diff --git a/doc/src/sgml/catalogs.sgml b/doc/src/sgml/catalogs.sgml
index f7335323fb..92382c620a 100644
--- a/doc/src/sgml/catalogs.sgml
+++ b/doc/src/sgml/catalogs.sgml
@@ -1,6 +1,6 @@
 <!--
  Documentation of the system catalogs, directed toward PostgreSQL developers
- $PostgreSQL: pgsql/doc/src/sgml/catalogs.sgml,v 2.92 2004/11/15 06:32:13 neilc Exp $
+ $PostgreSQL: pgsql/doc/src/sgml/catalogs.sgml,v 2.93 2004/12/01 19:00:27 tgl Exp $
  -->
 
 <chapter id="catalogs">
@@ -1079,11 +1079,12 @@
       <entry><type>int4</type></entry>
       <entry></entry>
       <entry>
-       Size of the on-disk representation of this table in pages (size
+       Size of the on-disk representation of this table in pages (of size
        <symbol>BLCKSZ</symbol>).
        This is only an estimate used by the planner.
        It is updated by <command>VACUUM</command>,
-       <command>ANALYZE</command>, and <command>CREATE INDEX</command>.
+       <command>ANALYZE</command>, and a few DDL commands
+       such as <command>CREATE INDEX</command>.
       </entry>
      </row>
 
@@ -1095,7 +1096,8 @@
        Number of rows in the table.
        This is only an estimate used by the planner.
        It is updated by <command>VACUUM</command>,
-       <command>ANALYZE</command>, and <command>CREATE INDEX</command>.
+       <command>ANALYZE</command>, and a few DDL commands
+       such as <command>CREATE INDEX</command>.
       </entry>
      </row>
 
diff --git a/doc/src/sgml/diskusage.sgml b/doc/src/sgml/diskusage.sgml
index ce09f7bc97..215519bc27 100644
--- a/doc/src/sgml/diskusage.sgml
+++ b/doc/src/sgml/diskusage.sgml
@@ -1,5 +1,5 @@
 <!--
-$PostgreSQL: pgsql/doc/src/sgml/diskusage.sgml,v 1.11 2004/06/21 04:06:03 tgl Exp $
+$PostgreSQL: pgsql/doc/src/sgml/diskusage.sgml,v 1.12 2004/12/01 19:00:27 tgl Exp $
 -->
 
 <chapter id="diskusage">
@@ -7,11 +7,7 @@ $PostgreSQL: pgsql/doc/src/sgml/diskusage.sgml,v 1.11 2004/06/21 04:06:03 tgl Ex
 
  <para>
   This chapter discusses how to monitor the disk usage of a
-  <productname>PostgreSQL</> database system.  In the current
-  release, the database administrator does not have much control over
-  the on-disk storage layout, so this chapter is mostly informative
-  and can give you some ideas how to manage the disk usage with
-  operating system tools.
+  <productname>PostgreSQL</> database system.
  </para>
 
  <sect1 id="disk-usage">
@@ -23,11 +19,12 @@ $PostgreSQL: pgsql/doc/src/sgml/diskusage.sgml,v 1.11 2004/06/21 04:06:03 tgl Ex
 
   <para>
    Each table has a primary heap disk file where most of the data is
-   stored. To store long column values, there is also a
-   <acronym>TOAST</> file associated with the table, named based on the
-   table's OID (actually <literal>pg_class.relfilenode</>), and an index on the
-   <acronym>TOAST</> table. There also may be indexes associated with
-   the base table.
+   stored. If the table has any columns with potentially-wide values,
+   there is also a <acronym>TOAST</> file associated with the table,
+   which is used to store values too wide to fit comfortably in the main
+   table.  There will be one index on the
+   <acronym>TOAST</> table, if present. There may also be indexes associated
+   with the base table.
   </para>
 
   <para>
@@ -45,18 +42,24 @@ SELECT relfilenode, relpages FROM pg_class WHERE relname = 'customer';
        16806 |       60
 (1 row)
 </programlisting>
-   Each page is typically 8 kilobytes. (Remember, <literal>relpages</>
-   is only updated by <command>VACUUM</> and <command>ANALYZE</>.)
+   Each page is typically 8 kilobytes. (Remember, <structfield>relpages</>
+   is only updated by <command>VACUUM</>, <command>ANALYZE</>, and
+   a few DDL commands such as <command>CREATE INDEX</>.)  The
+   <structfield>relfilenode</> value is of interest if you want to examine
+   the table's disk file directly.
   </para>
 
   <para>
    To show the space used by <acronym>TOAST</> tables, use a query
-   like the following, substituting the <literal>relfilenode</literal>
-   number of the heap (determined by the query above):
+   like the following:
 <programlisting>
 SELECT relname, relpages
-    FROM pg_class
-    WHERE relname = 'pg_toast_16806' OR relname = 'pg_toast_16806_index'
+    FROM pg_class,
+         (SELECT reltoastrelid FROM pg_class
+          WHERE relname = 'customer') ss
+    WHERE oid = ss.reltoastrelid
+       OR oid = (SELECT reltoastidxid FROM pg_class
+                 WHERE oid = ss.reltoastrelid)
     ORDER BY relname;
 
        relname        | relpages 
@@ -74,7 +77,7 @@ SELECT c2.relname, c2.relpages
     WHERE c.relname = 'customer'
         AND c.oid = i.indrelid
         AND c2.oid = i.indexrelid
-        ORDER BY c2.relname;
+    ORDER BY c2.relname;
 
        relname        | relpages 
 ----------------------+----------
@@ -113,13 +116,10 @@ SELECT relname, relpages FROM pg_class ORDER BY relpages DESC;
 
   <para>
    The most important disk monitoring task of a database administrator
-   is to make sure the disk doesn't grow full.  A filled data disk may
-   result in subsequent corruption of database indexes, but not of the
-   tables themselves. If the WAL files are on the same disk (as
-   is the case for a default configuration) then a filled disk during
-   database initialization may result in corrupted or incomplete WAL
-   files. This failure condition is detected and the database server
-   will refuse to start up.
+   is to make sure the disk doesn't grow full.  A filled data disk will
+   not result in data corruption, but it may well prevent useful activity
+   from occurring. If the disk holding the WAL files grows full, database
+   server panic and consequent shutdown may occur.
   </para>
 
   <para>
diff --git a/doc/src/sgml/perform.sgml b/doc/src/sgml/perform.sgml
index 6c23adb81b..687d322812 100644
--- a/doc/src/sgml/perform.sgml
+++ b/doc/src/sgml/perform.sgml
@@ -1,5 +1,5 @@
 <!--
-$PostgreSQL: pgsql/doc/src/sgml/perform.sgml,v 1.47 2004/11/15 06:32:14 neilc Exp $
+$PostgreSQL: pgsql/doc/src/sgml/perform.sgml,v 1.48 2004/12/01 19:00:27 tgl Exp $
 -->
 
  <chapter id="performance-tips">
@@ -389,14 +389,15 @@ SELECT relname, relkind, reltuples, relpages FROM pg_class WHERE relname LIKE 't
   <para>
    For efficiency reasons, <structfield>reltuples</structfield> 
    and <structfield>relpages</structfield> are not updated on-the-fly,
-   and so they usually contain only approximate values (which is good
-   enough for the planner's purposes).  They are initialized with dummy
-   values (presently 1000 and 10 respectively) when a table is created.
-   They are updated by certain commands, presently <command>VACUUM</>,
-   <command>ANALYZE</>, and <command>CREATE INDEX</>.  A stand-alone
+   and so they usually contain somewhat out-of-date values.
+   They are updated by <command>VACUUM</>, <command>ANALYZE</>, and a
+   few DDL commands such as <command>CREATE INDEX</>.  A stand-alone
    <command>ANALYZE</>, that is one not part of <command>VACUUM</>,
    generates an approximate <structfield>reltuples</structfield> value
-   since it does not read every row of the table.
+   since it does not read every row of the table.  The planner
+   will scale the values it finds in <structname>pg_class</structname>
+   to match the current physical table size, thus obtaining a closer
+   approximation.
   </para>
 
   <indexterm>
diff --git a/doc/src/sgml/release.sgml b/doc/src/sgml/release.sgml
index 391f9d06c5..3a59781039 100644
--- a/doc/src/sgml/release.sgml
+++ b/doc/src/sgml/release.sgml
@@ -1,5 +1,5 @@
 <!--
-$PostgreSQL: pgsql/doc/src/sgml/release.sgml,v 1.314 2004/11/27 21:56:04 petere Exp $
+$PostgreSQL: pgsql/doc/src/sgml/release.sgml,v 1.315 2004/12/01 19:00:27 tgl Exp $
 -->
 
 <appendix id="release">
@@ -527,6 +527,24 @@ $PostgreSQL: pgsql/doc/src/sgml/release.sgml,v 1.314 2004/11/27 21:56:04 petere
      </para>
     </listitem>
 
+    <listitem>
+     <para>
+      Use dynamically-generated table size estimates while planning (Tom)
+     </para>
+     <para>
+      The optimizer now uses a table's current actual size on disk as its
+      estimate of the number of blocks in the table, and it makes an estimate
+      of the number of rows in the table based on the current size on disk.
+      Formerly, the
+      <structname>pg_class</structname>.<structfield>relpages</structfield>
+      and
+      <structname>pg_class</structname>.<structfield>reltuples</structfield>
+      fields were used as-is, but these values might be quite out-of-date,
+      leading to poor choices of plans.  They are now treated only as an
+      indication of the table's density (rows per page).
+     </para>
+    </listitem>
+
     <listitem>
      <para>
       Improved index usage with <literal>OR</> clauses (Tom)
diff --git a/src/backend/access/nbtree/nbtree.c b/src/backend/access/nbtree/nbtree.c
index 771ff6cbe7..b36153d0d5 100644
--- a/src/backend/access/nbtree/nbtree.c
+++ b/src/backend/access/nbtree/nbtree.c
@@ -12,7 +12,7 @@
  * Portions Copyright (c) 1994, Regents of the University of California
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/access/nbtree/nbtree.c,v 1.122 2004/11/17 03:13:38 neilc Exp $
+ *	  $PostgreSQL: pgsql/src/backend/access/nbtree/nbtree.c,v 1.123 2004/12/01 19:00:37 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -785,6 +785,10 @@ btvacuumcleanup(PG_FUNCTION_ARGS)
 			 * Do the physical truncation.
 			 */
 			RelationTruncate(rel, new_pages);
+
+			/* update statistics */
+			stats->pages_removed = num_pages - new_pages;
+
 			num_pages = new_pages;
 		}
 	}
diff --git a/src/backend/catalog/heap.c b/src/backend/catalog/heap.c
index f5ec158d7a..e99646d0bc 100644
--- a/src/backend/catalog/heap.c
+++ b/src/backend/catalog/heap.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/catalog/heap.c,v 1.276 2004/08/31 17:10:36 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/catalog/heap.c,v 1.277 2004/12/01 19:00:39 tgl Exp $
  *
  *
  * INTERFACE ROUTINES
@@ -607,37 +607,22 @@ AddNewRelationTuple(Relation pg_class_desc,
 	 */
 	new_rel_reltup = new_rel_desc->rd_rel;
 
