<!--
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">
<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>
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>
<!--
-$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">
<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">
<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>
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
WHERE c.relname = 'customer'
AND c.oid = i.indrelid
AND c2.oid = i.indexrelid
- ORDER BY c2.relname;
+ ORDER BY c2.relname;
relname | relpages
----------------------+----------
<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>
<!--
-$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">
<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>
<!--
-$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">
</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)
* 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 $
*
*-------------------------------------------------------------------------
*/
* Do the physical truncation.
*/
RelationTruncate(rel, new_pages);
+
+ /* update statistics */
+ stats->pages_removed = num_pages - new_pages;
+
num_pages = new_pages;
}
}
*
*
* 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
*/
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;
*
*
* 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
#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"
#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,
/* 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);
*
* 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
* 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
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)
{
*
*
* 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 $
*
*-------------------------------------------------------------------------
*/
/* 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;
/*
*
*
* 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"
/* 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 */
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);
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);
}
tups_vacuumed,
nkeep,
nunused;
+ double *index_tups_vacuumed;
+ BlockNumber *index_pages_removed;
+ bool did_vacuum_index = false;
int i;
VacRUsage ru0;
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;
{
/* 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 */
/* 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? */
{
/* 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++)
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",
* 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;
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",
* 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
/* 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)?
*/
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
*
*
*
* 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 $
*
*-------------------------------------------------------------------------
*/
#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.
* 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)
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.
}
info->relam = indexRelation->rd_rel->relam;
- info->pages = indexRelation->rd_rel->relpages;
- info->tuples = indexRelation->rd_rel->reltuples;
info->amcostestimate = index_cost_estimator(indexRelation);
/*
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;
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
*
*
*
* 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 $
*
*-------------------------------------------------------------------------
*/
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",
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;
}
* 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 $
*
*-------------------------------------------------------------------------
*/
* 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 */
* 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 $
*
*-------------------------------------------------------------------------
*/
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 */
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)
five | NULLIF(a.i,b.i) | NULLIF(b.i,4)
------+-----------------+---------------
| | 1
- | 1 | 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
+ | 1 | 2
+ | | 2
+ | 3 | 2
| 4 | 2
+ | 1 | 3
+ | 2 | 3
+ | | 3
| 4 | 3
+ | 1 | 2
+ | | 2
+ | 3 | 2
| 4 | 2
+ | | 1
+ | 2 | 1
+ | 3 | 1
| 4 | 1
+ | 1 |
+ | 2 |
+ | 3 |
| 4 |
(24 rows)
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) */
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)
--
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 | |
+ | 1 | 4 | one | 3 | -3 | | 0
+ | 1 | 4 | one | 2 | 4 | 1 | -1
+ | 1 | 4 | one | 2 | 4 | 2 | 2
+ | 1 | 4 | one | 2 | 4 | 3 | -3
+ | 1 | 4 | one | 2 | 4 | 2 | 4
+ | 1 | 4 | one | 2 | 4 | 5 | -5
+ | 1 | 4 | one | 2 | 4 | 5 | -5
+ | 1 | 4 | one | 2 | 4 | 0 |
+ | 1 | 4 | one | 2 | 4 | |
+ | 1 | 4 | one | 2 | 4 | | 0
+ | 1 | 4 | one | 5 | -5 | 1 | -1
+ | 1 | 4 | one | 5 | -5 | 2 | 2
+ | 1 | 4 | one | 5 | -5 | 3 | -3
+ | 1 | 4 | one | 5 | -5 | 2 | 4
+ | 1 | 4 | one | 5 | -5 | 5 | -5
+ | 1 | 4 | one | 5 | -5 | 5 | -5
