zero  | 5 | -5 | 3 | -3
+     |   |   | null  | 5 | -5 | 3 | -3
      |   | 0 | zero  | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 5 | -5 | 2 |  4
+     | 2 | 3 | two   | 5 | -5 | 2 |  4
+     | 3 | 2 | three | 5 | -5 | 2 |  4
+     | 4 | 1 | four  | 5 | -5 | 2 |  4
+     | 5 | 0 | five  | 5 | -5 | 2 |  4
+     | 6 | 6 | six   | 5 | -5 | 2 |  4
+     | 7 | 7 | seven | 5 | -5 | 2 |  4
+     | 8 | 8 | eight | 5 | -5 | 2 |  4
+     | 0 |   | zero  | 5 | -5 | 2 |  4
+     |   |   | null  | 5 | -5 | 2 |  4
      |   | 0 | zero  | 5 | -5 | 2 |  4
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 0 |   
+     | 2 | 3 | two   | 5 | -5 | 0 |   
+     | 3 | 2 | three | 5 | -5 | 0 |   
+     | 4 | 1 | four  | 5 | -5 | 0 |   
+     | 5 | 0 | five  | 5 | -5 | 0 |   
+     | 6 | 6 | six   | 5 | -5 | 0 |   
+     | 7 | 7 | seven | 5 | -5 | 0 |   
+     | 8 | 8 | eight | 5 | -5 | 0 |   
+     | 0 |   | zero  | 5 | -5 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
      |   | 0 | zero  | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     |   |   | null  | 5 | -5 |   |   
      |   | 0 | zero  | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |  0
+     | 2 | 3 | two   | 5 | -5 |   |  0
+     | 3 | 2 | three | 5 | -5 |   |  0
+     | 4 | 1 | four  | 5 | -5 |   |  0
+     | 5 | 0 | five  | 5 | -5 |   |  0
+     | 6 | 6 | six   | 5 | -5 |   |  0
+     | 7 | 7 | seven | 5 | -5 |   |  0
+     | 8 | 8 | eight | 5 | -5 |   |  0
+     | 0 |   | zero  | 5 | -5 |   |  0
+     |   |   | null  | 5 | -5 |   |  0
      |   | 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   | 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 |   
-     | 2 | 3 | two   | 0 |    |   |   
-     | 2 | 3 | two   | 0 |    |   |  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 |   
-     | 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  | 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   | 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 | 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 | 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  | 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  | 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  | 0 |    | 1 | -1
+     | 1 | 4 | one   | 0 |    | 2 |  2
+     | 2 | 3 | two   | 0 |    | 2 |  2
+     | 3 | 2 | three | 0 |    | 2 |  2
+     | 4 | 1 | four  | 0 |    | 2 |  2
+     | 5 | 0 | five  | 0 |    | 2 |  2
+     | 6 | 6 | six   | 0 |    | 2 |  2
+     | 7 | 7 | seven | 0 |    | 2 |  2
+     | 8 | 8 | eight | 0 |    | 2 |  2
+     | 0 |   | zero  | 0 |    | 2 |  2
+     |   |   | null  | 0 |    | 2 |  2
      |   | 0 | zero  | 0 |    | 2 |  2
+     | 1 | 4 | one   | 0 |    | 3 | -3
+     | 2 | 3 | two   | 0 |    | 3 | -3
+     | 3 | 2 | three | 0 |    | 3 | -3
+     | 4 | 1 | four  | 0 |    | 3 | -3
+     | 5 | 0 | five  | 0 |    | 3 | -3
+     | 6 | 6 | six   | 0 |    | 3 | -3
+     | 7 | 7 | seven | 0 |    | 3 | -3
+     | 8 | 8 | eight | 0 |    | 3 | -3
+     | 0 |   | zero  | 0 |    | 3 | -3
+     |   |   | null  | 0 |    | 3 | -3
      |   | 0 | zero  | 0 |    | 3 | -3
+     | 1 | 4 | one   | 0 |    | 2 |  4
+     | 2 | 3 | two   | 0 |    | 2 |  4
+     | 3 | 2 | three | 0 |    | 2 |  4
+     | 4 | 1 | four  | 0 |    | 2 |  4
+     | 5 | 0 | five  | 0 |    | 2 |  4
+     | 6 | 6 | six   | 0 |    | 2 |  4
+     | 7 | 7 | seven | 0 |    | 2 |  4
+     | 8 | 8 | eight | 0 |    | 2 |  4
+     | 0 |   | zero  | 0 |    | 2 |  4
+     |   |   | null  | 0 |    | 2 |  4
      |   | 0 | zero  | 0 |    | 2 |  4
+     | 1 | 4 | one   | 0 |    | 5 | -5
+     | 2 | 3 | two   | 0 |    | 5 | -5
+     | 3 | 2 | three | 0 |    | 5 | -5
+     | 4 | 1 | four  | 0 |    | 5 | -5
+     | 5 | 0 | five  | 0 |    | 5 | -5
+     | 6 | 6 | six   | 0 |    | 5 | -5
+     | 7 | 7 | seven | 0 |    | 5 | -5
+     | 8 | 8 | eight | 0 |    | 5 | -5
+     | 0 |   | zero  | 0 |    | 5 | -5
+     |   |   | null  | 0 |    | 5 | -5
      |   | 0 | zero  | 0 |    | 5 | -5
+     | 1 | 4 | one   | 0 |    | 5 | -5
+     | 2 | 3 | two   | 0 |    | 5 | -5
+     | 3 | 2 | three | 0 |    | 5 | -5
+     | 4 | 1 | four  | 0 |    | 5 | -5
+     | 5 | 0 | five  | 0 |    | 5 | -5
+     | 6 | 6 | six   | 0 |    | 5 | -5
+     | 7 | 7 | seven | 0 |    | 5 | -5
+     | 8 | 8 | eight | 0 |    | 5 | -5
+     | 0 |   | zero  | 0 |    | 5 | -5
+     |   |   | null  | 0 |    | 5 | -5
      |   | 0 | zero  | 0 |    | 5 | -5
+     | 1 | 4 | one   | 0 |    | 0 |   
+     | 2 | 3 | two   | 0 |    | 0 |   
+     | 3 | 2 | three | 0 |    | 0 |   
+     | 4 | 1 | four  | 0 |    | 0 |   
+     | 5 | 0 | five  | 0 |    | 0 |   
+     | 6 | 6 | six   | 0 |    | 0 |   
+     | 7 | 7 | seven | 0 |    | 0 |   
+     | 8 | 8 | eight | 0 |    | 0 |   
+     | 0 |   | zero  | 0 |    | 0 |   
+     |   |   | null  | 0 |    | 0 |   
      |   | 0 | zero  | 0 |    | 0 |   
+     | 1 | 4 | one   | 0 |    |   |   
+     | 2 | 3 | two   | 0 |    |   |   
+     | 3 | 2 | three | 0 |    |   |   
+     | 4 | 1 | four  | 0 |    |   |   
+     | 5 | 0 | five  | 0 |    |   |   
+     | 6 | 6 | six   | 0 |    |   |   
+     | 7 | 7 | seven | 0 |    |   |   
+     | 8 | 8 | eight | 0 |    |   |   
+     | 0 |   | zero  | 0 |    |   |   
+     |   |   | null  | 0 |    |   |   
      |   | 0 | zero  | 0 |    |   |   
+     | 1 | 4 | one   | 0 |    |   |  0
+     | 2 | 3 | two   | 0 |    |   |  0
+     | 3 | 2 | three | 0 |    |   |  0
+     | 4 | 1 | four  | 0 |    |   |  0
+     | 5 | 0 | five  | 0 |    |   |  0
+     | 6 | 6 | six   | 0 |    |   |  0
+     | 7 | 7 | seven | 0 |    |   |  0
+     | 8 | 8 | eight | 0 |    |   |  0
+     | 0 |   | zero  | 0 |    |   |  0
+     |   |   | null  | 0 |    |   |  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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     |   |   | null  |   |    |   |   
-     |   |   | null  |   |    |   |  0
      |   | 0 | zero  |   |    | 1 | -1
+     | 1 | 4 | one   |   |    | 2 |  2
+     | 2 | 3 | two   |   |    | 2 |  2
+     | 3 | 2 | three |   |    | 2 |  2