-	/*
-	 * Here we insert bogus estimates of the size of the new relation. In
-	 * reality, of course, the new relation has 0 tuples and pages, and if
-	 * we were tracking these statistics accurately then we'd set the
-	 * fields that way.  But at present the stats will be updated only by
-	 * VACUUM or CREATE INDEX, and the user might insert a lot of tuples
-	 * before he gets around to doing either of those.	So, instead of
-	 * saying the relation is empty, we insert guesstimates.  The point is
-	 * to keep the optimizer from making really stupid choices on
-	 * never-yet-vacuumed tables; so the estimates need only be large
-	 * enough to discourage the optimizer from using nested-loop plans.
-	 * With this hack, nested-loop plans will be preferred only after the
-	 * table has been proven to be small by VACUUM or CREATE INDEX.
-	 * Maintaining the stats on-the-fly would solve the problem more
-	 * cleanly, but the overhead of that would likely cost more than it'd
-	 * save. (NOTE: CREATE INDEX inserts the same bogus estimates if it
-	 * finds the relation has 0 rows and pages. See index.c.)
-	 */
 	switch (relkind)
 	{
 		case RELKIND_RELATION:
 		case RELKIND_INDEX:
 		case RELKIND_TOASTVALUE:
-			new_rel_reltup->relpages = 10;		/* bogus estimates */
-			new_rel_reltup->reltuples = 1000;
+			/* The relation is real, but as yet empty */
+			new_rel_reltup->relpages = 0;
+			new_rel_reltup->reltuples = 0;
 			break;
 		case RELKIND_SEQUENCE:
+			/* Sequences always have a known size */
 			new_rel_reltup->relpages = 1;
 			new_rel_reltup->reltuples = 1;
 			break;
-		default:				/* views, etc */
+		default:
+			/* Views, etc, have no disk storage */
 			new_rel_reltup->relpages = 0;
 			new_rel_reltup->reltuples = 0;
 			break;
diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index 19fc60b6c8..d61fd274b6 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/catalog/index.c,v 1.241 2004/10/15 22:39:53 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/catalog/index.c,v 1.242 2004/12/01 19:00:39 tgl Exp $
  *
  *
  * INTERFACE ROUTINES
@@ -33,20 +33,15 @@
 #include "catalog/index.h"
 #include "catalog/indexing.h"
 #include "catalog/pg_constraint.h"
-#include "catalog/pg_index.h"
 #include "catalog/pg_opclass.h"
-#include "catalog/pg_proc.h"
 #include "catalog/pg_type.h"
 #include "executor/executor.h"
 #include "miscadmin.h"
 #include "optimizer/clauses.h"
-#include "optimizer/prep.h"
 #include "parser/parse_expr.h"
-#include "parser/parse_func.h"
 #include "storage/sinval.h"
 #include "storage/smgr.h"
 #include "utils/builtins.h"
-#include "utils/catcache.h"
 #include "utils/fmgroids.h"
 #include "utils/inval.h"
 #include "utils/lsyscache.h"
@@ -54,14 +49,6 @@
 #include "utils/syscache.h"
 
 
-/*
- * macros used in guessing how many tuples are on a page.
- */
-#define AVG_ATTR_SIZE 8
-#define NTUPLES_PER_PAGE(natts) \
-	((BLCKSZ - MAXALIGN(sizeof(PageHeaderData))) / \
-	((natts) * AVG_ATTR_SIZE + MAXALIGN(sizeof(HeapTupleHeaderData))))
-
 /* non-export function prototypes */
 static TupleDesc ConstructTupleDescriptor(Relation heapRelation,
 						 IndexInfo *indexInfo,
@@ -1153,6 +1140,8 @@ setNewRelfilenode(Relation relation)
 
 	/* update the pg_class row */
 	rd_rel->relfilenode = newrelfilenode;
+	rd_rel->relpages = 0;		/* it's empty until further notice */
+	rd_rel->reltuples = 0;
 	simple_heap_update(pg_class, &tuple->t_self, tuple);
 	CatalogUpdateIndexes(pg_class, tuple);
 
@@ -1170,7 +1159,7 @@ setNewRelfilenode(Relation relation)
  *
  * Update pg_class' relpages and reltuples statistics for the given relation
  * (which can be either a table or an index).  Note that this is not used
- * in the context of VACUUM.
+ * in the context of VACUUM, only CREATE INDEX.
  * ----------------
  */
 void
@@ -1209,7 +1198,8 @@ UpdateStats(Oid relid, double reltuples)
 	 * Find the tuple to update in pg_class.  Normally we make a copy of
 	 * the tuple using the syscache, modify it, and apply heap_update. But
 	 * in bootstrap mode we can't use heap_update, so we cheat and
-	 * overwrite the tuple in-place.
+	 * overwrite the tuple in-place.  (Note: as of PG 8.0 this isn't called
+	 * during bootstrap, but leave the code here for possible future use.)
 	 *
 	 * We also must cheat if reindexing pg_class itself, because the target
 	 * index may presently not be part of the set of indexes that
@@ -1245,45 +1235,14 @@ UpdateStats(Oid relid, double reltuples)
 		elog(ERROR, "could not find tuple for relation %u", relid);
 	rd_rel = (Form_pg_class) GETSTRUCT(tuple);
 
-	/*
-	 * Figure values to insert.
-	 *
-	 * If we found zero tuples in the scan, do NOT believe it; instead put a
-	 * bogus estimate into the statistics fields.  Otherwise, the common
-	 * pattern "CREATE TABLE; CREATE INDEX; insert data" leaves the table
-	 * with zero size statistics until a VACUUM is done.  The optimizer
-	 * will generate very bad plans if the stats claim the table is empty
-	 * when it is actually sizable.  See also CREATE TABLE in heap.c.
-	 *
-	 * Note: this path is also taken during bootstrap, because bootstrap.c
-	 * passes reltuples = 0 after loading a table.	We have to estimate
-	 * some number for reltuples based on the actual number of pages.
-	 */
-	relpages = RelationGetNumberOfBlocks(whichRel);
-
-	if (reltuples == 0)
-	{
-		if (relpages == 0)
-		{
-			/* Bogus defaults for a virgin table, same as heap.c */
-			reltuples = 1000;
-			relpages = 10;
-		}
-		else if (whichRel->rd_rel->relkind == RELKIND_INDEX && relpages <= 2)
-		{
-			/* Empty index, leave bogus defaults in place */
-			reltuples = 1000;
-		}
-		else
-			reltuples = ((double) relpages) * NTUPLES_PER_PAGE(whichRel->rd_rel->relnatts);
-	}
-
 	/*
 	 * Update statistics in pg_class, if they changed.	(Avoiding an
 	 * unnecessary update is not just a tiny performance improvement; it
 	 * also reduces the window wherein concurrent CREATE INDEX commands
 	 * may conflict.)
 	 */
+	relpages = RelationGetNumberOfBlocks(whichRel);
+
 	if (rd_rel->relpages != (int32) relpages ||
 		rd_rel->reltuples != (float4) reltuples)
 	{
diff --git a/src/backend/commands/vacuum.c b/src/backend/commands/vacuum.c
index 3d0c6e0e99..941e0d36e6 100644
--- a/src/backend/commands/vacuum.c
+++ b/src/backend/commands/vacuum.c
@@ -13,7 +13,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/commands/vacuum.c,v 1.295 2004/10/15 22:39:56 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/commands/vacuum.c,v 1.296 2004/12/01 19:00:41 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -646,7 +646,7 @@ vac_update_relstats(Oid relid, BlockNumber num_pages, double num_tuples,
 	/* overwrite the existing statistics in the tuple */
 	pgcform = (Form_pg_class) GETSTRUCT(&rtup);
 	pgcform->relpages = (int32) num_pages;
-	pgcform->reltuples = num_tuples;
+	pgcform->reltuples = (float4) num_tuples;
 	pgcform->relhasindex = hasindex;
 
 	/*
diff --git a/src/backend/commands/vacuumlazy.c b/src/backend/commands/vacuumlazy.c
index ff78ea00d1..f18e0f92f6 100644
--- a/src/backend/commands/vacuumlazy.c
+++ b/src/backend/commands/vacuumlazy.c
@@ -31,12 +31,14 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/commands/vacuumlazy.c,v 1.48 2004/10/25 15:42:02 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/commands/vacuumlazy.c,v 1.49 2004/12/01 19:00:42 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
 #include "postgres.h"
 
+#include <math.h>
+
 #include "access/genam.h"
 #include "access/heapam.h"
 #include "access/xlog.h"
@@ -67,6 +69,8 @@ typedef struct LVRelStats
 	/* Overall statistics about rel */
 	BlockNumber rel_pages;
 	double		rel_tuples;
+	BlockNumber	pages_removed;
+	double		tuples_deleted;
 	BlockNumber nonempty_pages; /* actually, last nonempty page + 1 */
 	Size		threshold;		/* minimum interesting free space */
 	/* List of TIDs of tuples we intend to delete */
@@ -94,12 +98,19 @@ static void lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 			   Relation *Irel, int nindexes);
 static void lazy_vacuum_heap(Relation onerel, LVRelStats *vacrelstats);
 static void lazy_scan_index(Relation indrel, LVRelStats *vacrelstats);
-static void lazy_vacuum_index(Relation indrel, LVRelStats *vacrelstats);
+static void lazy_vacuum_index(Relation indrel,
+							  double *index_tups_vacuumed,
+							  BlockNumber *index_pages_removed,
+							  LVRelStats *vacrelstats);
 static int lazy_vacuum_page(Relation onerel, BlockNumber blkno, Buffer buffer,
 				 int tupindex, LVRelStats *vacrelstats);
 static void lazy_truncate_heap(Relation onerel, LVRelStats *vacrelstats);
 static BlockNumber count_nondeletable_pages(Relation onerel,
 						 LVRelStats *vacrelstats);
+static void lazy_update_relstats(Relation rel, BlockNumber num_pages,
+								 BlockNumber pages_removed,
+								 double num_tuples, double tuples_removed,
+								 bool hasindex);
 static void lazy_space_alloc(LVRelStats *vacrelstats, BlockNumber relblocks);
 static void lazy_record_dead_tuple(LVRelStats *vacrelstats,
 					   ItemPointer itemptr);
@@ -169,8 +180,10 @@ lazy_vacuum_rel(Relation onerel, VacuumStmt *vacstmt)
 	lazy_update_fsm(onerel, vacrelstats);
 
 	/* Update statistics in pg_class */
-	vac_update_relstats(RelationGetRelid(onerel), vacrelstats->rel_pages,
-						vacrelstats->rel_tuples, hasindex);
+	lazy_update_relstats(onerel, vacrelstats->rel_pages,
+						 vacrelstats->pages_removed,
+						 vacrelstats->rel_tuples, vacrelstats->tuples_deleted,
+						 hasindex);
 }
 