+ | 1 | 4 | one | 5 | -5 | 0 |
+ | 1 | 4 | one | 5 | -5 | |
+ | 1 | 4 | one | 5 | -5 | | 0
+ | 1 | 4 | one | 5 | -5 | 1 | -1
+ | 1 | 4 | one | 5 | -5 | 2 | 2
+ | 1 | 4 | one | 5 | -5 | 3 | -3
+ | 1 | 4 | one | 5 | -5 | 2 | 4
+ | 1 | 4 | one | 5 | -5 | 5 | -5
+ | 1 | 4 | one | 5 | -5 | 5 | -5
+ | 1 | 4 | one | 5 | -5 | 0 |
+ | 1 | 4 | one | 5 | -5 | |
+ | 1 | 4 | one | 5 | -5 | | 0
+ | 1 | 4 | one | 0 | | 1 | -1
+ | 1 | 4 | one | 0 | | 2 | 2
+ | 1 | 4 | one | 0 | | 3 | -3
+ | 1 | 4 | one | 0 | | 2 | 4
+ | 1 | 4 | one | 0 | | 5 | -5
+ | 1 | 4 | one | 0 | | 5 | -5
+ | 1 | 4 | one | 0 | | 0 |
+ | 1 | 4 | one | 0 | | |
+ | 1 | 4 | one | 0 | | | 0
+ | 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
+ | 1 | 4 | one | | 0 | 1 | -1
+ | 1 | 4 | one | | 0 | 2 | 2
+ | 1 | 4 | one | | 0 | 3 | -3
+ | 1 | 4 | one | | 0 | 2 | 4
+ | 1 | 4 | one | | 0 | 5 | -5
+ | 1 | 4 | one | | 0 | 5 | -5
+ | 1 | 4 | one | | 0 | 0 |
+ | 1 | 4 | one | | 0 | |
+ | 1 | 4 | one | | 0 | | 0
+ | 2 | 3 | two | 1 | -1 | 1 | -1
+ | 2 | 3 | two | 1 | -1 | 2 | 2
+ | 2 | 3 | two | 1 | -1 | 3 | -3
+ | 2 | 3 | two | 1 | -1 | 2 | 4
+ | 2 | 3 | two | 1 | -1 | 5 | -5
+ | 2 | 3 | two | 1 | -1 | 5 | -5
+ | 2 | 3 | two | 1 | -1 | 0 |
+ | 2 | 3 | two | 1 | -1 | |
+ | 2 | 3 | two | 1 | -1 | | 0
+ | 2 | 3 | two | 2 | 2 | 1 | -1
+ | 2 | 3 | two | 2 | 2 | 2 | 2
+ | 2 | 3 | two | 2 | 2 | 3 | -3
+ | 2 | 3 | two | 2 | 2 | 2 | 4
+ | 2 | 3 | two | 2 | 2 | 5 | -5
+ | 2 | 3 | two | 2 | 2 | 5 | -5
+ | 2 | 3 | two | 2 | 2 | 0 |
+ | 2 | 3 | two | 2 | 2 | |
+ | 2 | 3 | two | 2 | 2 | | 0
+ | 2 | 3 | two | 3 | -3 | 1 | -1
+ | 2 | 3 | two | 3 | -3 | 2 | 2
+ | 2 | 3 | two | 3 | -3 | 3 | -3
+ | 2 | 3 | two | 3 | -3 | 2 | 4
+ | 2 | 3 | two | 3 | -3 | 5 | -5
+ | 2 | 3 | two | 3 | -3 | 5 | -5
+ | 2 | 3 | two | 3 | -3 | 0 |
+ | 2 | 3 | two | 3 | -3 | |
+ | 2 | 3 | two | 3 | -3 | | 0
+ | 2 | 3 | two | 2 | 4 | 1 | -1
+ | 2 | 3 | two | 2 | 4 | 2 | 2
+ | 2 | 3 | two | 2 | 4 | 3 | -3
+ | 2 | 3 | two | 2 | 4 | 2 | 4
+ | 2 | 3 | two | 2 | 4 | 5 | -5
+ | 2 | 3 | two | 2 | 4 | 5 | -5
+ | 2 | 3 | two | 2 | 4 | 0 |
+ | 2 | 3 | two | 2 | 4 | |
+ | 2 | 3 | two | 2 | 4 | | 0
+ | 2 | 3 | two | 5 | -5 | 1 | -1
+ | 2 | 3 | two | 5 | -5 | 2 | 2
+ | 2 | 3 | two | 5 | -5 | 3 | -3
+ | 2 | 3 | two | 5 | -5 | 2 | 4
+ | 2 | 3 | two | 5 | -5 | 5 | -5
+ | 2 | 3 | two | 5 | -5 | 5 | -5
+ | 2 | 3 | two | 5 | -5 | 0 |
+ | 2 | 3 | two | 5 | -5 | |
+ | 2 | 3 | two | 5 | -5 | | 0
+ | 2 | 3 | two | 5 | -5 | 1 | -1
+ | 2 | 3 | two | 5 | -5 | 2 | 2
+ | 2 | 3 | two | 5 | -5 | 3 | -3
+ | 2 | 3 | two | 5 | -5 | 2 | 4
+ | 2 | 3 | two | 5 | -5 | 5 | -5
+ | 2 | 3 | two | 5 | -5 | 5 | -5