+     | 4 | 1 | four  |   |    | 2 |  2
+     | 5 | 0 | five  |   |    | 2 |  2
+     | 6 | 6 | six   |   |    | 2 |  2
+     | 7 | 7 | seven |   |    | 2 |  2
+     | 8 | 8 | eight |   |    | 2 |  2
+     | 0 |   | zero  |   |    | 2 |  2
+     |   |   | null  |   |    | 2 |  2
      |   | 0 | zero  |   |    | 2 |  2
+     | 1 | 4 | one   |   |    | 3 | -3
+     | 2 | 3 | two   |   |    | 3 | -3
+     | 3 | 2 | three |   |    | 3 | -3
+     | 4 | 1 | four  |   |    | 3 | -3
+     | 5 | 0 | five  |   |    | 3 | -3
+     | 6 | 6 | six   |   |    | 3 | -3
+     | 7 | 7 | seven |   |    | 3 | -3
+     | 8 | 8 | eight |   |    | 3 | -3
+     | 0 |   | zero  |   |    | 3 | -3
+     |   |   | null  |   |    | 3 | -3
      |   | 0 | zero  |   |    | 3 | -3
+     | 1 | 4 | one   |   |    | 2 |  4
+     | 2 | 3 | two   |   |    | 2 |  4
+     | 3 | 2 | three |   |    | 2 |  4
+     | 4 | 1 | four  |   |    | 2 |  4
+     | 5 | 0 | five  |   |    | 2 |  4
+     | 6 | 6 | six   |   |    | 2 |  4
+     | 7 | 7 | seven |   |    | 2 |  4
+     | 8 | 8 | eight |   |    | 2 |  4
+     | 0 |   | zero  |   |    | 2 |  4
+     |   |   | null  |   |    | 2 |  4
      |   | 0 | zero  |   |    | 2 |  4
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 5 | -5
+     |   |   | null  |   |    | 5 | -5
      |   | 0 | zero  |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 5 | -5
+     |   |   | null  |   |    | 5 | -5
      |   | 0 | zero  |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 0 |   
+     | 2 | 3 | two   |   |    | 0 |   
+     | 3 | 2 | three |   |    | 0 |   
+     | 4 | 1 | four  |   |    | 0 |   
+     | 5 | 0 | five  |   |    | 0 |   
+     | 6 | 6 | six   |   |    | 0 |   
+     | 7 | 7 | seven |   |    | 0 |   
+     | 8 | 8 | eight |   |    | 0 |   
+     | 0 |   | zero  |   |    | 0 |   
+     |   |   | null  |   |    | 0 |   
      |   | 0 | zero  |   |    | 0 |   
+     | 1 | 4 | one   |   |    |   |   
+     | 2 | 3 | two   |   |    |   |   
+     | 3 | 2 | three |   |    |   |   
+     | 4 | 1 | four  |   |    |   |   
+     | 5 | 0 | five  |   |    |   |   
+     | 6 | 6 | six   |   |    |   |   
+     | 7 | 7 | seven |   |    |   |   
+     | 8 | 8 | eight |   |    |   |   
+     | 0 |   | zero  |   |    |   |   
+     |   |   | null  |   |    |   |   
      |   | 0 | zero  |   |    |   |   
+     | 1 | 4 | one   |   |    |   |  0
+     | 2 | 3 | two   |   |    |   |  0
+     | 3 | 2 | three |   |    |   |  0
+     | 4 | 1 | four  |   |    |   |  0
+     | 5 | 0 | five  |   |    |   |  0
+     | 6 | 6 | six   |   |    |   |  0
+     | 7 | 7 | seven |   |    |   |  0
+     | 8 | 8 | eight |   |    |   |  0
+     | 0 |   | zero  |   |    |   |  0
+     |   |   | null  |   |    |   |  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 |   
-     | 1 | 4 | one   |   |  0 |   |   
-     | 1 | 4 | one   |   |  0 |   |  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 |   
-     | 2 | 3 | two   |   |  0 |   |   
-     | 2 | 3 | two   |   |  0 |   |  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 |   
-     | 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  |   |  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   |   |  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 |   |  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 |   |  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  |   |  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  |   |  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  |   |  0 | 1 | -1
+     | 1 | 4 | one   |   |  0 | 2 |  2
+     | 2 | 3 | two   |   |  0 | 2 |  2
+     | 3 | 2 | three |   |  0 | 2 |  2
+     | 4 | 1 | four  |   |  0 | 2 |  2
+     | 5 | 0 | five  |   |  0 | 2 |  2
+     | 6 | 6 | six   |   |  0 | 2 |  2
+     | 7 | 7 | seven |   |  0 | 2 |  2
+     | 8 | 8 | eight |   |  0 | 2 |  2
+     | 0 |   | zero  |   |  0 | 2 |  2
+     |   |   | null  |   |  0 | 2 |  2
      |   | 0 | zero  |   |  0 | 2 |  2
+     | 1 | 4 | one   |   |  0 | 3 | -3
+     | 2 | 3 | two   |   |  0 | 3 | -3
+     | 3 | 2 | three |   |  0 | 3 | -3
+     | 4 | 1 | four  |   |  0 | 3 | -3
+     | 5 | 0 | five  |   |  0 | 3 | -3
+     | 6 | 6 | six   |   |  0 | 3 | -3
+     | 7 | 7 | seven |   |  0 | 3 | -3
+     | 8 | 8 | eight |   |  0 | 3 | -3
+     | 0 |   | zero  |   |  0 | 3 | -3
+     |   |   | null  |   |  0 | 3 | -3
      |   | 0 | zero  |   |  0 | 3 | -3
+     | 1 | 4 | one   |   |  0 | 2 |  4
+     | 2 | 3 | two   |   |  0 | 2 |  4
+     | 3 | 2 | three |   |  0 | 2 |  4
+     | 4 | 1 | four  |   |  0 | 2 |  4
+     | 5 | 0 | five  |   |  0 | 2 |  4
+     | 6 | 6 | six   |   |  0 | 2 |  4
+     | 7 | 7 | seven |   |  0 | 2 |  4
+     | 8 | 8 | eight |   |  0 | 2 |  4
+     | 0 |   | zero  |   |  0 | 2 |  4
+     |   |   | null  |   |  0 | 2 |  4
      |   | 0 | zero  |   |  0 | 2 |  4
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 5 | -5
      |   | 0 | zero  |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 5 | -5
      |   | 0 | zero  |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 0 |   
+     | 2 | 3 | two   |   |  0 | 0 |   
+     | 3 | 2 | three |   |  0 | 0 |   
+     | 4 | 1 | four  |   |  0 | 0 |   
+     | 5 | 0 | five  |   |  0 | 0 |   
+     | 6 | 6 | six   |   |  0 | 0 |   
+     | 7 | 7 | seven |   |  0 | 0 |   
+     | 8 | 8 | eight |   |  0 | 0 |   
+     | 0 |   | zero  |   |  0 | 0 |   
+     |   |   | null  |   |  0 | 0 |   
      |   | 0 | zero  |   |  0 | 0 |   
+     | 1 | 4 | one   |   |  0 |   |   
+     | 2 | 3 | two   |   |  0 |   |   
+     | 3 | 2 | three |   |  0 |   |   
+     | 4 | 1 | four  |   |  0 |   |   
+     | 5 | 0 | five  |   |  0 |   |   
+     | 6 | 6 | six   |   |  0 |   |   
+     | 7 | 7 | seven |   |  0 |   |   
+     | 8 | 8 | eight |   |  0 |   |   
+     | 0 |   | zero  |   |  0 |   |   
+     |   |   | null  |   |  0 |   |   
      |   | 0 | zero  |   |  0 |   |   
+     | 1 | 4 | one   |   |  0 |   |  0
+     | 2 | 3 | two   |   |  0 |   |  0
+     | 3 | 2 | three |   |  0 |   |  0
+     | 4 | 1 | four  |   |  0 |   |  0