 
@@ -195,6 +208,9 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 				tups_vacuumed,
 				nkeep,
 				nunused;
+	double	   *index_tups_vacuumed;
+	BlockNumber *index_pages_removed;
+	bool		did_vacuum_index = false;
 	int			i;
 	VacRUsage	ru0;
 
@@ -209,6 +225,16 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 	empty_pages = 0;
 	num_tuples = tups_vacuumed = nkeep = nunused = 0;
 
+	/*
+	 * Because index vacuuming is done in multiple passes, we have to keep
+	 * track of the total number of rows and pages removed from each index.
+	 * index_tups_vacuumed[i] is the number removed so far from the i'th
+	 * index.  (For partial indexes this could well be different from
+	 * tups_vacuumed.)  Likewise for index_pages_removed[i].
+	 */
+	index_tups_vacuumed = (double *) palloc0(nindexes * sizeof(double));
+	index_pages_removed = (BlockNumber *) palloc0(nindexes * sizeof(BlockNumber));
+
 	nblocks = RelationGetNumberOfBlocks(onerel);
 	vacrelstats->rel_pages = nblocks;
 	vacrelstats->nonempty_pages = 0;
@@ -238,7 +264,11 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 		{
 			/* Remove index entries */
 			for (i = 0; i < nindexes; i++)
-				lazy_vacuum_index(Irel[i], vacrelstats);
+				lazy_vacuum_index(Irel[i],
+								  &index_tups_vacuumed[i],
+								  &index_pages_removed[i],
+								  vacrelstats);
+			did_vacuum_index = true;
 			/* Remove tuples from heap */
 			lazy_vacuum_heap(onerel, vacrelstats);
 			/* Forget the now-vacuumed tuples, and press on */
@@ -400,6 +430,7 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 
 	/* save stats for use later */
 	vacrelstats->rel_tuples = num_tuples;
+	vacrelstats->tuples_deleted = tups_vacuumed;
 
 	/* If any tuples need to be deleted, perform final vacuum cycle */
 	/* XXX put a threshold on min number of tuples here? */
@@ -407,11 +438,14 @@ lazy_scan_heap(Relation onerel, LVRelStats *vacrelstats,
 	{
 		/* Remove index entries */
 		for (i = 0; i < nindexes; i++)
-			lazy_vacuum_index(Irel[i], vacrelstats);
+			lazy_vacuum_index(Irel[i],
+							  &index_tups_vacuumed[i],
+							  &index_pages_removed[i],
+							  vacrelstats);
 		/* Remove tuples from heap */
 		lazy_vacuum_heap(onerel, vacrelstats);
 	}
-	else
+	else if (!did_vacuum_index)
 	{
 		/* Must do post-vacuum cleanup and statistics update anyway */
 		for (i = 0; i < nindexes; i++)
@@ -588,9 +622,9 @@ lazy_scan_index(Relation indrel, LVRelStats *vacrelstats)
 		return;
 
 	/* now update statistics in pg_class */
-	vac_update_relstats(RelationGetRelid(indrel),
-						stats->num_pages, stats->num_index_tuples,
-						false);
+	lazy_update_relstats(indrel, stats->num_pages, stats->pages_removed,
+						 stats->num_index_tuples, stats->tuples_removed,
+						 false);
 
 	ereport(elevel,
 	   (errmsg("index \"%s\" now contains %.0f row versions in %u pages",
@@ -611,11 +645,17 @@ lazy_scan_index(Relation indrel, LVRelStats *vacrelstats)
  *		Delete all the index entries pointing to tuples listed in
  *		vacrelstats->dead_tuples.
  *
+ *		Increment *index_tups_vacuumed by the number of index entries
+ *		removed, and *index_pages_removed by the number of pages removed.
+ *
  *		Finally, we arrange to update the index relation's statistics in
  *		pg_class.
  */
 static void
-lazy_vacuum_index(Relation indrel, LVRelStats *vacrelstats)
+lazy_vacuum_index(Relation indrel,
+				  double *index_tups_vacuumed,
+				  BlockNumber *index_pages_removed,
+				  LVRelStats *vacrelstats)
 {
 	IndexBulkDeleteResult *stats;
 	IndexVacuumCleanupInfo vcinfo;
@@ -652,10 +692,14 @@ lazy_vacuum_index(Relation indrel, LVRelStats *vacrelstats)
 	if (!stats)
 		return;
 
+	/* accumulate total removed over multiple index-cleaning cycles */
+	*index_tups_vacuumed += stats->tuples_removed;
+	*index_pages_removed += stats->pages_removed;
+
 	/* now update statistics in pg_class */
-	vac_update_relstats(RelationGetRelid(indrel),
-						stats->num_pages, stats->num_index_tuples,
-						false);
+	lazy_update_relstats(indrel, stats->num_pages, *index_pages_removed,
+						 stats->num_index_tuples, *index_tups_vacuumed,
+						 false);
 
 	ereport(elevel,
 	   (errmsg("index \"%s\" now contains %.0f row versions in %u pages",
@@ -741,8 +785,6 @@ lazy_truncate_heap(Relation onerel, LVRelStats *vacrelstats)
 	 * Do the physical truncation.
 	 */
 	RelationTruncate(onerel, new_rel_pages);
-	vacrelstats->rel_pages = new_rel_pages;		/* save new number of
-												 * blocks */
 
 	/*
 	 * Drop free-space info for removed blocks; these must not get entered
@@ -763,6 +805,10 @@ lazy_truncate_heap(Relation onerel, LVRelStats *vacrelstats)
 	/* We destroyed the heap ordering, so mark array unordered */
 	vacrelstats->fs_is_heap = false;
 
+	/* update statistics */
+	vacrelstats->rel_pages = new_rel_pages;
+	vacrelstats->pages_removed = old_rel_pages - new_rel_pages;
+
 	/*
 	 * We keep the exclusive lock until commit (perhaps not necessary)?
 	 */
@@ -886,6 +932,51 @@ count_nondeletable_pages(Relation onerel, LVRelStats *vacrelstats)
 	return vacrelstats->nonempty_pages;
 }
 
+/*
+ * lazy_update_relstats - update pg_class statistics for a table or index
+ *
+ * We always want to set relpages to an accurate value.  However, for lazy
+ * VACUUM it seems best to set reltuples to the average of the number of
+ * rows before vacuuming and the number after vacuuming, rather than just
+ * using the number after vacuuming.  This will result in the best average
+ * performance in a steady-state situation where VACUUMs are performed
+ * regularly on a table of roughly constant size, assuming that the physical
+ * number of pages in the table stays about the same throughout.  (Note that
+ * we do not apply the same logic to VACUUM FULL, because it repacks the table
+ * and thereby boosts the tuple density.)
+ *
+ * An important point is that when the table size has decreased a lot during
+ * vacuuming, the old reltuples count might give an overestimate of the tuple
+ * density.  We handle this by scaling down the old reltuples count by the
+ * fraction by which the table has shortened before we merge it with the
+ * new reltuples count.  In particular this means that when relpages goes to
+ * zero, reltuples will immediately go to zero as well, causing the planner
+ * to fall back on other estimation procedures as the table grows again.
+ *
+ * Because we do this math independently for the table and the indexes, it's
+ * quite possible to end up with an index's reltuples different from the
+ * table's, which is silly except in the case of partial indexes.  We don't
+ * worry too much about that here; the planner contains filtering logic to
+ * ensure it only uses sane estimates.
+ */
+static void
+lazy_update_relstats(Relation rel, BlockNumber num_pages,
+					 BlockNumber pages_removed,
+					 double num_tuples, double tuples_removed,
+					 bool hasindex)
+{
+	double	old_num_tuples;
+
+	old_num_tuples = num_tuples + tuples_removed;
+	if (pages_removed > 0)
+		old_num_tuples *= (double) num_pages / (double) (num_pages + pages_removed);
+	if (old_num_tuples > num_tuples)
+		num_tuples = ceil((num_tuples + old_num_tuples) * 0.5);
+
+	vac_update_relstats(RelationGetRelid(rel), num_pages, num_tuples,
+						hasindex);
+}
+
 /*
  * lazy_space_alloc - space allocation decisions for lazy vacuum
  *
diff --git a/src/backend/optimizer/util/plancat.c b/src/backend/optimizer/util/plancat.c
index ed76fe8fb8..b4f42ac123 100644
--- a/src/backend/optimizer/util/plancat.c
+++ b/src/backend/optimizer/util/plancat.c
@@ -9,7 +9,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/optimizer/util/plancat.c,v 1.97 2004/10/01 17:11:50 tgl Exp $
+ *	  $PostgreSQL: pgsql/src/backend/optimizer/util/plancat.c,v 1.98 2004/12/01 19:00:43 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -38,6 +38,10 @@
 #include "miscadmin.h"
 
 
+static void estimate_rel_size(Relation rel, int32 *attr_widths,
+							  BlockNumber *pages, double *tuples);
+
+
 /*
  * get_relation_info -
  *	  Retrieves catalog information for a given relation.
@@ -50,6 +54,10 @@
  *	indexlist	list of IndexOptInfos for relation's indexes
  *	pages		number of pages
  *	tuples		number of tuples
+ *
+ * Also, initialize the attr_needed[] and attr_widths[] arrays.  In most
+ * cases these are left as zeroes, but sometimes we need to compute attr
+ * widths here, and we may as well cache the results for costsize.c.
  */
 void
 get_relation_info(Oid relationObjectId, RelOptInfo *rel)
@@ -64,6 +72,18 @@ get_relation_info(Oid relationObjectId, RelOptInfo *rel)
 	rel->min_attr = FirstLowInvalidHeapAttributeNumber + 1;
 	rel->max_attr = RelationGetNumberOfAttributes(relation);
 
+	Assert(rel->max_attr >= rel->min_attr);
+	rel->attr_needed = (Relids *)
+		palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(Relids));
+	rel->attr_widths = (int32 *)
+		palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(int32));
+
+	/*
+	 * Estimate relation size.
+	 */
+	estimate_rel_size(relation, rel->attr_widths - rel->min_attr,
+					  &rel->pages, &rel->tuples);
+
 	/*
 	 * Make list of indexes.  Ignore indexes on system catalogs if told
 	 * to.
@@ -121,8 +141,6 @@ get_relation_info(Oid relationObjectId, RelOptInfo *rel)
 			}
 
 			info->relam = indexRelation->rd_rel->relam;
-			info->pages = indexRelation->rd_rel->relpages;
-			info->tuples = indexRelation->rd_rel->reltuples;
 			info->amcostestimate = index_cost_estimator(indexRelation);
 
 			/*
@@ -156,6 +174,26 @@ get_relation_info(Oid relationObjectId, RelOptInfo *rel)
 			info->predOK = false;		/* set later in indxpath.c */
 			info->unique = index->indisunique;
 