+ | 2 | 3 | two | 5 | -5 | 0 |
+ | 2 | 3 | two | 5 | -5 | |
+ | 2 | 3 | two | 5 | -5 | | 0
+ | 2 | 3 | two | 0 | | 1 | -1
+ | 2 | 3 | two | 0 | | 2 | 2
+ | 2 | 3 | two | 0 | | 3 | -3
+ | 2 | 3 | two | 0 | | 2 | 4
+ | 2 | 3 | two | 0 | | 5 | -5
+ | 2 | 3 | two | 0 | | 5 | -5
+ | 2 | 3 | two | 0 | | 0 |
+ | 2 | 3 | two | 0 | | |
+ | 2 | 3 | two | 0 | | | 0
+ | 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
+ | 2 | 3 | two | | 0 | 1 | -1
+ | 2 | 3 | two | | 0 | 2 | 2
+ | 2 | 3 | two | | 0 | 3 | -3
+ | 2 | 3 | two | | 0 | 2 | 4
+ | 2 | 3 | two | | 0 | 5 | -5
+ | 2 | 3 | two | | 0 | 5 | -5
+ | 2 | 3 | two | | 0 | 0 |
+ | 2 | 3 | two | | 0 | |
+ | 2 | 3 | two | | 0 | | 0
+ | 3 | 2 | three | 1 | -1 | 1 | -1
+ | 3 | 2 | three | 1 | -1 | 2 | 2
+ | 3 | 2 | three | 1 | -1 | 3 | -3
+ | 3 | 2 | three | 1 | -1 | 2 | 4
+ | 3 | 2 | three | 1 | -1 | 5 | -5
+ | 3 | 2 | three | 1 | -1 | 5 | -5
+ | 3 | 2 | three | 1 | -1 | 0 |
+ | 3 | 2 | three | 1 | -1 | |
+ | 3 | 2 | three | 1 | -1 | | 0
+ | 3 | 2 | three | 2 | 2 | 1 | -1
+ | 3 | 2 | three | 2 | 2 | 2 | 2
+ | 3 | 2 | three | 2 | 2 | 3 | -3
+ | 3 | 2 | three | 2 | 2 | 2 | 4
+ | 3 | 2 | three | 2 | 2 | 5 | -5
+ | 3 | 2 | three | 2 | 2 | 5 | -5
+ | 3 | 2 | three | 2 | 2 | 0 |
+ | 3 | 2 | three | 2 | 2 | |
+ | 3 | 2 | three | 2 | 2 | | 0
+ | 3 | 2 | three | 3 | -3 | 1 | -1
+ | 3 | 2 | three | 3 | -3 | 2 | 2
+ | 3 | 2 | three | 3 | -3 | 3 | -3
+ | 3 | 2 | three | 3 | -3 | 2 | 4
+ | 3 | 2 | three | 3 | -3 | 5 | -5
+ | 3 | 2 | three | 3 | -3 | 5 | -5
+ | 3 | 2 | three | 3 | -3 | 0 |
+ | 3 | 2 | three | 3 | -3 | |
+ | 3 | 2 | three | 3 | -3 | | 0
+ | 3 | 2 | three | 2 | 4 | 1 | -1
+ | 3 | 2 | three | 2 | 4 | 2 | 2
+ | 3 | 2 | three | 2 | 4 | 3 | -3
+ | 3 | 2 | three | 2 | 4 | 2 | 4
+ | 3 | 2 | three | 2 | 4 | 5 | -5
+ | 3 | 2 | three | 2 | 4 | 5 | -5
+ | 3 | 2 | three | 2 | 4 | 0 |
+ | 3 | 2 | three | 2 | 4 | |
+ | 3 | 2 | three | 2 | 4 | | 0
+ | 3 | 2 | three | 5 | -5 | 1 | -1
+ | 3 | 2 | three | 5 | -5 | 2 | 2
+ | 3 | 2 | three | 5 | -5 | 3 | -3
+ | 3 | 2 | three | 5 | -5 | 2 | 4
+ | 3 | 2 | three | 5 | -5 | 5 | -5
+ | 3 | 2 | three | 5 | -5 | 5 | -5
+ | 3 | 2 | three | 5 | -5 | 0 |
+ | 3 | 2 | three | 5 | -5 | |
+ | 3 | 2 | three | 5 | -5 | | 0
+ | 3 | 2 | three | 5 | -5 | 1 | -1
+ | 3 | 2 | three | 5 | -5 | 2 | 2
+ | 3 | 2 | three | 5 | -5 | 3 | -3
+ | 3 | 2 | three | 5 | -5 | 2 | 4
+ | 3 | 2 | three | 5 | -5 | 5 | -5
+ | 3 | 2 | three | 5 | -5 | 5 | -5
+ | 3 | 2 | three | 5 | -5 | 0 |
+ | 3 | 2 | three | 5 | -5 | |
+ | 3 | 2 | three | 5 | -5 | | 0
+ | 3 | 2 | three | 0 | | 1 | -1
+ | 3 | 2 | three | 0 | | 2 | 2