+     | 5 | 0 | five  |   |  0 |   |  0
+     | 6 | 6 | six   |   |  0 |   |  0
+     | 7 | 7 | seven |   |  0 |   |  0
+     | 8 | 8 | eight |   |  0 |   |  0
+     | 0 |   | zero  |   |  0 |   |  0
+     |   |   | null  |   |  0 |   |  0
      |   | 0 | zero  |   |  0 |   |  0
 (891 rows)
 
diff --git a/src/test/regress/expected/join_1.out b/src/test/regress/expected/join_1.out
index e8c8f44d048..7f8134bee5d 100644
--- a/src/test/regress/expected/join_1.out
+++ b/src/test/regress/expected/join_1.out
@@ -660,895 +660,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 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   | 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 | 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  | 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  | 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   | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 1 | -1 | 2 |  2
+     | 2 | 3 | two   | 1 | -1 | 2 |  2
+     | 3 | 2 | three | 1 | -1 | 2 |  2
+     | 4 | 1 | four  | 1 | -1 | 2 |  2
+     | 5 | 0 | five  | 1 | -1 | 2 |  2
+     | 6 | 6 | six   | 1 | -1 | 2 |  2
+     | 7 | 7 | seven | 1 | -1 | 2 |  2
+     | 8 | 8 | eight | 1 | -1 | 2 |  2
+     | 0 |   | zero  | 1 | -1 | 2 |  2
+     |   |   | null  | 1 | -1 | 2 |  2
      |   | 0 | zero  | 1 | -1 | 2 |  2
+     | 1 | 4 | one   | 1 | -1 | 3 | -3
+     | 2 | 3 | two   | 1 | -1 | 3 | -3
+     | 3 | 2 | three | 1 | -1 | 3 | -3
+     | 4 | 1 | four  | 1 | -1 | 3 | -3
+     | 5 | 0 | five  | 1 | -1 | 3 | -3
+     | 6 | 6 | six   | 1 | -1 | 3 | -3
+     | 7 | 7 | seven | 1 | -1 | 3 | -3
+     | 8 | 8 | eight | 1 | -1 | 3 | -3
+     | 0 |   | zero  | 1 | -1 | 3 | -3
+     |   |   | null  | 1 | -1 | 3 | -3
      |   | 0 | zero  | 1 | -1 | 3 | -3
+     | 1 | 4 | one   | 1 | -1 | 2 |  4
+     | 2 | 3 | two   | 1 | -1 | 2 |  4
+     | 3 | 2 | three | 1 | -1 | 2 |  4
+     | 4 | 1 | four  | 1 | -1 | 2 |  4
+     | 5 | 0 | five  | 1 | -1 | 2 |  4
+     | 6 | 6 | six   | 1 | -1 | 2 |  4
+     | 7 | 7 | seven | 1 | -1 | 2 |  4
+     | 8 | 8 | eight | 1 | -1 | 2 |  4
+     | 0 |   | zero  | 1 | -1 | 2 |  4
+     |   |   | null  | 1 | -1 | 2 |  4
      |   | 0 | zero  | 1 | -1 | 2 |  4
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 5 | -5
      |   | 0 | zero  | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 5 | -5
+     | 2 | 3 | two   | 1 | -1 | 5 | -5
+     | 3 | 2 | three | 1 | -1 | 5 | -5
+     | 4 | 1 | four  | 1 | -1 | 5 | -5
+     | 5 | 0 | five  | 1 | -1 | 5 | -5
+     | 6 | 6 | six   | 1 | -1 | 5 | -5
+     | 7 | 7 | seven | 1 | -1 | 5 | -5
+     | 8 | 8 | eight | 1 | -1 | 5 | -5
+     | 0 |   | zero  | 1 | -1 | 5 | -5
+     |   |   | null  | 1 | -1 | 5 | -5
      |   | 0 | zero  | 1 | -1 | 5 | -5
+     | 1 | 4 | one   | 1 | -1 | 0 |   
+     | 2 | 3 | two   | 1 | -1 | 0 |   
+     | 3 | 2 | three | 1 | -1 | 0 |   
+     | 4 | 1 | four  | 1 | -1 | 0 |   
+     | 5 | 0 | five  | 1 | -1 | 0 |   
+     | 6 | 6 | six   | 1 | -1 | 0 |   
+     | 7 | 7 | seven | 1 | -1 | 0 |   
+     | 8 | 8 | eight | 1 | -1 | 0 |   
+     | 0 |   | zero  | 1 | -1 | 0 |   
+     |   |   | null  | 1 | -1 | 0 |   
      |   | 0 | zero  | 1 | -1 | 0 |   
+     | 1 | 4 | one   | 1 | -1 |   |   
+     | 2 | 3 | two   | 1 | -1 |   |   
+     | 3 | 2 | three | 1 | -1 |   |   
+     | 4 | 1 | four  | 1 | -1 |   |   
+     | 5 | 0 | five  | 1 | -1 |   |   
+     | 6 | 6 | six   | 1 | -1 |   |   
+     | 7 | 7 | seven | 1 | -1 |   |   
+     | 8 | 8 | eight | 1 | -1 |   |   
+     | 0 |   | zero  | 1 | -1 |   |   
+     |   |   | null  | 1 | -1 |   |   
      |   | 0 | zero  | 1 | -1 |   |   
+     | 1 | 4 | one   | 1 | -1 |   |  0
+     | 2 | 3 | two   | 1 | -1 |   |  0
+     | 3 | 2 | three | 1 | -1 |   |  0
+     | 4 | 1 | four  | 1 | -1 |   |  0
+     | 5 | 0 | five  | 1 | -1 |   |  0
+     | 6 | 6 | six   | 1 | -1 |   |  0
+     | 7 | 7 | seven | 1 | -1 |   |  0
+     | 8 | 8 | eight | 1 | -1 |   |  0
+     | 0 |   | zero  | 1 | -1 |   |  0
+     |   |   | null  | 1 | -1 |   |  0
      |   | 0 | zero  | 1 | -1 |   |  0
      | 1 | 4 | one   | 2 |  2 | 1 | -1
-     | 1 | 4 | one   | 2 |  2 | 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   | 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 | 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  | 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  | 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   | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 2 |  2 | 2 |  2
+     | 2 | 3 | two   | 2 |  2 | 2 |  2
+     | 3 | 2 | three | 2 |  2 | 2 |  2
+     | 4 | 1 | four  | 2 |  2 | 2 |  2
+     | 5 | 0 | five  | 2 |  2 | 2 |  2
+     | 6 | 6 | six   | 2 |  2 | 2 |  2
+     | 7 | 7 | seven | 2 |  2 | 2 |  2
+     | 8 | 8 | eight | 2 |  2 | 2 |  2
+     | 0 |   | zero  | 2 |  2 | 2 |  2
+     |   |   | null  | 2 |  2 | 2 |  2
      |   | 0 | zero  | 2 |  2 | 2 |  2
+     | 1 | 4 | one   | 2 |  2 | 3 | -3
+     | 2 | 3 | two   | 2 |  2 | 3 | -3
+     | 3 | 2 | three | 2 |  2 | 3 | -3
+     | 4 | 1 | four  | 2 |  2 | 3 | -3
+     | 5 | 0 | five  | 2 |  2 | 3 | -3
+     | 6 | 6 | six   | 2 |  2 | 3 | -3
+     | 7 | 7 | seven | 2 |  2 | 3 | -3
+     | 8 | 8 | eight | 2 |  2 | 3 | -3
+     | 0 |   | zero  | 2 |  2 | 3 | -3
+     |   |   | null  | 2 |  2 | 3 | -3
      |   | 0 | zero  | 2 |  2 | 3 | -3
+     | 1 | 4 | one   | 2 |  2 | 2 |  4
+     | 2 | 3 | two   | 2 |  2 | 2 |  4
+     | 3 | 2 | three | 2 |  2 | 2 |  4
+     | 4 | 1 | four  | 2 |  2 | 2 |  4
+     | 5 | 0 | five  | 2 |  2 | 2 |  4
+     | 6 | 6 | six   | 2 |  2 | 2 |  4
+     | 7 | 7 | seven | 2 |  2 | 2 |  4
+     | 8 | 8 | eight | 2 |  2 | 2 |  4
+     | 0 |   | zero  | 2 |  2 | 2 |  4
+     |   |   | null  | 2 |  2 | 2 |  4
      |   | 0 | zero  | 2 |  2 | 2 |  4
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 5 | -5
      |   | 0 | zero  | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 5 | -5
+     | 2 | 3 | two   | 2 |  2 | 5 | -5
+     | 3 | 2 | three | 2 |  2 | 5 | -5
+     | 4 | 1 | four  | 2 |  2 | 5 | -5