+			/*
+			 * Estimate the index size.  If it's not a partial index, we
+			 * lock the number-of-tuples estimate to equal the parent table;
+			 * if it is partial then we have to use the same methods as we
+			 * would for a table, except we can be sure that the index is
+			 * not larger than the table.
+			 */
+			if (info->indpred == NIL)
+			{
+				info->pages = RelationGetNumberOfBlocks(indexRelation);
+				info->tuples = rel->tuples;
+			}
+			else
+			{
+				estimate_rel_size(indexRelation, NULL,
+								  &info->pages, &info->tuples);
+				if (info->tuples > rel->tuples)
+					info->tuples = rel->tuples;
+			}
+
 			/* initialize cached join info to empty */
 			info->outer_relids = NULL;
 			info->inner_paths = NIL;
@@ -170,13 +208,110 @@ get_relation_info(Oid relationObjectId, RelOptInfo *rel)
 
 	rel->indexlist = indexinfos;
 
-	rel->pages = relation->rd_rel->relpages;
-	rel->tuples = relation->rd_rel->reltuples;
-
 	/* XXX keep the lock here? */
 	heap_close(relation, AccessShareLock);
 }
 
+/*
+ * estimate_rel_size - estimate # pages and # tuples in a table or index
+ *
+ * If attr_widths isn't NULL, it points to the zero-index entry of the
+ * relation's attr_width[] cache; we fill this in if we have need to compute
+ * the attribute widths for estimation purposes.
+ */
+static void
+estimate_rel_size(Relation rel, int32 *attr_widths,
+				  BlockNumber *pages, double *tuples)
+{
+	BlockNumber	curpages;
+	BlockNumber	relpages;
+	double		reltuples;
+	double		density;
+
+	switch (rel->rd_rel->relkind)
+	{
+		case RELKIND_RELATION:
+		case RELKIND_INDEX:
+		case RELKIND_TOASTVALUE:
+			/* it has storage, ok to call the smgr */
+			*pages = curpages = RelationGetNumberOfBlocks(rel);
+			/* quick exit if rel is clearly empty */
+			if (curpages == 0)
+			{
+				*tuples = 0;
+				break;
+			}
+			/* coerce values in pg_class to more desirable types */
+			relpages = (BlockNumber) rel->rd_rel->relpages;
+			reltuples = (double) rel->rd_rel->reltuples;
+			/*
+			 * If it's an index, discount the metapage.  This is a kluge
+			 * because it assumes more than it ought to about index contents;
+			 * it's reasonably OK for btrees but a bit suspect otherwise.
+			 */
+			if (rel->rd_rel->relkind == RELKIND_INDEX &&
+				relpages > 0)
+			{
+				curpages--;
+				relpages--;
+			}
+			/* estimate number of tuples from previous tuple density */
+			if (relpages > 0)
+				density = reltuples / (double) relpages;
+			else
+			{
+				/*
+				 * When we have no data because the relation was truncated,
+				 * estimate tuple width from attribute datatypes.  We assume
+				 * here that the pages are completely full, which is OK for
+				 * tables (since they've presumably not been VACUUMed yet)
+				 * but is probably an overestimate for indexes.  Fortunately
+				 * get_relation_info() can clamp the overestimate to the
+				 * parent table's size.
+				 */
+				int32	tuple_width = 0;
+				int		i;
+
+				for (i = 1; i <= RelationGetNumberOfAttributes(rel); i++)
+				{
+					Form_pg_attribute att = rel->rd_att->attrs[i - 1];
+					int32		item_width;
+
+					if (att->attisdropped)
+						continue;
+					/* This should match set_rel_width() in costsize.c */
+					item_width = get_attavgwidth(RelationGetRelid(rel), i);
+					if (item_width <= 0)
+					{
+						item_width = get_typavgwidth(att->atttypid,
+													 att->atttypmod);
+						Assert(item_width > 0);
+					}
+					if (attr_widths != NULL)
+						attr_widths[i] = item_width;
+					tuple_width += item_width;
+				}
+				tuple_width = MAXALIGN(tuple_width);
+				tuple_width += MAXALIGN(sizeof(HeapTupleHeaderData));
+				tuple_width += sizeof(ItemPointerData);
+				/* note: integer division is intentional here */
+				density = (BLCKSZ - sizeof(PageHeaderData)) / tuple_width;
+			}
+			*tuples = rint(density * (double) curpages);
+			break;
+		case RELKIND_SEQUENCE:
+			/* Sequences always have a known size */
+			*pages = 1;
+			*tuples = 1;
+			break;
+		default:
+			/* else it has no disk storage; probably shouldn't get here? */
+			*pages = 0;
+			*tuples = 0;
+			break;
+	}
+}
+
 /*
  * build_physical_tlist
  *
diff --git a/src/backend/optimizer/util/relnode.c b/src/backend/optimizer/util/relnode.c
index bdef23fc26..a612de8df4 100644
--- a/src/backend/optimizer/util/relnode.c
+++ b/src/backend/optimizer/util/relnode.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/optimizer/util/relnode.c,v 1.62 2004/08/29 05:06:44 momjian Exp $
+ *	  $PostgreSQL: pgsql/src/backend/optimizer/util/relnode.c,v 1.63 2004/12/01 19:00:43 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -159,10 +159,14 @@ make_base_rel(Query *root, int relid)
 			break;
 		case RTE_SUBQUERY:
 		case RTE_FUNCTION:
-			/* Subquery or function --- need only set up attr range */
+			/* Subquery or function --- set up attr range and arrays */
 			/* Note: 0 is included in range to support whole-row Vars */
 			rel->min_attr = 0;
 			rel->max_attr = list_length(rte->eref->colnames);
+			rel->attr_needed = (Relids *)
+				palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(Relids));
+			rel->attr_widths = (int32 *)
+				palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(int32));
 			break;
 		default:
 			elog(ERROR, "unrecognized RTE kind: %d",
@@ -170,12 +174,6 @@ make_base_rel(Query *root, int relid)
 			break;
 	}
 
-	Assert(rel->max_attr >= rel->min_attr);
-	rel->attr_needed = (Relids *)
-		palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(Relids));
-	rel->attr_widths = (int32 *)
-		palloc0((rel->max_attr - rel->min_attr + 1) * sizeof(int32));
-
 	return rel;
 }
 
diff --git a/src/include/access/genam.h b/src/include/access/genam.h
index 01874b1fd6..bfbebb6ca4 100644
--- a/src/include/access/genam.h
+++ b/src/include/access/genam.h
@@ -7,7 +7,7 @@
  * Portions Copyright (c) 1996-2004, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
- * $PostgreSQL: pgsql/src/include/access/genam.h,v 1.45 2004/08/29 04:13:03 momjian Exp $
+ * $PostgreSQL: pgsql/src/include/access/genam.h,v 1.46 2004/12/01 19:00:45 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -28,10 +28,15 @@
  * an index AM could choose to have bulk-delete return a larger struct
  * of which this is just the first field; this provides a way for bulk-delete
  * to communicate additional private data to vacuum-cleanup.
+ *
+ * Note: pages_removed is the amount by which the index physically shrank,
+ * if any (ie the change in its total size on disk).  pages_deleted and
+ * pages_free refer to free space within the index file.
  */
 typedef struct IndexBulkDeleteResult
 {
 	BlockNumber num_pages;		/* pages remaining in index */
+	BlockNumber pages_removed;	/* # removed by bulk-delete operation */
 	double		num_index_tuples;		/* tuples remaining */
 	double		tuples_removed; /* # removed by bulk-delete operation */
 	BlockNumber pages_deleted;	/* # unused pages in index */
diff --git a/src/include/nodes/relation.h b/src/include/nodes/relation.h
index 8d0d6a60ba..c07f8e1f96 100644
--- a/src/include/nodes/relation.h
+++ b/src/include/nodes/relation.h
@@ -7,7 +7,7 @@
  * Portions Copyright (c) 1996-2004, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
- * $PostgreSQL: pgsql/src/include/nodes/relation.h,v 1.100 2004/11/26 21:08:35 tgl Exp $
+ * $PostgreSQL: pgsql/src/include/nodes/relation.h,v 1.101 2004/12/01 19:00:53 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -255,7 +255,7 @@ typedef struct IndexOptInfo
 	Oid			indexoid;		/* OID of the index relation */
 
 	/* statistics from pg_class */
-	long		pages;			/* number of disk pages in index */
+	BlockNumber	pages;			/* number of disk pages in index */
 	double		tuples;			/* number of index tuples in index */
 
 	/* index descriptor information */
diff --git a/src/test/regress/expected/case.out b/src/test/regress/expected/case.out
index 409a5a536a..e0b94fff6a 100644
--- a/src/test/regress/expected/case.out
+++ b/src/test/regress/expected/case.out
@@ -156,29 +156,29 @@ SELECT COALESCE(a.f, b.i, b.j)
   FROM CASE_TBL a, CASE2_TBL b;
  coalesce 
 ----------
-     10.1
-     10.1
-     10.1
-     10.1
-     10.1
      10.1
      20.2
-     20.2
-     20.2
-     20.2
-     20.2
-     20.2
-    -30.3
-    -30.3
-    -30.3
-    -30.3
-    -30.3
     -30.3
         1
+     10.1
+     20.2
+    -30.3
         2
+     10.1
+     20.2
+    -30.3
         3
+     10.1
+     20.2
+    -30.3
         2
+     10.1
+     20.2
+    -30.3
         1
+     10.1
+     20.2
+    -30.3
        -6
 (24 rows)
 
@@ -197,28 +197,28 @@ SELECT '' AS Five, NULLIF(a.i,b.i) AS "NULLIF(a.i,b.i)",
  five | NULLIF(a.i,b.i) | NULLIF(b.i,4) 
 ------+-----------------+---------------
       |                 |             1
+      |               2 |             1
+      |               3 |             1
+      |               4 |             1
       |               1 |             2
+      |                 |             2
+      |               3 |             2
+      |               4 |             2
       |               1 |             3
-      |               1 |             2
-      |                 |             1
-      |               1 |              
-      |               2 |             1
-      |                 |             2
       |               2 |             3
-      |                 |             2
-      |               2 |             1
-      |               2 |              
-      |               3 |             1
-      |               3 |             2
       |                 |             3
-      |               3 |             2
-      |               3 |             1
-      |               3 |              
-      |               4 |             1
-      |               4 |             2
       |               4 |             3
+      |               1 |             2
+      |                 |             2
+      |               3 |             2
       |               4 |             2
+      |                 |             1
+      |               2 |             1
+      |               3 |             1
       |               4 |             1
+      |               1 |              
+      |               2 |              
+      |               3 |              
       |               4 |              
 (24 rows)
 
diff --git a/src/test/regress/expected/inherit.out b/src/test/regress/expected/inherit.out
index e1205a9b00..a04da28e16 100644
--- a/src/test/regress/expected/inherit.out
+++ b/src/test/regress/expected/inherit.out
@@ -561,13 +561,13 @@ SELECT relname, bar.* FROM bar, pg_class where bar.tableoid = pg_class.oid;
  relname | f1 | f2  
 ---------+----+-----
  bar     |  4 |   4
- bar     |  1 | 101
- bar     |  2 | 102
  bar     |  3 | 103
+ bar     |  2 | 102
+ bar     |  1 | 101
  bar2    |  4 |   4
- bar2    |  1 | 101
- bar2    |  2 | 102
  bar2    |  3 | 103
+ bar2    |  2 | 102
+ bar2    |  1 | 101
 (8 rows)
 