+ | 3 | 2 | three | 0 | | 3 | -3
+ | 3 | 2 | three | 0 | | 2 | 4
+ | 3 | 2 | three | 0 | | 5 | -5
+ | 3 | 2 | three | 0 | | 5 | -5
+ | 3 | 2 | three | 0 | | 0 |
+ | 3 | 2 | three | 0 | | |
+ | 3 | 2 | three | 0 | | | 0
+ | 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
+ | 3 | 2 | three | | 0 | 1 | -1
+ | 3 | 2 | three | | 0 | 2 | 2
+ | 3 | 2 | three | | 0 | 3 | -3
+ | 3 | 2 | three | | 0 | 2 | 4
+ | 3 | 2 | three | | 0 | 5 | -5
+ | 3 | 2 | three | | 0 | 5 | -5
+ | 3 | 2 | three | | 0 | 0 |
+ | 3 | 2 | three | | 0 | |
+ | 3 | 2 | three | | 0 | | 0
+ | 4 | 1 | four | 1 | -1 | 1 | -1
+ | 4 | 1 | four | 1 | -1 | 2 | 2
+ | 4 | 1 | four | 1 | -1 | 3 | -3
+ | 4 | 1 | four | 1 | -1 | 2 | 4
+ | 4 | 1 | four | 1 | -1 | 5 | -5
+ | 4 | 1 | four | 1 | -1 | 5 | -5
+ | 4 | 1 | four | 1 | -1 | 0 |
+ | 4 | 1 | four | 1 | -1 | |
+ | 4 | 1 | four | 1 | -1 | | 0
+ | 4 | 1 | four | 2 | 2 | 1 | -1
+ | 4 | 1 | four | 2 | 2 | 2 | 2
+ | 4 | 1 | four | 2 | 2 | 3 | -3
+ | 4 | 1 | four | 2 | 2 | 2 | 4
+ | 4 | 1 | four | 2 | 2 | 5 | -5
+ | 4 | 1 | four | 2 | 2 | 5 | -5
+ | 4 | 1 | four | 2 | 2 | 0 |
+ | 4 | 1 | four | 2 | 2 | |
+ | 4 | 1 | four | 2 | 2 | | 0
+ | 4 | 1 | four | 3 | -3 | 1 | -1
+ | 4 | 1 | four | 3 | -3 | 2 | 2
+ | 4 | 1 | four | 3 | -3 | 3 | -3
+ | 4 | 1 | four | 3 | -3 | 2 | 4
+ | 4 | 1 | four | 3 | -3 | 5 | -5
+ | 4 | 1 | four | 3 | -3 | 5 | -5
+ | 4 | 1 | four | 3 | -3 | 0 |
| 4 | 1 | four | 3 | -3 | |
+ | 4 | 1 | four | 3 | -3 | | 0
+ | 4 | 1 | four | 2 | 4 | 1 | -1
+ | 4 | 1 | four | 2 | 4 | 2 | 2
+ | 4 | 1 | four | 2 | 4 | 3 | -3
+ | 4 | 1 | four | 2 | 4 | 2 | 4
+ | 4 | 1 | four | 2 | 4 | 5 | -5
+ | 4 | 1 | four | 2 | 4 | 5 | -5
+ | 4 | 1 | four | 2 | 4 | 0 |
+ | 4 | 1 | four | 2 | 4 | |
+ | 4 | 1 | four | 2 | 4 | | 0
+ | 4 | 1 | four | 5 | -5 | 1 | -1
+ | 4 | 1 | four | 5 | -5 | 2 | 2
+ | 4 | 1 | four | 5 | -5 | 3 | -3
+ | 4 | 1 | four | 5 | -5 | 2 | 4
+ | 4 | 1 | four | 5 | -5 | 5 | -5
+ | 4 | 1 | four | 5 | -5 | 5 | -5
+ | 4 | 1 | four | 5 | -5 | 0 |
+ | 4 | 1 | four | 5 | -5 | |
+ | 4 | 1 | four | 5 | -5 | | 0
+ | 4 | 1 | four | 5 | -5 | 1 | -1
+ | 4 | 1 | four | 5 | -5 | 2 | 2
+ | 4 | 1 | four | 5 | -5 | 3 | -3
+ | 4 | 1 | four | 5 | -5 | 2 | 4
+ | 4 | 1 | four | 5 | -5 | 5 | -5
+ | 4 | 1 | four | 5 | -5 | 5 | -5
+ | 4 | 1 | four | 5 | -5 | 0 |
+ | 4 | 1 | four | 5 | -5 | |
+ | 4 | 1 | four | 5 | -5 | | 0
+ | 4 | 1 | four | 0 | | 1 | -1
+ | 4 | 1 | four | 0 | | 2 | 2
+ | 4 | 1 | four | 0 | | 3 | -3
+ | 4 | 1 | four | 0 | | 2 | 4
+ | 4 | 1 | four | 0 | | 5 | -5
+ | 4 | 1 | four | 0 | | 5 | -5
+ | 4 | 1 | four | 0 | | 0 |
+ | 4 | 1 | four | 0 | | |
+ | 4 | 1 | four | 0 | | | 0