+     | 5 | 0 | five  | 2 |  2 | 5 | -5
+     | 6 | 6 | six   | 2 |  2 | 5 | -5
+     | 7 | 7 | seven | 2 |  2 | 5 | -5
+     | 8 | 8 | eight | 2 |  2 | 5 | -5
+     | 0 |   | zero  | 2 |  2 | 5 | -5
+     |   |   | null  | 2 |  2 | 5 | -5
      |   | 0 | zero  | 2 |  2 | 5 | -5
+     | 1 | 4 | one   | 2 |  2 | 0 |   
+     | 2 | 3 | two   | 2 |  2 | 0 |   
+     | 3 | 2 | three | 2 |  2 | 0 |   
+     | 4 | 1 | four  | 2 |  2 | 0 |   
+     | 5 | 0 | five  | 2 |  2 | 0 |   
+     | 6 | 6 | six   | 2 |  2 | 0 |   
+     | 7 | 7 | seven | 2 |  2 | 0 |   
+     | 8 | 8 | eight | 2 |  2 | 0 |   
+     | 0 |   | zero  | 2 |  2 | 0 |   
+     |   |   | null  | 2 |  2 | 0 |   
      |   | 0 | zero  | 2 |  2 | 0 |   
+     | 1 | 4 | one   | 2 |  2 |   |   
+     | 2 | 3 | two   | 2 |  2 |   |   
+     | 3 | 2 | three | 2 |  2 |   |   
+     | 4 | 1 | four  | 2 |  2 |   |   
+     | 5 | 0 | five  | 2 |  2 |   |   
+     | 6 | 6 | six   | 2 |  2 |   |   
+     | 7 | 7 | seven | 2 |  2 |   |   
+     | 8 | 8 | eight | 2 |  2 |   |   
+     | 0 |   | zero  | 2 |  2 |   |   
+     |   |   | null  | 2 |  2 |   |   
      |   | 0 | zero  | 2 |  2 |   |   
+     | 1 | 4 | one   | 2 |  2 |   |  0
+     | 2 | 3 | two   | 2 |  2 |   |  0
+     | 3 | 2 | three | 2 |  2 |   |  0
+     | 4 | 1 | four  | 2 |  2 |   |  0
+     | 5 | 0 | five  | 2 |  2 |   |  0
+     | 6 | 6 | six   | 2 |  2 |   |  0
+     | 7 | 7 | seven | 2 |  2 |   |  0
+     | 8 | 8 | eight | 2 |  2 |   |  0
+     | 0 |   | zero  | 2 |  2 |   |  0
+     |   |   | null  | 2 |  2 |   |  0
      |   | 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   | 3 | -3 | 2 |  4
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 0 |   
-     | 1 | 4 | one   | 3 | -3 |   |   
-     | 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   | 3 | -3 | 2 |  4
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 0 |   
-     | 2 | 3 | two   | 3 | -3 |   |   
-     | 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 | 3 | -3 | 2 |  4
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 0 |   
-     | 3 | 2 | three | 3 | -3 |   |   
-     | 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  | 3 | -3 | 2 |  4
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 0 |   
-     | 4 | 1 | four  | 3 | -3 |   |   
-     | 4 | 1 | four  | 3 | -3 |   |  0
      | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 2 |  2
-     | 5 | 0 | five  | 3 | -3 | 3 | -3
-     | 5 | 0 | five  | 3 | -3 | 2 |  4
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 0 |   
-     | 5 | 0 | five  | 3 | -3 |   |   
-     | 5 | 0 | five  | 3 | -3 |   |  0
      | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 2 |  2
-     | 6 | 6 | six   | 3 | -3 | 3 | -3
-     | 6 | 6 | six   | 3 | -3 | 2 |  4
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 0 |   
-     | 6 | 6 | six   | 3 | -3 |   |   
-     | 6 | 6 | six   | 3 | -3 |   |  0
      | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 2 |  2
-     | 7 | 7 | seven | 3 | -3 | 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 |   
-     | 7 | 7 | seven | 3 | -3 |   |   
-     | 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 | 3 | -3 | 2 |  4
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 0 |   
-     | 8 | 8 | eight | 3 | -3 |   |   
-     | 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  | 3 | -3 | 2 |  4
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 0 |   
-     | 0 |   | zero  | 3 | -3 |   |   
-     | 0 |   | zero  | 3 | -3 |   |  0
      |   |   | null  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 2 |  2
-     |   |   | null  | 3 | -3 | 3 | -3
-     |   |   | null  | 3 | -3 | 2 |  4
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 0 |   
-     |   |   | null  | 3 | -3 |   |   
-     |   |   | null  | 3 | -3 |   |  0
      |   | 0 | zero  | 3 | -3 | 1 | -1
+     | 1 | 4 | one   | 3 | -3 | 2 |  2
+     | 2 | 3 | two   | 3 | -3 | 2 |  2
+     | 3 | 2 | three | 3 | -3 | 2 |  2
+     | 4 | 1 | four  | 3 | -3 | 2 |  2
+     | 5 | 0 | five  | 3 | -3 | 2 |  2
+     | 6 | 6 | six   | 3 | -3 | 2 |  2
+     | 7 | 7 | seven | 3 | -3 | 2 |  2
+     | 8 | 8 | eight | 3 | -3 | 2 |  2
+     | 0 |   | zero  | 3 | -3 | 2 |  2
+     |   |   | null  | 3 | -3 | 2 |  2
      |   | 0 | zero  | 3 | -3 | 2 |  2
+     | 1 | 4 | one   | 3 | -3 | 3 | -3
+     | 2 | 3 | two   | 3 | -3 | 3 | -3
+     | 3 | 2 | three | 3 | -3 | 3 | -3
+     | 4 | 1 | four  | 3 | -3 | 3 | -3
+     | 5 | 0 | five  | 3 | -3 | 3 | -3
+     | 6 | 6 | six   | 3 | -3 | 3 | -3
+     | 7 | 7 | seven | 3 | -3 | 3 | -3
+     | 8 | 8 | eight | 3 | -3 | 3 | -3
+     | 0 |   | zero  | 3 | -3 | 3 | -3
+     |   |   | null  | 3 | -3 | 3 | -3
      |   | 0 | zero  | 3 | -3 | 3 | -3
+     | 1 | 4 | one   | 3 | -3 | 2 |  4
+     | 2 | 3 | two   | 3 | -3 | 2 |  4
+     | 3 | 2 | three | 3 | -3 | 2 |  4
+     | 4 | 1 | four  | 3 | -3 | 2 |  4
+     | 5 | 0 | five  | 3 | -3 | 2 |  4
+     | 6 | 6 | six   | 3 | -3 | 2 |  4
+     | 7 | 7 | seven | 3 | -3 | 2 |  4
+     | 8 | 8 | eight | 3 | -3 | 2 |  4
+     | 0 |   | zero  | 3 | -3 | 2 |  4
+     |   |   | null  | 3 | -3 | 2 |  4
      |   | 0 | zero  | 3 | -3 | 2 |  4
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 4 | 1 | four  | 3 | -3 | 5 | -5
+     | 5 | 0 | five  | 3 | -3 | 5 | -5
+     | 6 | 6 | six   | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     |   |   | null  | 3 | -3 | 5 | -5
      |   | 0 | zero  | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 5 | -5
+     | 2 | 3 | two   | 3 | -3 | 5 | -5
+     | 3 | 2 | three | 3 | -3 | 5 | -5
+     | 4 | 1 | four  | 3 | -3 | 5 | -5
+     | 5 | 0 | five  | 3 | -3 | 5 | -5
+     | 6 | 6 | six   | 3 | -3 | 5 | -5
+     | 7 | 7 | seven | 3 | -3 | 5 | -5
+     | 8 | 8 | eight | 3 | -3 | 5 | -5
+     | 0 |   | zero  | 3 | -3 | 5 | -5
+     |   |   | null  | 3 | -3 | 5 | -5
      |   | 0 | zero  | 3 | -3 | 5 | -5
+     | 1 | 4 | one   | 3 | -3 | 0 |   
+     | 2 | 3 | two   | 3 | -3 | 0 |   
+     | 3 | 2 | three | 3 | -3 | 0 |   
+     | 4 | 1 | four  | 3 | -3 | 0 |   