 /* Test inheritance of structure (LIKE) */
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 471e149b8c..ec708f7766 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -214,13 +214,13 @@ SELECT '' AS "xxx", t1.a, t2.e
   WHERE t1.a = t2.d;
  xxx | a | e  
 -----+---+----
-     | 0 |   
      | 1 | -1
      | 2 |  2
-     | 2 |  4
      | 3 | -3
+     | 2 |  4
      | 5 | -5
      | 5 | -5
+     | 0 |   
 (7 rows)
 
 --
@@ -660,895 +660,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 1 | -1
-     | 2 | 3 | two   | 1 | -1 | 1 | -1
-     | 3 | 2 | three | 1 | -1 | 1 | -1
-     | 4 | 1 | four  | 1 | -1 | 1 | -1
-     | 5 | 0 | five  | 1 | -1 | 1 | -1
-     | 6 | 6 | six   | 1 | -1 | 1 | -1
-     | 7 | 7 | seven | 1 | -1 | 1 | -1
-     | 8 | 8 | eight | 1 | -1 | 1 | -1
-     | 0 |   | zero  | 1 | -1 | 1 | -1
-     |   |   | null  | 1 | -1 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 2 |  2 | 1 | -1
-     | 3 | 2 | three | 2 |  2 | 1 | -1
-     | 4 | 1 | four  | 2 |  2 | 1 | -1
-     | 5 | 0 | five  | 2 |  2 | 1 | -1
-     | 6 | 6 | six   | 2 |  2 | 1 | -1
-     | 7 | 7 | seven | 2 |  2 | 1 | -1
-     | 8 | 8 | eight | 2 |  2 | 1 | -1
-     | 0 |   | zero  | 2 |  2 | 1 | -1
-     |   |   | null  | 2 |  2 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 3 | -3 | 1 | -1
-     | 3 | 2 | three | 3 | -3 | 1 | -1
-     | 4 | 1 | four  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 8 | 8 | eight | 3 | -3 | 1 | -1
-     | 0 |   | zero  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 6 | 6 | six   | 2 |  4 | 1 | -1
-     | 7 | 7 | seven | 2 |  4 | 1 | -1
-     | 8 | 8 | eight | 2 |  4 | 1 | -1
-     | 0 |   | zero  | 2 |  4 | 1 | -1
-     |   |   | null  | 2 |  4 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 0 |    | 1 | -1
-     | 3 | 2 | three | 0 |    | 1 | -1
-     | 4 | 1 | four  | 0 |    | 1 | -1
-     | 5 | 0 | five  | 0 |    | 1 | -1
-     | 6 | 6 | six   | 0 |    | 1 | -1
-     | 7 | 7 | seven | 0 |    | 1 | -1
-     | 8 | 8 | eight | 0 |    | 1 | -1
-     | 0 |   | zero  | 0 |    | 1 | -1
-     |   |   | null  | 0 |    | 1 | -1
-     |   | 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
-     | 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   |   |    | 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
-     | 2 | 3 | two   |   |  0 | 1 | -1
-     | 3 | 2 | three |   |  0 | 1 | -1
-     | 4 | 1 | four  |   |  0 | 1 | -1
-     | 5 | 0 | five  |   |  0 | 1 | -1
-     | 6 | 6 | six   |   |  0 | 1 | -1
-     | 7 | 7 | seven |   |  0 | 1 | -1
-     | 8 | 8 | eight |   |  0 | 1 | -1
-     | 0 |   | zero  |   |  0 | 1 | -1
-     |   |   | null  |   |  0 | 1 | -1
-     |   | 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
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      | 2 | 3 | two   |   |  0 |   |  0
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      | 3 | 2 | three |   |  0 |   |  0
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      | 6 | 6 | six   |   |  0 |   |  0
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      | 7 | 7 | seven |   |  0 |   |  0
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      | 8 | 8 | eight |   |  0 |   |  0
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+     |   | 0 | zero  | 2 |  4 | 5 | -5
+     |   | 0 | zero  | 2 |  4 | 0 |   
+     |   | 0 | zero  | 2 |  4 |   |   
+     |   | 0 | zero  | 2 |  4 |   |  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
+     |   | 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
+     |   | 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
+     |   | 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
+     |   | 0 | zero  |   |  0 | 1 | -1
+     |   | 0 | zero  |   |  0 | 2 |  2
+     |   | 0 | zero  |   |  0 | 3 | -3
+     |   | 0 | zero  |   |  0 | 2 |  4
+     |   | 0 | zero  |   |  0 | 5 | -5
+     |   | 0 | zero  |   |  0 | 5 | -5
+     |   | 0 | zero  |   |  0 | 0 |   
+     |   | 0 | zero  |   |  0 |   |   
      |   | 0 | zero  |   |  0 |   |  0
 (891 rows)
 
@@ -1567,13 +1567,13 @@ SELECT '' AS "xxx", *
   FROM J1_TBL INNER JOIN J2_TBL USING (i);
  xxx | i | j |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
      | 2 | 3 | two   |  4
+     | 2 | 3 | two   |  2
      | 3 | 2 | three | -3
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
 (7 rows)
 
 -- Same as above, slightly different syntax
@@ -1581,13 +1581,13 @@ SELECT '' AS "xxx", *
   FROM J1_TBL JOIN J2_TBL USING (i);
  xxx | i | j |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
      | 2 | 3 | two   |  4
+     | 2 | 3 | two   |  2
      | 3 | 2 | three | -3
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
 (7 rows)
 
 SELECT '' AS "xxx", *
@@ -1623,35 +1623,35 @@ SELECT '' AS "xxx", *
   FROM J1_TBL NATURAL JOIN J2_TBL;
  xxx | i | j |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
      | 2 | 3 | two   |  4
+     | 2 | 3 | two   |  2
      | 3 | 2 | three | -3
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
 (7 rows)
 
 SELECT '' AS "xxx", *
   FROM J1_TBL t1 (a, b, c) NATURAL JOIN J2_TBL t2 (a, d);
  xxx | a | b |   c   | d  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
      | 2 | 3 | two   |  4
+     | 2 | 3 | two   |  2
      | 3 | 2 | three | -3
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
 (7 rows)
 
 SELECT '' AS "xxx", *
   FROM J1_TBL t1 (a, b, c) NATURAL JOIN J2_TBL t2 (d, a);
  xxx | a | b |  c   | d 
 -----+---+---+------+---
-     | 0 |   | zero |  
      | 2 | 3 | two  | 2
      | 4 | 1 | four | 2
+     | 0 |   | zero |  
 (3 rows)
 
 -- mismatch number of columns
@@ -1660,13 +1660,13 @@ SELECT '' AS "xxx", *
   FROM J1_TBL t1 (a, b) NATURAL JOIN J2_TBL t2 (a);
  xxx | a | b |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
      | 2 | 3 | two   |  4
+     | 2 | 3 | two   |  2
      | 3 | 2 | three | -3
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
 (7 rows)
 
 --
@@ -1676,22 +1676,22 @@ SELECT '' AS "xxx", *
   FROM J1_TBL JOIN J2_TBL ON (J1_TBL.i = J2_TBL.i);
  xxx | i | j |   t   | i | k  
 -----+---+---+-------+---+----
-     | 0 |   | zero  | 0 |   
      | 1 | 4 | one   | 1 | -1
-     | 2 | 3 | two   | 2 |  2
      | 2 | 3 | two   | 2 |  4
+     | 2 | 3 | two   | 2 |  2
      | 3 | 2 | three | 3 | -3
      | 5 | 0 | five  | 5 | -5
      | 5 | 0 | five  | 5 | -5
+     | 0 |   | zero  | 0 |   
 (7 rows)
 
 SELECT '' AS "xxx", *
   FROM J1_TBL JOIN J2_TBL ON (J1_TBL.i = J2_TBL.k);
  xxx | i | j |  t   | i | k 
 -----+---+---+------+---+---
-     | 0 |   | zero |   | 0
      | 2 | 3 | two  | 2 | 2
      | 4 | 1 | four | 2 | 4
+     | 0 |   | zero |   | 0
 (3 rows)
 