+ | 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
+ | 4 | 1 | four | | 0 | 1 | -1
+ | 4 | 1 | four | | 0 | 2 | 2
+ | 4 | 1 | four | | 0 | 3 | -3
+ | 4 | 1 | four | | 0 | 2 | 4
+ | 4 | 1 | four | | 0 | 5 | -5
+ | 4 | 1 | four | | 0 | 5 | -5
+ | 4 | 1 | four | | 0 | 0 |
+ | 4 | 1 | four | | 0 | |
+ | 4 | 1 | four | | 0 | | 0
+ | 5 | 0 | five | 1 | -1 | 1 | -1
+ | 5 | 0 | five | 1 | -1 | 2 | 2
+ | 5 | 0 | five | 1 | -1 | 3 | -3
+ | 5 | 0 | five | 1 | -1 | 2 | 4
+ | 5 | 0 | five | 1 | -1 | 5 | -5
+ | 5 | 0 | five | 1 | -1 | 5 | -5
+ | 5 | 0 | five | 1 | -1 | 0 |
+ | 5 | 0 | five | 1 | -1 | |
+ | 5 | 0 | five | 1 | -1 | | 0
+ | 5 | 0 | five | 2 | 2 | 1 | -1
+ | 5 | 0 | five | 2 | 2 | 2 | 2
+ | 5 | 0 | five | 2 | 2 | 3 | -3
+ | 5 | 0 | five | 2 | 2 | 2 | 4
+ | 5 | 0 | five | 2 | 2 | 5 | -5
+ | 5 | 0 | five | 2 | 2 | 5 | -5
+ | 5 | 0 | five | 2 | 2 | 0 |
+ | 5 | 0 | five | 2 | 2 | |
+ | 5 | 0 | five | 2 | 2 | | 0
+ | 5 | 0 | five | 3 | -3 | 1 | -1
+ | 5 | 0 | five | 3 | -3 | 2 | 2
+ | 5 | 0 | five | 3 | -3 | 3 | -3
+ | 5 | 0 | five | 3 | -3 | 2 | 4
+ | 5 | 0 | five | 3 | -3 | 5 | -5
+ | 5 | 0 | five | 3 | -3 | 5 | -5
+ | 5 | 0 | five | 3 | -3 | 0 |
| 5 | 0 | five | 3 | -3 | |
+ | 5 | 0 | five | 3 | -3 | | 0
+ | 5 | 0 | five | 2 | 4 | 1 | -1
+ | 5 | 0 | five | 2 | 4 | 2 | 2
+ | 5 | 0 | five | 2 | 4 | 3 | -3
+ | 5 | 0 | five | 2 | 4 | 2 | 4
+ | 5 | 0 | five | 2 | 4 | 5 | -5
+ | 5 | 0 | five | 2 | 4 | 5 | -5
+ | 5 | 0 | five | 2 | 4 | 0 |
+ | 5 | 0 | five | 2 | 4 | |
+ | 5 | 0 | five | 2 | 4 | | 0
+ | 5 | 0 | five | 5 | -5 | 1 | -1
+ | 5 | 0 | five | 5 | -5 | 2 | 2
+ | 5 | 0 | five | 5 | -5 | 3 | -3
+ | 5 | 0 | five | 5 | -5 | 2 | 4
+ | 5 | 0 | five | 5 | -5 | 5 | -5
+ | 5 | 0 | five | 5 | -5 | 5 | -5
+ | 5 | 0 | five | 5 | -5 | 0 |
+ | 5 | 0 | five | 5 | -5 | |
+ | 5 | 0 | five | 5 | -5 | | 0
+ | 5 | 0 | five | 5 | -5 | 1 | -1
+ | 5 | 0 | five | 5 | -5 | 2 | 2
+ | 5 | 0 | five | 5 | -5 | 3 | -3
+ | 5 | 0 | five | 5 | -5 | 2 | 4
+ | 5 | 0 | five | 5 | -5 | 5 | -5
+ | 5 | 0 | five | 5 | -5 | 5 | -5
+ | 5 | 0 | five | 5 | -5 | 0 |
+ | 5 | 0 | five | 5 | -5 | |
+ | 5 | 0 | five | 5 | -5 | | 0
+ | 5 | 0 | five | 0 | | 1 | -1
+ | 5 | 0 | five | 0 | | 2 | 2
+ | 5 | 0 | five | 0 | | 3 | -3
+ | 5 | 0 | five | 0 | | 2 | 4
+ | 5 | 0 | five | 0 | | 5 | -5
+ | 5 | 0 | five | 0 | | 5 | -5
+ | 5 | 0 | five | 0 | | 0 |
+ | 5 | 0 | five | 0 | | |
+ | 5 | 0 | five | 0 | | | 0
+ | 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
+ | 5 | 0 | five | | 0 | 1 | -1
+ | 5 | 0 | five | | 0 | 2 | 2
+ | 5 | 0 | five | | 0 | 3 | -3
+ | 5 | 0 | five | | 0 | 2 | 4
+ | 5 | 0 | five | | 0 | 5 | -5