+     | 5 | 0 | five  | 3 | -3 | 0 |   
+     | 6 | 6 | six   | 3 | -3 | 0 |   
+     | 7 | 7 | seven | 3 | -3 | 0 |   
+     | 8 | 8 | eight | 3 | -3 | 0 |   
+     | 0 |   | zero  | 3 | -3 | 0 |   
+     |   |   | null  | 3 | -3 | 0 |   
      |   | 0 | zero  | 3 | -3 | 0 |   
+     | 1 | 4 | one   | 3 | -3 |   |   
+     | 2 | 3 | two   | 3 | -3 |   |   
+     | 3 | 2 | three | 3 | -3 |   |   
+     | 4 | 1 | four  | 3 | -3 |   |   
+     | 5 | 0 | five  | 3 | -3 |   |   
+     | 6 | 6 | six   | 3 | -3 |   |   
+     | 7 | 7 | seven | 3 | -3 |   |   
+     | 8 | 8 | eight | 3 | -3 |   |   
+     | 0 |   | zero  | 3 | -3 |   |   
+     |   |   | null  | 3 | -3 |   |   
      |   | 0 | zero  | 3 | -3 |   |   
+     | 1 | 4 | one   | 3 | -3 |   |  0
+     | 2 | 3 | two   | 3 | -3 |   |  0
+     | 3 | 2 | three | 3 | -3 |   |  0
+     | 4 | 1 | four  | 3 | -3 |   |  0
+     | 5 | 0 | five  | 3 | -3 |   |  0
+     | 6 | 6 | six   | 3 | -3 |   |  0
+     | 7 | 7 | seven | 3 | -3 |   |  0
+     | 8 | 8 | eight | 3 | -3 |   |  0
+     | 0 |   | zero  | 3 | -3 |   |  0
+     |   |   | null  | 3 | -3 |   |  0
      |   | 0 | zero  | 3 | -3 |   |  0
      | 1 | 4 | one   | 2 |  4 | 1 | -1
-     | 1 | 4 | one   | 2 |  4 | 2 |  2
-     | 1 | 4 | one   | 2 |  4 | 3 | -3
-     | 1 | 4 | one   | 2 |  4 | 2 |  4
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 0 |   
-     | 1 | 4 | one   | 2 |  4 |   |   
-     | 1 | 4 | one   | 2 |  4 |   |  0
      | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 2 | 3 | two   | 2 |  4 | 2 |  2
-     | 2 | 3 | two   | 2 |  4 | 3 | -3
-     | 2 | 3 | two   | 2 |  4 | 2 |  4
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 0 |   
-     | 2 | 3 | two   | 2 |  4 |   |   
-     | 2 | 3 | two   | 2 |  4 |   |  0
      | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 2 |  2
-     | 3 | 2 | three | 2 |  4 | 3 | -3
-     | 3 | 2 | three | 2 |  4 | 2 |  4
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 0 |   
-     | 3 | 2 | three | 2 |  4 |   |   
-     | 3 | 2 | three | 2 |  4 |   |  0
      | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 2 |  2
-     | 4 | 1 | four  | 2 |  4 | 3 | -3
-     | 4 | 1 | four  | 2 |  4 | 2 |  4
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 0 |   
-     | 4 | 1 | four  | 2 |  4 |   |   
-     | 4 | 1 | four  | 2 |  4 |   |  0
      | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 2 |  2
-     | 5 | 0 | five  | 2 |  4 | 3 | -3
-     | 5 | 0 | five  | 2 |  4 | 2 |  4
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 0 |   
-     | 5 | 0 | five  | 2 |  4 |   |   
-     | 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   | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 0 |   
-     | 6 | 6 | six   | 2 |  4 |   |   
-     | 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 | 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 | 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  | 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  | 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
+     | 1 | 4 | one   | 2 |  4 | 2 |  2
+     | 2 | 3 | two   | 2 |  4 | 2 |  2
+     | 3 | 2 | three | 2 |  4 | 2 |  2
+     | 4 | 1 | four  | 2 |  4 | 2 |  2
+     | 5 | 0 | five  | 2 |  4 | 2 |  2
+     | 6 | 6 | six   | 2 |  4 | 2 |  2
+     | 7 | 7 | seven | 2 |  4 | 2 |  2
+     | 8 | 8 | eight | 2 |  4 | 2 |  2
+     | 0 |   | zero  | 2 |  4 | 2 |  2
+     |   |   | null  | 2 |  4 | 2 |  2
      |   | 0 | zero  | 2 |  4 | 2 |  2
+     | 1 | 4 | one   | 2 |  4 | 3 | -3
+     | 2 | 3 | two   | 2 |  4 | 3 | -3
+     | 3 | 2 | three | 2 |  4 | 3 | -3
+     | 4 | 1 | four  | 2 |  4 | 3 | -3
+     | 5 | 0 | five  | 2 |  4 | 3 | -3
+     | 6 | 6 | six   | 2 |  4 | 3 | -3
+     | 7 | 7 | seven | 2 |  4 | 3 | -3
+     | 8 | 8 | eight | 2 |  4 | 3 | -3
+     | 0 |   | zero  | 2 |  4 | 3 | -3
+     |   |   | null  | 2 |  4 | 3 | -3
      |   | 0 | zero  | 2 |  4 | 3 | -3
+     | 1 | 4 | one   | 2 |  4 | 2 |  4
+     | 2 | 3 | two   | 2 |  4 | 2 |  4
+     | 3 | 2 | three | 2 |  4 | 2 |  4
+     | 4 | 1 | four  | 2 |  4 | 2 |  4
+     | 5 | 0 | five  | 2 |  4 | 2 |  4
+     | 6 | 6 | six   | 2 |  4 | 2 |  4
+     | 7 | 7 | seven | 2 |  4 | 2 |  4
+     | 8 | 8 | eight | 2 |  4 | 2 |  4
+     | 0 |   | zero  | 2 |  4 | 2 |  4
+     |   |   | null  | 2 |  4 | 2 |  4
      |   | 0 | zero  | 2 |  4 | 2 |  4
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 5 | -5
      |   | 0 | zero  | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 5 | -5
+     | 2 | 3 | two   | 2 |  4 | 5 | -5
+     | 3 | 2 | three | 2 |  4 | 5 | -5
+     | 4 | 1 | four  | 2 |  4 | 5 | -5
+     | 5 | 0 | five  | 2 |  4 | 5 | -5
+     | 6 | 6 | six   | 2 |  4 | 5 | -5
+     | 7 | 7 | seven | 2 |  4 | 5 | -5
+     | 8 | 8 | eight | 2 |  4 | 5 | -5
+     | 0 |   | zero  | 2 |  4 | 5 | -5
+     |   |   | null  | 2 |  4 | 5 | -5
      |   | 0 | zero  | 2 |  4 | 5 | -5
+     | 1 | 4 | one   | 2 |  4 | 0 |   
+     | 2 | 3 | two   | 2 |  4 | 0 |   
+     | 3 | 2 | three | 2 |  4 | 0 |   
+     | 4 | 1 | four  | 2 |  4 | 0 |   
+     | 5 | 0 | five  | 2 |  4 | 0 |   
+     | 6 | 6 | six   | 2 |  4 | 0 |   
+     | 7 | 7 | seven | 2 |  4 | 0 |   
+     | 8 | 8 | eight | 2 |  4 | 0 |   
+     | 0 |   | zero  | 2 |  4 | 0 |   
+     |   |   | null  | 2 |  4 | 0 |   
      |   | 0 | zero  | 2 |  4 | 0 |   
+     | 1 | 4 | one   | 2 |  4 |   |   
+     | 2 | 3 | two   | 2 |  4 |   |   
+     | 3 | 2 | three | 2 |  4 |   |   
+     | 4 | 1 | four  | 2 |  4 |   |   
+     | 5 | 0 | five  | 2 |  4 |   |   
+     | 6 | 6 | six   | 2 |  4 |   |   
+     | 7 | 7 | seven | 2 |  4 |   |   
+     | 8 | 8 | eight | 2 |  4 |   |   
+     | 0 |   | zero  | 2 |  4 |   |   
+     |   |   | null  | 2 |  4 |   |   
      |   | 0 | zero  | 2 |  4 |   |   
+     | 1 | 4 | one   | 2 |  4 |   |  0
+     | 2 | 3 | two   | 2 |  4 |   |  0
+     | 3 | 2 | three | 2 |  4 |   |  0
+     | 4 | 1 | four  | 2 |  4 |   |  0
+     | 5 | 0 | five  | 2 |  4 |   |  0
+     | 6 | 6 | six   | 2 |  4 |   |  0
+     | 7 | 7 | seven | 2 |  4 |   |  0