 --
@@ -1760,13 +1760,13 @@ SELECT '' AS "xxx", *
   FROM J1_TBL RIGHT OUTER JOIN J2_TBL USING (i);
  xxx | i | j |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
      | 2 | 3 | two   |  2
-     | 2 | 3 | two   |  4
      | 3 | 2 | three | -3
+     | 2 | 3 | two   |  4
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
      |   |   |       |   
      |   |   |       |  0
 (9 rows)
@@ -1775,13 +1775,13 @@ SELECT '' AS "xxx", *
   FROM J1_TBL RIGHT JOIN J2_TBL USING (i);
  xxx | i | j |   t   | k  
 -----+---+---+-------+----
-     | 0 |   | zero  |   
      | 1 | 4 | one   | -1
      | 2 | 3 | two   |  2
-     | 2 | 3 | two   |  4
      | 3 | 2 | three | -3
+     | 2 | 3 | two   |  4
      | 5 | 0 | five  | -5
      | 5 | 0 | five  | -5
+     | 0 |   | zero  |   
      |   |   |       |   
      |   |   |       |  0
 (9 rows)
diff --git a/src/test/regress/expected/join_1.out b/src/test/regress/expected/join_1.out
deleted file mode 100644
index 27c7d29dd9..0000000000
--- a/src/test/regress/expected/join_1.out
+++ /dev/null
@@ -1,2149 +0,0 @@
---
--- JOIN
--- Test JOIN clauses
---
-CREATE TABLE J1_TBL (
-  i integer,
-  j integer,
-  t text
-);
-CREATE TABLE J2_TBL (
-  i integer,
-  k integer
-);
-INSERT INTO J1_TBL VALUES (1, 4, 'one');
-INSERT INTO J1_TBL VALUES (2, 3, 'two');
-INSERT INTO J1_TBL VALUES (3, 2, 'three');
-INSERT INTO J1_TBL VALUES (4, 1, 'four');
-INSERT INTO J1_TBL VALUES (5, 0, 'five');
-INSERT INTO J1_TBL VALUES (6, 6, 'six');
-INSERT INTO J1_TBL VALUES (7, 7, 'seven');
-INSERT INTO J1_TBL VALUES (8, 8, 'eight');
-INSERT INTO J1_TBL VALUES (0, NULL, 'zero');
-INSERT INTO J1_TBL VALUES (NULL, NULL, 'null');
-INSERT INTO J1_TBL VALUES (NULL, 0, 'zero');
-INSERT INTO J2_TBL VALUES (1, -1);
-INSERT INTO J2_TBL VALUES (2, 2);
-INSERT INTO J2_TBL VALUES (3, -3);
-INSERT INTO J2_TBL VALUES (2, 4);
-INSERT INTO J2_TBL VALUES (5, -5);
-INSERT INTO J2_TBL VALUES (5, -5);
-INSERT INTO J2_TBL VALUES (0, NULL);
-INSERT INTO J2_TBL VALUES (NULL, NULL);
-INSERT INTO J2_TBL VALUES (NULL, 0);
---
--- CORRELATION NAMES
--- Make sure that table/column aliases are supported
--- before diving into more complex join syntax.
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL AS tx;
- xxx | i | j |   t   
------+---+---+-------
-     | 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
-(11 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL tx;
- xxx | i | j |   t   
------+---+---+-------
-     | 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
-(11 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL AS t1 (a, b, c);
- xxx | a | b |   c   
------+---+---+-------
-     | 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
-(11 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c);
- xxx | a | b |   c   
------+---+---+-------
-     | 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
-(11 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c), J2_TBL t2 (d, e);
- xxx | a | b |   c   | d | e  
------+---+---+-------+---+----
-     | 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
-     |   | 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
-(99 rows)
-
-SELECT '' AS "xxx", t1.a, t2.e
-  FROM J1_TBL t1 (a, b, c), J2_TBL t2 (d, e)
-  WHERE t1.a = t2.d;
- xxx | a | e  
------+---+----
-     | 0 |   
-     | 1 | -1
-     | 2 |  4
-     | 2 |  2
-     | 3 | -3
-     | 5 | -5
-     | 5 | -5
-(7 rows)
-
---
--- CROSS JOIN
--- Qualifications are not allowed on cross joins,
--- which degenerate into a standard unqualified inner join.
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL CROSS JOIN J2_TBL;
- xxx | i | j |   t   | i | k  
------+---+---+-------+---+----
-     | 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
-     |   | 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
-(99 rows)
-
--- ambiguous column
-SELECT '' AS "xxx", i, k, t
-  FROM J1_TBL CROSS JOIN J2_TBL;
-ERROR:  column reference "i" is ambiguous
--- resolve previous ambiguity by specifying the table name
-SELECT '' AS "xxx", t1.i, k, t
-  FROM J1_TBL t1 CROSS JOIN J2_TBL t2;
- xxx | i | k  |   t   
------+---+----+-------
-     | 1 | -1 | one
-     | 1 |  2 | one
-     | 1 | -3 | one
-     | 1 |  4 | one
-     | 1 | -5 | one
-     | 1 | -5 | one
-     | 1 |    | one
-     | 1 |    | one
-     | 1 |  0 | one
-     | 2 | -1 | two
-     | 2 |  2 | two
-     | 2 | -3 | two
-     | 2 |  4 | two
-     | 2 | -5 | two
-     | 2 | -5 | two
-     | 2 |    | two
-     | 2 |    | two
-     | 2 |  0 | two
-     | 3 | -1 | three
-     | 3 |  2 | three
-     | 3 | -3 | three
-     | 3 |  4 | three
-     | 3 | -5 | three
-     | 3 | -5 | three
-     | 3 |    | three
-     | 3 |    | three
-     | 3 |  0 | three
-     | 4 | -1 | four
-     | 4 |  2 | four
-     | 4 | -3 | four
-     | 4 |  4 | four
-     | 4 | -5 | four
-     | 4 | -5 | four
-     | 4 |    | four
-     | 4 |    | four
-     | 4 |  0 | four
-     | 5 | -1 | five
-     | 5 |  2 | five
-     | 5 | -3 | five
-     | 5 |  4 | five
-     | 5 | -5 | five
-     | 5 | -5 | five
-     | 5 |    | five
-     | 5 |    | five
-     | 5 |  0 | five
-     | 6 | -1 | six
-     | 6 |  2 | six
-     | 6 | -3 | six
-     | 6 |  4 | six
-     | 6 | -5 | six
-     | 6 | -5 | six
-     | 6 |    | six
-     | 6 |    | six
-     | 6 |  0 | six
-     | 7 | -1 | seven
-     | 7 |  2 | seven
-     | 7 | -3 | seven
-     | 7 |  4 | seven
-     | 7 | -5 | seven
-     | 7 | -5 | seven
-     | 7 |    | seven
-     | 7 |    | seven
-     | 7 |  0 | seven
-     | 8 | -1 | eight
-     | 8 |  2 | eight
-     | 8 | -3 | eight
-     | 8 |  4 | eight
-     | 8 | -5 | eight
-     | 8 | -5 | eight
-     | 8 |    | eight
-     | 8 |    | eight
-     | 8 |  0 | eight
-     | 0 | -1 | zero
-     | 0 |  2 | zero
-     | 0 | -3 | zero
-     | 0 |  4 | zero
-     | 0 | -5 | zero
-     | 0 | -5 | zero
-     | 0 |    | zero
-     | 0 |    | zero
-     | 0 |  0 | zero
-     |   | -1 | null
-     |   |  2 | null
-     |   | -3 | null
-     |   |  4 | null
-     |   | -5 | null
-     |   | -5 | null
-     |   |    | null
-     |   |    | null
-     |   |  0 | null
-     |   | -1 | zero
-     |   |  2 | zero
-     |   | -3 | zero
-     |   |  4 | zero
-     |   | -5 | zero
-     |   | -5 | zero
-     |   |    | zero
-     |   |    | zero
-     |   |  0 | zero
-(99 rows)
-
-SELECT '' AS "xxx", ii, tt, kk
-  FROM (J1_TBL CROSS JOIN J2_TBL)
-    AS tx (ii, jj, tt, ii2, kk);
- xxx | ii |  tt   | kk 
------+----+-------+----
-     |  1 | one   | -1
-     |  1 | one   |  2
-     |  1 | one   | -3
-     |  1 | one   |  4
-     |  1 | one   | -5
-     |  1 | one   | -5
-     |  1 | one   |   
-     |  1 | one   |   
-     |  1 | one   |  0
-     |  2 | two   | -1
-     |  2 | two   |  2
-     |  2 | two   | -3
-     |  2 | two   |  4
-     |  2 | two   | -5
-     |  2 | two   | -5
-     |  2 | two   |   
-     |  2 | two   |   
-     |  2 | two   |  0
-     |  3 | three | -1
-     |  3 | three |  2
-     |  3 | three | -3
-     |  3 | three |  4
-     |  3 | three | -5
-     |  3 | three | -5
-     |  3 | three |   
-     |  3 | three |   
-     |  3 | three |  0
-     |  4 | four  | -1
-     |  4 | four  |  2
-     |  4 | four  | -3
-     |  4 | four  |  4
-     |  4 | four  | -5
-     |  4 | four  | -5
-     |  4 | four  |   
-     |  4 | four  |   
-     |  4 | four  |  0
-     |  5 | five  | -1
-     |  5 | five  |  2
-     |  5 | five  | -3
-     |  5 | five  |  4
-     |  5 | five  | -5
-     |  5 | five  | -5
-     |  5 | five  |   
-     |  5 | five  |   
-     |  5 | five  |  0
-     |  6 | six   | -1
-     |  6 | six   |  2
-     |  6 | six   | -3
-     |  6 | six   |  4
-     |  6 | six   | -5
-     |  6 | six   | -5
-     |  6 | six   |   
-     |  6 | six   |   
-     |  6 | six   |  0
-     |  7 | seven | -1
-     |  7 | seven |  2
-     |  7 | seven | -3
-     |  7 | seven |  4
-     |  7 | seven | -5
-     |  7 | seven | -5
-     |  7 | seven |   
-     |  7 | seven |   
-     |  7 | seven |  0
-     |  8 | eight | -1
-     |  8 | eight |  2
-     |  8 | eight | -3
-     |  8 | eight |  4
-     |  8 | eight | -5
-     |  8 | eight | -5
-     |  8 | eight |   
-     |  8 | eight |   
-     |  8 | eight |  0
-     |  0 | zero  | -1
-     |  0 | zero  |  2
-     |  0 | zero  | -3
-     |  0 | zero  |  4
-     |  0 | zero  | -5
-     |  0 | zero  | -5
-     |  0 | zero  |   
-     |  0 | zero  |   
-     |  0 | zero  |  0
-     |    | null  | -1
-     |    | null  |  2
-     |    | null  | -3
-     |    | null  |  4
-     |    | null  | -5
-     |    | null  | -5
-     |    | null  |   
-     |    | null  |   
-     |    | null  |  0
-     |    | zero  | -1
-     |    | zero  |  2
-     |    | zero  | -3
-     |    | zero  |  4
-     |    | zero  | -5
-     |    | zero  | -5
-     |    | zero  |   
-     |    | zero  |   
-     |    | zero  |  0
-(99 rows)
-
-SELECT '' AS "xxx", tx.ii, tx.jj, tx.kk
-  FROM (J1_TBL t1 (a, b, c) CROSS JOIN J2_TBL t2 (d, e))
-    AS tx (ii, jj, tt, ii2, kk);
- xxx | ii | jj | kk 
------+----+----+----
-     |  1 |  4 | -1
-     |  1 |  4 |  2
-     |  1 |  4 | -3
-     |  1 |  4 |  4
-     |  1 |  4 | -5
-     |  1 |  4 | -5
-     |  1 |  4 |   
-     |  1 |  4 |   
-     |  1 |  4 |  0
-     |  2 |  3 | -1
-     |  2 |  3 |  2
-     |  2 |  3 | -3
-     |  2 |  3 |  4
-     |  2 |  3 | -5
-     |  2 |  3 | -5
-     |  2 |  3 |   
-     |  2 |  3 |   
-     |  2 |  3 |  0
-     |  3 |  2 | -1
-     |  3 |  2 |  2
-     |  3 |  2 | -3
-     |  3 |  2 |  4
-     |  3 |  2 | -5
-     |  3 |  2 | -5
-     |  3 |  2 |   
-     |  3 |  2 |   
-     |  3 |  2 |  0
-     |  4 |  1 | -1
-     |  4 |  1 |  2
-     |  4 |  1 | -3
-     |  4 |  1 |  4