+ | 5 | 0 | five | | 0 | 5 | -5
+ | 5 | 0 | five | | 0 | 0 |
+ | 5 | 0 | five | | 0 | |
+ | 5 | 0 | five | | 0 | | 0
+ | 6 | 6 | six | 1 | -1 | 1 | -1
+ | 6 | 6 | six | 1 | -1 | 2 | 2
+ | 6 | 6 | six | 1 | -1 | 3 | -3
+ | 6 | 6 | six | 1 | -1 | 2 | 4
+ | 6 | 6 | six | 1 | -1 | 5 | -5
+ | 6 | 6 | six | 1 | -1 | 5 | -5
+ | 6 | 6 | six | 1 | -1 | 0 |
+ | 6 | 6 | six | 1 | -1 | |
+ | 6 | 6 | six | 1 | -1 | | 0
+ | 6 | 6 | six | 2 | 2 | 1 | -1
+ | 6 | 6 | six | 2 | 2 | 2 | 2
+ | 6 | 6 | six | 2 | 2 | 3 | -3
+ | 6 | 6 | six | 2 | 2 | 2 | 4
+ | 6 | 6 | six | 2 | 2 | 5 | -5
+ | 6 | 6 | six | 2 | 2 | 5 | -5
+ | 6 | 6 | six | 2 | 2 | 0 |
+ | 6 | 6 | six | 2 | 2 | |
+ | 6 | 6 | six | 2 | 2 | | 0
+ | 6 | 6 | six | 3 | -3 | 1 | -1
+ | 6 | 6 | six | 3 | -3 | 2 | 2
+ | 6 | 6 | six | 3 | -3 | 3 | -3
+ | 6 | 6 | six | 3 | -3 | 2 | 4
+ | 6 | 6 | six | 3 | -3 | 5 | -5
+ | 6 | 6 | six | 3 | -3 | 5 | -5
+ | 6 | 6 | six | 3 | -3 | 0 |
| 6 | 6 | six | 3 | -3 | |
+ | 6 | 6 | six | 3 | -3 | | 0
+ | 6 | 6 | six | 2 | 4 | 1 | -1
+ | 6 | 6 | six | 2 | 4 | 2 | 2
+ | 6 | 6 | six | 2 | 4 | 3 | -3
+ | 6 | 6 | six | 2 | 4 | 2 | 4
+ | 6 | 6 | six | 2 | 4 | 5 | -5
+ | 6 | 6 | six | 2 | 4 | 5 | -5
+ | 6 | 6 | six | 2 | 4 | 0 |
+ | 6 | 6 | six | 2 | 4 | |
+ | 6 | 6 | six | 2 | 4 | | 0
+ | 6 | 6 | six | 5 | -5 | 1 | -1
+ | 6 | 6 | six | 5 | -5 | 2 | 2
+ | 6 | 6 | six | 5 | -5 | 3 | -3
+ | 6 | 6 | six | 5 | -5 | 2 | 4
+ | 6 | 6 | six | 5 | -5 | 5 | -5
+ | 6 | 6 | six | 5 | -5 | 5 | -5
+ | 6 | 6 | six | 5 | -5 | 0 |
+ | 6 | 6 | six | 5 | -5 | |
+ | 6 | 6 | six | 5 | -5 | | 0
+ | 6 | 6 | six | 5 | -5 | 1 | -1
+ | 6 | 6 | six | 5 | -5 | 2 | 2
+ | 6 | 6 | six | 5 | -5 | 3 | -3
+ | 6 | 6 | six | 5 | -5 | 2 | 4
+ | 6 | 6 | six | 5 | -5 | 5 | -5
+ | 6 | 6 | six | 5 | -5 | 5 | -5
+ | 6 | 6 | six | 5 | -5 | 0 |
+ | 6 | 6 | six | 5 | -5 | |
+ | 6 | 6 | six | 5 | -5 | | 0
+ | 6 | 6 | six | 0 | | 1 | -1
+ | 6 | 6 | six | 0 | | 2 | 2
+ | 6 | 6 | six | 0 | | 3 | -3
+ | 6 | 6 | six | 0 | | 2 | 4
+ | 6 | 6 | six | 0 | | 5 | -5
+ | 6 | 6 | six | 0 | | 5 | -5
+ | 6 | 6 | six | 0 | | 0 |
+ | 6 | 6 | six | 0 | | |
+ | 6 | 6 | six | 0 | | | 0
+ | 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
+ | 6 | 6 | six | | 0 | 1 | -1
+ | 6 | 6 | six | | 0 | 2 | 2
+ | 6 | 6 | six | | 0 | 3 | -3
+ | 6 | 6 | six | | 0 | 2 | 4
+ | 6 | 6 | six | | 0 | 5 | -5
+ | 6 | 6 | six | | 0 | 5 | -5
+ | 6 | 6 | six | | 0 | 0 |
+ | 6 | 6 | six | | 0 | |
+ | 6 | 6 | six | | 0 | | 0
+ | 7 | 7 | seven | 1 | -1 | 1 | -1
+ | 7 | 7 | seven | 1 | -1 | 2 | 2
+ | 7 | 7 | seven | 1 | -1 | 3 | -3
+ | 7 | 7 | seven | 1 | -1 | 2 | 4
+ | 7 | 7 | seven | 1 | -1 | 5 | -5