+     | 8 | 8 | eight | 2 |  4 |   |  0
+     | 0 |   | zero  | 2 |  4 |   |  0
+     |   |   | null  | 2 |  4 |   |  0
      |   | 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   | 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   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |  0
      | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |  0
      | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |  0
      | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |  0
      | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |  0
      | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |  0
      | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 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  | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |  0
      |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
+     | 2 | 3 | two   | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 5 | 0 | five  | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 0 |   | zero  | 5 | -5 | 2 |  2
+     |   |   | null  | 5 | -5 | 2 |  2
      |   | 0 | zero  | 5 | -5 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 2 | 3 | two   | 5 | -5 | 3 | -3
+     | 3 | 2 | three | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 5 | 0 | five  | 5 | -5 | 3 | -3
+     | 6 | 6 | six   | 5 | -5 | 3 | -3
+     | 7 | 7 | seven | 5 | -5 | 3 | -3
+     | 8 | 8 | eight | 5 | -5 | 3 | -3
+     | 0 |   | zero  | 5 | -5 | 3 | -3
+     |   |   | null  | 5 | -5 | 3 | -3
      |   | 0 | zero  | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 5 | -5 | 2 |  4
+     | 2 | 3 | two   | 5 | -5 | 2 |  4
+     | 3 | 2 | three | 5 | -5 | 2 |  4
+     | 4 | 1 | four  | 5 | -5 | 2 |  4
+     | 5 | 0 | five  | 5 | -5 | 2 |  4
+     | 6 | 6 | six   | 5 | -5 | 2 |  4
+     | 7 | 7 | seven | 5 | -5 | 2 |  4
+     | 8 | 8 | eight | 5 | -5 | 2 |  4
+     | 0 |   | zero  | 5 | -5 | 2 |  4
+     |   |   | null  | 5 | -5 | 2 |  4
      |   | 0 | zero  | 5 | -5 | 2 |  4
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 0 |   
+     | 2 | 3 | two   | 5 | -5 | 0 |   
+     | 3 | 2 | three | 5 | -5 | 0 |   
+     | 4 | 1 | four  | 5 | -5 | 0 |   
+     | 5 | 0 | five  | 5 | -5 | 0 |   
+     | 6 | 6 | six   | 5 | -5 | 0 |   
+     | 7 | 7 | seven | 5 | -5 | 0 |   
+     | 8 | 8 | eight | 5 | -5 | 0 |   
+     | 0 |   | zero  | 5 | -5 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
      |   | 0 | zero  | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     |   |   | null  | 5 | -5 |   |   
      |   | 0 | zero  | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |  0
+     | 2 | 3 | two   | 5 | -5 |   |  0
+     | 3 | 2 | three | 5 | -5 |   |  0
+     | 4 | 1 | four  | 5 | -5 |   |  0
+     | 5 | 0 | five  | 5 | -5 |   |  0
+     | 6 | 6 | six   | 5 | -5 |   |  0
+     | 7 | 7 | seven | 5 | -5 |   |  0
+     | 8 | 8 | eight | 5 | -5 |   |  0
+     | 0 |   | zero  | 5 | -5 |   |  0
+     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 |   |  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   | 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   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |  0
      | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |  0
      | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |  0
      | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |  0
      | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |  0
      | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |  0
      | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 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  | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |  0
      |   |   | null  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |  0
      |   | 0 | zero  | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 2 |  2
+     | 2 | 3 | two   | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 4 | 1 | four  | 5 | -5 | 2 |  2
+     | 5 | 0 | five  | 5 | -5 | 2 |  2
+     | 6 | 6 | six   | 5 | -5 | 2 |  2
+     | 7 | 7 | seven | 5 | -5 | 2 |  2
+     | 8 | 8 | eight | 5 | -5 | 2 |  2
+     | 0 |   | zero  | 5 | -5 | 2 |  2
+     |   |   | null  | 5 | -5 | 2 |  2
      |   | 0 | zero  | 5 | -5 | 2 |  2
+     | 1 | 4 | one   | 5 | -5 | 3 | -3
+     | 2 | 3 | two   | 5 | -5 | 3 | -3
+     | 3 | 2 | three | 5 | -5 | 3 | -3
+     | 4 | 1 | four  | 5 | -5 | 3 | -3
+     | 5 | 0 | five  | 5 | -5 | 3 | -3
+     | 6 | 6 | six   | 5 | -5 | 3 | -3
+     | 7 | 7 | seven | 5 | -5 | 3 | -3
+     | 8 | 8 | eight | 5 | -5 | 3 | -3
+     | 0 |   | zero  | 5 | -5 | 3 | -3
+     |   |   | null  | 5 | -5 | 3 | -3
      |   | 0 | zero  | 5 | -5 | 3 | -3
+     | 1 | 4 | one   | 5 | -5 | 2 |  4
+     | 2 | 3 | two   | 5 | -5 | 2 |  4
+     | 3 | 2 | three | 5 | -5 | 2 |  4
+     | 4 | 1 | four  | 5 | -5 | 2 |  4
+     | 5 | 0 | five  | 5 | -5 | 2 |  4
+     | 6 | 6 | six   | 5 | -5 | 2 |  4
+     | 7 | 7 | seven | 5 | -5 | 2 |  4
+     | 8 | 8 | eight | 5 | -5 | 2 |  4
+     | 0 |   | zero  | 5 | -5 | 2 |  4
+     |   |   | null  | 5 | -5 | 2 |  4
      |   | 0 | zero  | 5 | -5 | 2 |  4
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 5 | -5
+     | 2 | 3 | two   | 5 | -5 | 5 | -5
+     | 3 | 2 | three | 5 | -5 | 5 | -5
+     | 4 | 1 | four  | 5 | -5 | 5 | -5
+     | 5 | 0 | five  | 5 | -5 | 5 | -5
+     | 6 | 6 | six   | 5 | -5 | 5 | -5
+     | 7 | 7 | seven | 5 | -5 | 5 | -5
+     | 8 | 8 | eight | 5 | -5 | 5 | -5
+     | 0 |   | zero  | 5 | -5 | 5 | -5
+     |   |   | null  | 5 | -5 | 5 | -5
      |   | 0 | zero  | 5 | -5 | 5 | -5
+     | 1 | 4 | one   | 5 | -5 | 0 |   
+     | 2 | 3 | two   | 5 | -5 | 0 |   
+     | 3 | 2 | three | 5 | -5 | 0 |   
+     | 4 | 1 | four  | 5 | -5 | 0 |   
+     | 5 | 0 | five  | 5 | -5 | 0 |   
+     | 6 | 6 | six   | 5 | -5 | 0 |   
+     | 7 | 7 | seven | 5 | -5 | 0 |   
+     | 8 | 8 | eight | 5 | -5 | 0 |   
+     | 0 |   | zero  | 5 | -5 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
      |   | 0 | zero  | 5 | -5 | 0 |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     |   |   | null  | 5 | -5 |   |   