-     |  4 |  1 | -5
-     |  4 |  1 | -5
-     |  4 |  1 |   
-     |  4 |  1 |   
-     |  4 |  1 |  0
-     |  5 |  0 | -1
-     |  5 |  0 |  2
-     |  5 |  0 | -3
-     |  5 |  0 |  4
-     |  5 |  0 | -5
-     |  5 |  0 | -5
-     |  5 |  0 |   
-     |  5 |  0 |   
-     |  5 |  0 |  0
-     |  6 |  6 | -1
-     |  6 |  6 |  2
-     |  6 |  6 | -3
-     |  6 |  6 |  4
-     |  6 |  6 | -5
-     |  6 |  6 | -5
-     |  6 |  6 |   
-     |  6 |  6 |   
-     |  6 |  6 |  0
-     |  7 |  7 | -1
-     |  7 |  7 |  2
-     |  7 |  7 | -3
-     |  7 |  7 |  4
-     |  7 |  7 | -5
-     |  7 |  7 | -5
-     |  7 |  7 |   
-     |  7 |  7 |   
-     |  7 |  7 |  0
-     |  8 |  8 | -1
-     |  8 |  8 |  2
-     |  8 |  8 | -3
-     |  8 |  8 |  4
-     |  8 |  8 | -5
-     |  8 |  8 | -5
-     |  8 |  8 |   
-     |  8 |  8 |   
-     |  8 |  8 |  0
-     |  0 |    | -1
-     |  0 |    |  2
-     |  0 |    | -3
-     |  0 |    |  4
-     |  0 |    | -5
-     |  0 |    | -5
-     |  0 |    |   
-     |  0 |    |   
-     |  0 |    |  0
-     |    |    | -1
-     |    |    |  2
-     |    |    | -3
-     |    |    |  4
-     |    |    | -5
-     |    |    | -5
-     |    |    |   
-     |    |    |   
-     |    |    |  0
-     |    |  0 | -1
-     |    |  0 |  2
-     |    |  0 | -3
-     |    |  0 |  4
-     |    |  0 | -5
-     |    |  0 | -5
-     |    |  0 |   
-     |    |  0 |   
-     |    |  0 |  0
-(99 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL CROSS JOIN J2_TBL a CROSS JOIN J2_TBL b;
- xxx | i | j |   t   | i | k  | i | k  
------+---+---+-------+---+----+---+----
-     | 1 | 4 | one   | 1 | -1 | 1 | -1
-     | 2 | 3 | two   | 1 | -1 | 1 | -1
-     | 3 | 2 | three | 1 | -1 | 1 | -1
-     | 4 | 1 | four  | 1 | -1 | 1 | -1
-     | 5 | 0 | five  | 1 | -1 | 1 | -1
-     | 6 | 6 | six   | 1 | -1 | 1 | -1
-     | 7 | 7 | seven | 1 | -1 | 1 | -1
-     | 8 | 8 | eight | 1 | -1 | 1 | -1
-     | 0 |   | zero  | 1 | -1 | 1 | -1
-     |   |   | null  | 1 | -1 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 2 |  2 | 1 | -1
-     | 3 | 2 | three | 2 |  2 | 1 | -1
-     | 4 | 1 | four  | 2 |  2 | 1 | -1
-     | 5 | 0 | five  | 2 |  2 | 1 | -1
-     | 6 | 6 | six   | 2 |  2 | 1 | -1
-     | 7 | 7 | seven | 2 |  2 | 1 | -1
-     | 8 | 8 | eight | 2 |  2 | 1 | -1
-     | 0 |   | zero  | 2 |  2 | 1 | -1
-     |   |   | null  | 2 |  2 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 3 | -3 | 1 | -1
-     | 3 | 2 | three | 3 | -3 | 1 | -1
-     | 4 | 1 | four  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 8 | 8 | eight | 3 | -3 | 1 | -1
-     | 0 |   | zero  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 6 | 6 | six   | 2 |  4 | 1 | -1
-     | 7 | 7 | seven | 2 |  4 | 1 | -1
-     | 8 | 8 | eight | 2 |  4 | 1 | -1
-     | 0 |   | zero  | 2 |  4 | 1 | -1
-     |   |   | null  | 2 |  4 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 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
-     | 2 | 3 | two   | 0 |    | 1 | -1
-     | 3 | 2 | three | 0 |    | 1 | -1
-     | 4 | 1 | four  | 0 |    | 1 | -1
-     | 5 | 0 | five  | 0 |    | 1 | -1
-     | 6 | 6 | six   | 0 |    | 1 | -1
-     | 7 | 7 | seven | 0 |    | 1 | -1
-     | 8 | 8 | eight | 0 |    | 1 | -1
-     | 0 |   | zero  | 0 |    | 1 | -1
-     |   |   | null  | 0 |    | 1 | -1
-     |   | 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
-     | 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   |   |    | 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
-     | 2 | 3 | two   |   |  0 | 1 | -1
-     | 3 | 2 | three |   |  0 | 1 | -1
-     | 4 | 1 | four  |   |  0 | 1 | -1
-     | 5 | 0 | five  |   |  0 | 1 | -1
-     | 6 | 6 | six   |   |  0 | 1 | -1
-     | 7 | 7 | seven |   |  0 | 1 | -1
-     | 8 | 8 | eight |   |  0 | 1 | -1
-     | 0 |   | zero  |   |  0 | 1 | -1
-     |   |   | null  |   |  0 | 1 | -1
-     |   | 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)
-
---
---
--- Inner joins (equi-joins)
---
---
---
--- Inner joins (equi-joins) with USING clause
--- The USING syntax changes the shape of the resulting table
--- by including a column in the USING clause only once in the result.
---
--- Inner equi-join on specified column
-SELECT '' AS "xxx", *
-  FROM J1_TBL INNER JOIN J2_TBL USING (i);
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
--- Same as above, slightly different syntax
-SELECT '' AS "xxx", *
-  FROM J1_TBL JOIN J2_TBL USING (i);
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c) JOIN J2_TBL t2 (a, d) USING (a)
-  ORDER BY a, d;
- xxx | a | b |   c   | d  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
-     | 2 | 3 | two   |  4
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c) JOIN J2_TBL t2 (a, b) USING (b)
-  ORDER BY b, t1.a;
- xxx | b | a |   c   | a 
------+---+---+-------+---
-     | 0 | 5 | five  |  
-     | 0 |   | zero  |  
-     | 2 | 3 | three | 2
-     | 4 | 1 | one   | 2
-(4 rows)
-
---
--- NATURAL JOIN
--- Inner equi-join on all columns with the same name
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL NATURAL JOIN J2_TBL;
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c) NATURAL JOIN J2_TBL t2 (a, d);
- xxx | a | b |   c   | d  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b, c) NATURAL JOIN J2_TBL t2 (d, a);
- xxx | a | b |  c   | d 
------+---+---+------+---
-     | 0 |   | zero |  
-     | 2 | 3 | two  | 2
-     | 4 | 1 | four | 2
-(3 rows)
-
--- mismatch number of columns
--- currently, Postgres will fill in with underlying names
-SELECT '' AS "xxx", *
-  FROM J1_TBL t1 (a, b) NATURAL JOIN J2_TBL t2 (a);
- xxx | a | b |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-(7 rows)
-
---
--- Inner joins (equi-joins)
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL JOIN J2_TBL ON (J1_TBL.i = J2_TBL.i);
- xxx | i | j |   t   | i | k  
------+---+---+-------+---+----
-     | 0 |   | zero  | 0 |   
-     | 1 | 4 | one   | 1 | -1
-     | 2 | 3 | two   | 2 |  4
-     | 2 | 3 | two   | 2 |  2
-     | 3 | 2 | three | 3 | -3
-     | 5 | 0 | five  | 5 | -5
-     | 5 | 0 | five  | 5 | -5
-(7 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL JOIN J2_TBL ON (J1_TBL.i = J2_TBL.k);
- xxx | i | j |  t   | i | k 
------+---+---+------+---+---
-     | 0 |   | zero |   | 0
-     | 2 | 3 | two  | 2 | 2
-     | 4 | 1 | four | 2 | 4
-(3 rows)
-
---
--- Non-equi-joins
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL JOIN J2_TBL ON (J1_TBL.i <= J2_TBL.k);
- xxx | i | j |   t   | i | k 
------+---+---+-------+---+---
-     | 1 | 4 | one   | 2 | 2
-     | 1 | 4 | one   | 2 | 4
-     | 2 | 3 | two   | 2 | 2
-     | 2 | 3 | two   | 2 | 4
-     | 3 | 2 | three | 2 | 4
-     | 4 | 1 | four  | 2 | 4
-     | 0 |   | zero  | 2 | 2
-     | 0 |   | zero  | 2 | 4
-     | 0 |   | zero  |   | 0
-(9 rows)
-
---
--- Outer joins
--- Note that OUTER is a noise word
---
-SELECT '' AS "xxx", *
-  FROM J1_TBL LEFT OUTER JOIN J2_TBL USING (i)
-  ORDER BY i;
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 4 | 1 | four  |   
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     | 6 | 6 | six   |   
-     | 7 | 7 | seven |   
-     | 8 | 8 | eight |   
-     |   | 0 | zero  |   
-     |   |   | null  |   
-(13 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL LEFT JOIN J2_TBL USING (i)
-  ORDER BY i;
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 4 | 1 | four  |   
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     | 6 | 6 | six   |   
-     | 7 | 7 | seven |   
-     | 8 | 8 | eight |   
-     |   | 0 | zero  |   
-     |   |   | null  |   
-(13 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL RIGHT OUTER JOIN J2_TBL USING (i);
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     |   |   |       |  0
-     |   |   |       |   
-(9 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL RIGHT JOIN J2_TBL USING (i);
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  4
-     | 2 | 3 | two   |  2
-     | 3 | 2 | three | -3
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     |   |   |       |  0
-     |   |   |       |   
-(9 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL FULL OUTER JOIN J2_TBL USING (i)
-  ORDER BY i, t;
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
-     | 2 | 3 | two   |  4
-     | 3 | 2 | three | -3
-     | 4 | 1 | four  |   
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     | 6 | 6 | six   |   
-     | 7 | 7 | seven |   
-     | 8 | 8 | eight |   
-     |   |   | null  |   
-     |   | 0 | zero  |   
-     |   |   |       |   
-     |   |   |       |  0
-(15 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL FULL JOIN J2_TBL USING (i)
-  ORDER BY i, t;
- xxx | i | j |   t   | k  
------+---+---+-------+----
-     | 0 |   | zero  |   
-     | 1 | 4 | one   | -1
-     | 2 | 3 | two   |  2
-     | 2 | 3 | two   |  4
-     | 3 | 2 | three | -3
-     | 4 | 1 | four  |   
-     | 5 | 0 | five  | -5
-     | 5 | 0 | five  | -5
-     | 6 | 6 | six   |   
-     | 7 | 7 | seven |   
-     | 8 | 8 | eight |   
-     |   |   | null  |   
-     |   | 0 | zero  |   
-     |   |   |       |   
-     |   |   |       |  0
-(15 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL LEFT JOIN J2_TBL USING (i) WHERE (k = 1);
- xxx | i | j | t | k 
------+---+---+---+---
-(0 rows)
-
-SELECT '' AS "xxx", *
-  FROM J1_TBL LEFT JOIN J2_TBL USING (i) WHERE (i = 1);
- xxx | i | j |  t  | k  
------+---+---+-----+----
-     | 1 | 4 | one | -1
-(1 row)
-
---
--- More complicated constructs
---
--- UNION JOIN isn't implemented yet
-SELECT '' AS "xxx", *
-  FROM J1_TBL UNION JOIN J2_TBL;
-ERROR:  UNION JOIN is not implemented
---
--- Multiway full join
---