      |   | 0 | zero  | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |  0
+     | 2 | 3 | two   | 5 | -5 |   |  0
+     | 3 | 2 | three | 5 | -5 |   |  0
+     | 4 | 1 | four  | 5 | -5 |   |  0
+     | 5 | 0 | five  | 5 | -5 |   |  0
+     | 6 | 6 | six   | 5 | -5 |   |  0
+     | 7 | 7 | seven | 5 | -5 |   |  0
+     | 8 | 8 | eight | 5 | -5 |   |  0
+     | 0 |   | zero  | 5 | -5 |   |  0
+     |   |   | null  | 5 | -5 |   |  0
      |   | 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   | 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 |   
-     | 2 | 3 | two   | 0 |    |   |   
-     | 2 | 3 | two   | 0 |    |   |  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 |   
-     | 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  | 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   | 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 | 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 | 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  | 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  | 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  | 0 |    | 1 | -1
+     | 1 | 4 | one   | 0 |    | 2 |  2
+     | 2 | 3 | two   | 0 |    | 2 |  2
+     | 3 | 2 | three | 0 |    | 2 |  2
+     | 4 | 1 | four  | 0 |    | 2 |  2
+     | 5 | 0 | five  | 0 |    | 2 |  2
+     | 6 | 6 | six   | 0 |    | 2 |  2
+     | 7 | 7 | seven | 0 |    | 2 |  2
+     | 8 | 8 | eight | 0 |    | 2 |  2
+     | 0 |   | zero  | 0 |    | 2 |  2
+     |   |   | null  | 0 |    | 2 |  2
      |   | 0 | zero  | 0 |    | 2 |  2
+     | 1 | 4 | one   | 0 |    | 3 | -3
+     | 2 | 3 | two   | 0 |    | 3 | -3
+     | 3 | 2 | three | 0 |    | 3 | -3
+     | 4 | 1 | four  | 0 |    | 3 | -3
+     | 5 | 0 | five  | 0 |    | 3 | -3
+     | 6 | 6 | six   | 0 |    | 3 | -3
+     | 7 | 7 | seven | 0 |    | 3 | -3
+     | 8 | 8 | eight | 0 |    | 3 | -3
+     | 0 |   | zero  | 0 |    | 3 | -3
+     |   |   | null  | 0 |    | 3 | -3
      |   | 0 | zero  | 0 |    | 3 | -3
+     | 1 | 4 | one   | 0 |    | 2 |  4
+     | 2 | 3 | two   | 0 |    | 2 |  4
+     | 3 | 2 | three | 0 |    | 2 |  4
+     | 4 | 1 | four  | 0 |    | 2 |  4
+     | 5 | 0 | five  | 0 |    | 2 |  4
+     | 6 | 6 | six   | 0 |    | 2 |  4
+     | 7 | 7 | seven | 0 |    | 2 |  4
+     | 8 | 8 | eight | 0 |    | 2 |  4
+     | 0 |   | zero  | 0 |    | 2 |  4
+     |   |   | null  | 0 |    | 2 |  4
      |   | 0 | zero  | 0 |    | 2 |  4
+     | 1 | 4 | one   | 0 |    | 5 | -5
+     | 2 | 3 | two   | 0 |    | 5 | -5
+     | 3 | 2 | three | 0 |    | 5 | -5
+     | 4 | 1 | four  | 0 |    | 5 | -5
+     | 5 | 0 | five  | 0 |    | 5 | -5
+     | 6 | 6 | six   | 0 |    | 5 | -5
+     | 7 | 7 | seven | 0 |    | 5 | -5
+     | 8 | 8 | eight | 0 |    | 5 | -5
+     | 0 |   | zero  | 0 |    | 5 | -5
+     |   |   | null  | 0 |    | 5 | -5
      |   | 0 | zero  | 0 |    | 5 | -5
+     | 1 | 4 | one   | 0 |    | 5 | -5
+     | 2 | 3 | two   | 0 |    | 5 | -5
+     | 3 | 2 | three | 0 |    | 5 | -5
+     | 4 | 1 | four  | 0 |    | 5 | -5
+     | 5 | 0 | five  | 0 |    | 5 | -5
+     | 6 | 6 | six   | 0 |    | 5 | -5
+     | 7 | 7 | seven | 0 |    | 5 | -5
+     | 8 | 8 | eight | 0 |    | 5 | -5
+     | 0 |   | zero  | 0 |    | 5 | -5
+     |   |   | null  | 0 |    | 5 | -5
      |   | 0 | zero  | 0 |    | 5 | -5
+     | 1 | 4 | one   | 0 |    | 0 |   
+     | 2 | 3 | two   | 0 |    | 0 |   
+     | 3 | 2 | three | 0 |    | 0 |   
+     | 4 | 1 | four  | 0 |    | 0 |   
+     | 5 | 0 | five  | 0 |    | 0 |   
+     | 6 | 6 | six   | 0 |    | 0 |   
+     | 7 | 7 | seven | 0 |    | 0 |   
+     | 8 | 8 | eight | 0 |    | 0 |   
+     | 0 |   | zero  | 0 |    | 0 |   
+     |   |   | null  | 0 |    | 0 |   
      |   | 0 | zero  | 0 |    | 0 |   
+     | 1 | 4 | one   | 0 |    |   |   
+     | 2 | 3 | two   | 0 |    |   |   
+     | 3 | 2 | three | 0 |    |   |   
+     | 4 | 1 | four  | 0 |    |   |   
+     | 5 | 0 | five  | 0 |    |   |   
+     | 6 | 6 | six   | 0 |    |   |   
+     | 7 | 7 | seven | 0 |    |   |   
+     | 8 | 8 | eight | 0 |    |   |   
+     | 0 |   | zero  | 0 |    |   |   
+     |   |   | null  | 0 |    |   |   
      |   | 0 | zero  | 0 |    |   |   
+     | 1 | 4 | one   | 0 |    |   |  0
+     | 2 | 3 | two   | 0 |    |   |  0
+     | 3 | 2 | three | 0 |    |   |  0
+     | 4 | 1 | four  | 0 |    |   |  0
+     | 5 | 0 | five  | 0 |    |   |  0
+     | 6 | 6 | six   | 0 |    |   |  0
+     | 7 | 7 | seven | 0 |    |   |  0
+     | 8 | 8 | eight | 0 |    |   |  0
+     | 0 |   | zero  | 0 |    |   |  0
+     |   |   | null  | 0 |    |   |  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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     | 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 |   
-     |   |   | null  |   |    |   |   
-     |   |   | null  |   |    |   |  0
      |   | 0 | zero  |   |    | 1 | -1
+     | 1 | 4 | one   |   |    | 2 |  2
+     | 2 | 3 | two   |   |    | 2 |  2
+     | 3 | 2 | three |   |    | 2 |  2
+     | 4 | 1 | four  |   |    | 2 |  2
+     | 5 | 0 | five  |   |    | 2 |  2
+     | 6 | 6 | six   |   |    | 2 |  2
+     | 7 | 7 | seven |   |    | 2 |  2
+     | 8 | 8 | eight |   |    | 2 |  2
+     | 0 |   | zero  |   |    | 2 |  2
+     |   |   | null  |   |    | 2 |  2
      |   | 0 | zero  |   |    | 2 |  2
+     | 1 | 4 | one   |   |    | 3 | -3
+     | 2 | 3 | two   |   |    | 3 | -3
+     | 3 | 2 | three |   |    | 3 | -3
+     | 4 | 1 | four  |   |    | 3 | -3
+     | 5 | 0 | five  |   |    | 3 | -3
+     | 6 | 6 | six   |   |    | 3 | -3
+     | 7 | 7 | seven |   |    | 3 | -3
+     | 8 | 8 | eight |   |    | 3 | -3
+     | 0 |   | zero  |   |    | 3 | -3
+     |   |   | null  |   |    | 3 | -3
      |   | 0 | zero  |   |    | 3 | -3
+     | 1 | 4 | one   |   |    | 2 |  4
+     | 2 | 3 | two   |   |    | 2 |  4
+     | 3 | 2 | three |   |    | 2 |  4
+     | 4 | 1 | four  |   |    | 2 |  4
+     | 5 | 0 | five  |   |    | 2 |  4
+     | 6 | 6 | six   |   |    | 2 |  4
+     | 7 | 7 | seven |   |    | 2 |  4
+     | 8 | 8 | eight |   |    | 2 |  4
+     | 0 |   | zero  |   |    | 2 |  4
+     |   |   | null  |   |    | 2 |  4
      |   | 0 | zero  |   |    | 2 |  4
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 5 | -5
+     |   |   | null  |   |    | 5 | -5
      |   | 0 | zero  |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 5 | -5
+     | 2 | 3 | two   |   |    | 5 | -5
+     | 3 | 2 | three |   |    | 5 | -5
+     | 4 | 1 | four  |   |    | 5 | -5
+     | 5 | 0 | five  |   |    | 5 | -5
+     | 6 | 6 | six   |   |    | 5 | -5
+     | 7 | 7 | seven |   |    | 5 | -5
+     | 8 | 8 | eight |   |    | 5 | -5
+     | 0 |   | zero  |   |    | 5 | -5
+     |   |   | null  |   |    | 5 | -5
      |   | 0 | zero  |   |    | 5 | -5
+     | 1 | 4 | one   |   |    | 0 |   
+     | 2 | 3 | two   |   |    | 0 |   
+     | 3 | 2 | three |   |    | 0 |   
+     | 4 | 1 | four  |   |    | 0 |   
+     | 5 | 0 | five  |   |    | 0 |   
+     | 6 | 6 | six   |   |    | 0 |   
+     | 7 | 7 | seven |   |    | 0 |   
+     | 8 | 8 | eight |   |    | 0 |   
+     | 0 |   | zero  |   |    | 0 |   
+     |   |   | null  |   |    | 0 |   
      |   | 0 | zero  |   |    | 0 |   
+     | 1 | 4 | one   |   |    |   |   
+     | 2 | 3 | two   |   |    |   |   
+     | 3 | 2 | three |   |    |   |   
+     | 4 | 1 | four  |   |    |   |   
+     | 5 | 0 | five  |   |    |   |   
+     | 6 | 6 | six   |   |    |   |   
+     | 7 | 7 | seven |   |    |   |   
+     | 8 | 8 | eight |   |    |   |   
+     | 0 |   | zero  |   |    |   |   
+     |   |   | null  |   |    |   |   
      |   | 0 | zero  |   |    |   |   
+     | 1 | 4 | one   |   |    |   |  0
+     | 2 | 3 | two   |   |    |   |  0
+     | 3 | 2 | three |   |    |   |  0
+     | 4 | 1 | four  |   |    |   |  0
+     | 5 | 0 | five  |   |    |   |  0
+     | 6 | 6 | six   |   |    |   |  0
+     | 7 | 7 | seven |   |    |   |  0
+     | 8 | 8 | eight |   |    |   |  0
+     | 0 |   | zero  |   |    |   |  0
+     |   |   | null  |   |    |   |  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 |   
-     | 1 | 4 | one   |   |  0 |   |   
-     | 1 | 4 | one   |   |  0 |   |  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 |   
-     | 2 | 3 | two   |   |  0 |   |   
-     | 2 | 3 | two   |   |  0 |   |  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 |   
-     | 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  |   |  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   |   |  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 |   |  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 |   |  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  |   |  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  |   |  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  |   |  0 | 1 | -1
+     | 1 | 4 | one   |   |  0 | 2 |  2
+     | 2 | 3 | two   |   |  0 | 2 |  2
+     | 3 | 2 | three |   |  0 | 2 |  2
+     | 4 | 1 | four  |   |  0 | 2 |  2
+     | 5 | 0 | five  |   |  0 | 2 |  2
+     | 6 | 6 | six   |   |  0 | 2 |  2
+     | 7 | 7 | seven |   |  0 | 2 |  2
+     | 8 | 8 | eight |   |  0 | 2 |  2
+     | 0 |   | zero  |   |  0 | 2 |  2
+     |   |   | null  |   |  0 | 2 |  2
      |   | 0 | zero  |   |  0 | 2 |  2
+     | 1 | 4 | one   |   |  0 | 3 | -3
+     | 2 | 3 | two   |   |  0 | 3 | -3
+     | 3 | 2 | three |   |  0 | 3 | -3
+     | 4 | 1 | four  |   |  0 | 3 | -3
+     | 5 | 0 | five  |   |  0 | 3 | -3
+     | 6 | 6 | six   |   |  0 | 3 | -3
+     | 7 | 7 | seven |   |  0 | 3 | -3
+     | 8 | 8 | eight |   |  0 | 3 | -3
+     | 0 |   | zero  |   |  0 | 3 | -3
+     |   |   | null  |   |  0 | 3 | -3
      |   | 0 | zero  |   |  0 | 3 | -3
+     | 1 | 4 | one   |   |  0 | 2 |  4
+     | 2 | 3 | two   |   |  0 | 2 |  4
+     | 3 | 2 | three |   |  0 | 2 |  4
+     | 4 | 1 | four  |   |  0 | 2 |  4
+     | 5 | 0 | five  |   |  0 | 2 |  4
+     | 6 | 6 | six   |   |  0 | 2 |  4
+     | 7 | 7 | seven |   |  0 | 2 |  4
+     | 8 | 8 | eight |   |  0 | 2 |  4
+     | 0 |   | zero  |   |  0 | 2 |  4
+     |   |   | null  |   |  0 | 2 |  4
      |   | 0 | zero  |   |  0 | 2 |  4
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 5 | -5
      |   | 0 | zero  |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 5 | -5
+     | 2 | 3 | two   |   |  0 | 5 | -5
+     | 3 | 2 | three |   |  0 | 5 | -5
+     | 4 | 1 | four  |   |  0 | 5 | -5
+     | 5 | 0 | five  |   |  0 | 5 | -5
+     | 6 | 6 | six   |   |  0 | 5 | -5
+     | 7 | 7 | seven |   |  0 | 5 | -5
+     | 8 | 8 | eight |   |  0 | 5 | -5
+     | 0 |   | zero  |   |  0 | 5 | -5
+     |   |   | null  |   |  0 | 5 | -5
      |   | 0 | zero  |   |  0 | 5 | -5
+     | 1 | 4 | one   |   |  0 | 0 |   
+     | 2 | 3 | two   |   |  0 | 0 |   
+     | 3 | 2 | three |   |  0 | 0 |   
+     | 4 | 1 | four  |   |  0 | 0 |   
+     | 5 | 0 | five  |   |  0 | 0 |   
+     | 6 | 6 | six   |   |  0 | 0 |   
+     | 7 | 7 | seven |   |  0 | 0 |   
+     | 8 | 8 | eight |   |  0 | 0 |   
+     | 0 |   | zero  |   |  0 | 0 |   
+     |   |   | null  |   |  0 | 0 |   
      |   | 0 | zero  |   |  0 | 0 |   
+     | 1 | 4 | one   |   |  0 |   |   
+     | 2 | 3 | two   |   |  0 |   |   
+     | 3 | 2 | three |   |  0 |   |   
+     | 4 | 1 | four  |   |  0 |   |   
+     | 5 | 0 | five  |   |  0 |   |   
+     | 6 | 6 | six   |   |  0 |   |   
+     | 7 | 7 | seven |   |  0 |   |   
+     | 8 | 8 | eight |   |  0 |   |   
+     | 0 |   | zero  |   |  0 |   |   
+     |   |   | null  |   |  0 |   |   
      |   | 0 | zero  |   |  0 |   |   
+     | 1 | 4 | one   |   |  0 |   |  0
+     | 2 | 3 | two   |   |  0 |   |  0
+     | 3 | 2 | three |   |  0 |   |  0
+     | 4 | 1 | four  |   |  0 |   |  0
+     | 5 | 0 | five  |   |  0 |   |  0
+     | 6 | 6 | six   |   |  0 |   |  0
+     | 7 | 7 | seven |   |  0 |   |  0
+     | 8 | 8 | eight |   |  0 |   |  0
+     | 0 |   | zero  |   |  0 |   |  0
+     |   |   | null  |   |  0 |   |  0
      |   | 0 | zero  |   |  0 |   |  0
 (891 rows)