-CREATE TABLE t1 (name TEXT, n INTEGER);
-CREATE TABLE t2 (name TEXT, n INTEGER);
-CREATE TABLE t3 (name TEXT, n INTEGER);
-INSERT INTO t1 VALUES ( 'aa', 11 );
-INSERT INTO t2 VALUES ( 'aa', 12 );
-INSERT INTO t2 VALUES ( 'bb', 22 );
-INSERT INTO t2 VALUES ( 'dd', 42 );
-INSERT INTO t3 VALUES ( 'aa', 13 );
-INSERT INTO t3 VALUES ( 'bb', 23 );
-INSERT INTO t3 VALUES ( 'cc', 33 );
-SELECT * FROM t1 FULL JOIN t2 USING (name) FULL JOIN t3 USING (name);
- name | n  | n  | n  
-------+----+----+----
- aa   | 11 | 12 | 13
- bb   |    | 22 | 23
- cc   |    |    | 33
- dd   |    | 42 |   
-(4 rows)
-
---
--- Test interactions of join syntax and subqueries
---
--- Basic cases (we expect planner to pull up the subquery here)
-SELECT * FROM
-(SELECT * FROM t2) as s2
-INNER JOIN
-(SELECT * FROM t3) s3
-USING (name);
- name | n  | n  
-------+----+----
- aa   | 12 | 13
- bb   | 22 | 23
-(2 rows)
-
-SELECT * FROM
-(SELECT * FROM t2) as s2
-LEFT JOIN
-(SELECT * FROM t3) s3
-USING (name);
- name | n  | n  
-------+----+----
- aa   | 12 | 13
- bb   | 22 | 23
- dd   | 42 |   
-(3 rows)
-
-SELECT * FROM
-(SELECT * FROM t2) as s2
-FULL JOIN
-(SELECT * FROM t3) s3
-USING (name);
- name | n  | n  
-------+----+----
- aa   | 12 | 13
- bb   | 22 | 23
- cc   |    | 33
- dd   | 42 |   
-(4 rows)
-
--- Cases with non-nullable expressions in subquery results;
--- make sure these go to null as expected
-SELECT * FROM
-(SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-NATURAL INNER JOIN
-(SELECT name, n as s3_n, 3 as s3_2 FROM t3) s3;
- name | s2_n | s2_2 | s3_n | s3_2 
-------+------+------+------+------
- aa   |   12 |    2 |   13 |    3
- bb   |   22 |    2 |   23 |    3
-(2 rows)
-
-SELECT * FROM
-(SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-NATURAL LEFT JOIN
-(SELECT name, n as s3_n, 3 as s3_2 FROM t3) s3;
- name | s2_n | s2_2 | s3_n | s3_2 
-------+------+------+------+------
- aa   |   12 |    2 |   13 |    3
- bb   |   22 |    2 |   23 |    3
- dd   |   42 |    2 |      |     
-(3 rows)
-
-SELECT * FROM
-(SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-NATURAL FULL JOIN
-(SELECT name, n as s3_n, 3 as s3_2 FROM t3) s3;
- name | s2_n | s2_2 | s3_n | s3_2 
-------+------+------+------+------
- aa   |   12 |    2 |   13 |    3
- bb   |   22 |    2 |   23 |    3
- cc   |      |      |   33 |    3
- dd   |   42 |    2 |      |     
-(4 rows)
-
-SELECT * FROM
-(SELECT name, n as s1_n, 1 as s1_1 FROM t1) as s1
-NATURAL INNER JOIN
-(SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-NATURAL INNER JOIN
-(SELECT name, n as s3_n, 3 as s3_2 FROM t3) s3;
- name | s1_n | s1_1 | s2_n | s2_2 | s3_n | s3_2 
-------+------+------+------+------+------+------
- aa   |   11 |    1 |   12 |    2 |   13 |    3
-(1 row)
-
-SELECT * FROM
-(SELECT name, n as s1_n, 1 as s1_1 FROM t1) as s1
-NATURAL FULL JOIN
-(SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-NATURAL FULL JOIN
-(SELECT name, n as s3_n, 3 as s3_2 FROM t3) s3;
- name | s1_n | s1_1 | s2_n | s2_2 | s3_n | s3_2 
-------+------+------+------+------+------+------
- aa   |   11 |    1 |   12 |    2 |   13 |    3
- bb   |      |      |   22 |    2 |   23 |    3
- cc   |      |      |      |      |   33 |    3
- dd   |      |      |   42 |    2 |      |     
-(4 rows)
-
-SELECT * FROM
-(SELECT name, n as s1_n FROM t1) as s1
-NATURAL FULL JOIN
-  (SELECT * FROM
-    (SELECT name, n as s2_n FROM t2) as s2
-    NATURAL FULL JOIN
-    (SELECT name, n as s3_n FROM t3) as s3
-  ) ss2;
- name | s1_n | s2_n | s3_n 
-------+------+------+------
- aa   |   11 |   12 |   13
- bb   |      |   22 |   23
- cc   |      |      |   33
- dd   |      |   42 |     
-(4 rows)
-
-SELECT * FROM
-(SELECT name, n as s1_n FROM t1) as s1
-NATURAL FULL JOIN
-  (SELECT * FROM
-    (SELECT name, n as s2_n, 2 as s2_2 FROM t2) as s2
-    NATURAL FULL JOIN
-    (SELECT name, n as s3_n FROM t3) as s3
-  ) ss2;
- name | s1_n | s2_n | s2_2 | s3_n 
-------+------+------+------+------
- aa   |   11 |   12 |    2 |   13
- bb   |      |   22 |    2 |   23
- cc   |      |      |      |   33
- dd   |      |   42 |    2 |     
-(4 rows)
-
--- Test for propagation of nullability constraints into sub-joins
-create temp table x (x1 int, x2 int);
-insert into x values (1,11);
-insert into x values (2,22);
-insert into x values (3,null);
-insert into x values (4,44);
-insert into x values (5,null);
-create temp table y (y1 int, y2 int);
-insert into y values (1,111);
-insert into y values (2,222);
-insert into y values (3,333);
-insert into y values (4,null);
-select * from x;
- x1 | x2 
-----+----
-  1 | 11
-  2 | 22
-  3 |   
-  4 | 44
-  5 |   
-(5 rows)
-
-select * from y;
- y1 | y2  
-----+-----
-  1 | 111
-  2 | 222
-  3 | 333
-  4 |    
-(4 rows)
-
-select * from x left join y on (x1 = y1 and x2 is not null);
- x1 | x2 | y1 | y2  
-----+----+----+-----
-  1 | 11 |  1 | 111
-  2 | 22 |  2 | 222
-  3 |    |    |    
-  4 | 44 |  4 |    
-  5 |    |    |    
-(5 rows)
-
-select * from x left join y on (x1 = y1 and y2 is not null);
- x1 | x2 | y1 | y2  
-----+----+----+-----
-  1 | 11 |  1 | 111
-  2 | 22 |  2 | 222
-  3 |    |  3 | 333
-  4 | 44 |    |    
-  5 |    |    |    
-(5 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  3 |    |  3 | 333 |   3 |    
-  4 | 44 |  4 |     |   4 |  44
-  5 |    |    |     |   5 |    
-(5 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1 and x2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  3 |    |  3 | 333 |     |    
-  4 | 44 |  4 |     |   4 |  44
-  5 |    |    |     |     |    
-(5 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1 and y2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  3 |    |  3 | 333 |   3 |    
-  4 | 44 |  4 |     |     |    
-  5 |    |    |     |     |    
-(5 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1 and xx2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  3 |    |  3 | 333 |     |    
-  4 | 44 |  4 |     |   4 |  44
-  5 |    |    |     |     |    
-(5 rows)
-
--- these should NOT give the same answers as above
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1) where (x2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  4 | 44 |  4 |     |   4 |  44
-(3 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1) where (y2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  3 |    |  3 | 333 |   3 |    
-(3 rows)
-
-select * from (x left join y on (x1 = y1)) left join x xx(xx1,xx2)
-on (x1 = xx1) where (xx2 is not null);
- x1 | x2 | y1 | y2  | xx1 | xx2 
-----+----+----+-----+-----+-----
-  1 | 11 |  1 | 111 |   1 |  11
-  2 | 22 |  2 | 222 |   2 |  22
-  4 | 44 |  4 |     |   4 |  44
-(3 rows)
-
---
--- regression test: check for bug with propagation of implied equality
--- to outside an IN
---
-select count(*) from tenk1 a where unique1 in
-  (select unique1 from tenk1 b join tenk1 c using (unique1)
-   where b.unique2 = 42);
- count 
--------
-     1
-(1 row)
-
---
--- Clean up
---
-DROP TABLE t1;
-DROP TABLE t2;
-DROP TABLE t3;
-DROP TABLE J1_TBL;
-DROP TABLE J2_TBL;
diff --git a/src/test/regress/expected/polymorphism.out b/src/test/regress/expected/polymorphism.out
index 55687467a0..23ee8b839e 100644
--- a/src/test/regress/expected/polymorphism.out
+++ b/src/test/regress/expected/polymorphism.out
@@ -349,184 +349,184 @@ insert into t values(3,array[3],'b');
 select f3, myaggp01a(*) from t group by f3;
  f3 | myaggp01a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp03a(*) from t group by f3;
  f3 | myaggp03a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp03b(*) from t group by f3;
  f3 | myaggp03b 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp05a(f1) from t group by f3;
  f3 | myaggp05a 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggp06a(f1) from t group by f3;
  f3 | myaggp06a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp08a(f1) from t group by f3;
  f3 | myaggp08a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp09a(f1) from t group by f3;
  f3 | myaggp09a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp09b(f1) from t group by f3;
  f3 | myaggp09b 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggp10a(f1) from t group by f3;
  f3 | myaggp10a 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggp10b(f1) from t group by f3;
  f3 | myaggp10b 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggp20a(f1) from t group by f3;
  f3 | myaggp20a 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggp20b(f1) from t group by f3;
  f3 | myaggp20b 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggn01a(*) from t group by f3;
  f3 | myaggn01a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn01b(*) from t group by f3;
  f3 | myaggn01b 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn03a(*) from t group by f3;
  f3 | myaggn03a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn05a(f1) from t group by f3;
  f3 | myaggn05a 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggn05b(f1) from t group by f3;
  f3 | myaggn05b 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)
 
 select f3, myaggn06a(f1) from t group by f3;
  f3 | myaggn06a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn06b(f1) from t group by f3;
  f3 | myaggn06b 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn08a(f1) from t group by f3;
  f3 | myaggn08a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn08b(f1) from t group by f3;
  f3 | myaggn08b 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn09a(f1) from t group by f3;
  f3 | myaggn09a 
 ----+-----------
- b  | {}
  c  | {}
  a  | {}
+ b  | {}
 (3 rows)
 
 select f3, myaggn10a(f1) from t group by f3;
  f3 | myaggn10a 
 ----+-----------
- b  | {1,2,3}
  c  | {1,2}
  a  | {1,2,3}
+ b  | {1,2,3}
 (3 rows)