+ | 7 | 7 | seven | 1 | -1 | 5 | -5
+ | 7 | 7 | seven | 1 | -1 | 0 |
+ | 7 | 7 | seven | 1 | -1 | |
+ | 7 | 7 | seven | 1 | -1 | | 0
+ | 7 | 7 | seven | 2 | 2 | 1 | -1
+ | 7 | 7 | seven | 2 | 2 | 2 | 2
+ | 7 | 7 | seven | 2 | 2 | 3 | -3
+ | 7 | 7 | seven | 2 | 2 | 2 | 4
+ | 7 | 7 | seven | 2 | 2 | 5 | -5
+ | 7 | 7 | seven | 2 | 2 | 5 | -5
+ | 7 | 7 | seven | 2 | 2 | 0 |
+ | 7 | 7 | seven | 2 | 2 | |
+ | 7 | 7 | seven | 2 | 2 | | 0
+ | 7 | 7 | seven | 3 | -3 | 1 | -1
+ | 7 | 7 | seven | 3 | -3 | 2 | 2
+ | 7 | 7 | seven | 3 | -3 | 3 | -3
+ | 7 | 7 | seven | 3 | -3 | 2 | 4
+ | 7 | 7 | seven | 3 | -3 | 5 | -5
+ | 7 | 7 | seven | 3 | -3 | 5 | -5
+ | 7 | 7 | seven | 3 | -3 | 0 |
| 7 | 7 | seven | 3 | -3 | |
+ | 7 | 7 | seven | 3 | -3 | | 0
+ | 7 | 7 | seven | 2 | 4 | 1 | -1
+ | 7 | 7 | seven | 2 | 4 | 2 | 2
+ | 7 | 7 | seven | 2 | 4 | 3 | -3
+ | 7 | 7 | seven | 2 | 4 | 2 | 4
+ | 7 | 7 | seven | 2 | 4 | 5 | -5
+ | 7 | 7 | seven | 2 | 4 | 5 | -5
+ | 7 | 7 | seven | 2 | 4 | 0 |
+ | 7 | 7 | seven | 2 | 4 | |
+ | 7 | 7 | seven | 2 | 4 | | 0
+ | 7 | 7 | seven | 5 | -5 | 1 | -1
+ | 7 | 7 | seven | 5 | -5 | 2 | 2
+ | 7 | 7 | seven | 5 | -5 | 3 | -3
+ | 7 | 7 | seven | 5 | -5 | 2 | 4
+ | 7 | 7 | seven | 5 | -5 | 5 | -5
+ | 7 | 7 | seven | 5 | -5 | 5 | -5
+ | 7 | 7 | seven | 5 | -5 | 0 |
+ | 7 | 7 | seven | 5 | -5 | |
+ | 7 | 7 | seven | 5 | -5 | | 0
+ | 7 | 7 | seven | 5 | -5 | 1 | -1
+ | 7 | 7 | seven | 5 | -5 | 2 | 2
+ | 7 | 7 | seven | 5 | -5 | 3 | -3
+ | 7 | 7 | seven | 5 | -5 | 2 | 4
+ | 7 | 7 | seven | 5 | -5 | 5 | -5
+ | 7 | 7 | seven | 5 | -5 | 5 | -5
+ | 7 | 7 | seven | 5 | -5 | 0 |
+ | 7 | 7 | seven | 5 | -5 | |
+ | 7 | 7 | seven | 5 | -5 | | 0
+ | 7 | 7 | seven | 0 | | 1 | -1
+ | 7 | 7 | seven | 0 | | 2 | 2
+ | 7 | 7 | seven | 0 | | 3 | -3
+ | 7 | 7 | seven | 0 | | 2 | 4
+ | 7 | 7 | seven | 0 | | 5 | -5
+ | 7 | 7 | seven | 0 | | 5 | -5
+ | 7 | 7 | seven | 0 | | 0 |
+ | 7 | 7 | seven | 0 | | |
+ | 7 | 7 | seven | 0 | | | 0
+ | 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
+ | 7 | 7 | seven | | 0 | 1 | -1
+ | 7 | 7 | seven | | 0 | 2 | 2
+ | 7 | 7 | seven | | 0 | 3 | -3
+ | 7 | 7 | seven | | 0 | 2 | 4
+ | 7 | 7 | seven | | 0 | 5 | -5
+ | 7 | 7 | seven | | 0 | 5 | -5
+ | 7 | 7 | seven | | 0 | 0 |
+ | 7 | 7 | seven | | 0 | |
+ | 7 | 7 | seven | | 0 | | 0
+ | 8 | 8 | eight | 1 | -1 | 1 | -1
+ | 8 | 8 | eight | 1 | -1 | 2 | 2
+ | 8 | 8 | eight | 1 | -1 | 3 | -3
+ | 8 | 8 | eight | 1 | -1 | 2 | 4
+ | 8 | 8 | eight | 1 | -1 | 5 | -5
+ | 8 | 8 | eight | 1 | -1 | 5 | -5
+ | 8 | 8 | eight | 1 | -1 | 0 |
+ | 8 | 8 | eight | 1 | -1 | |
+ | 8 | 8 | eight | 1 | -1 | | 0
+ | 8 | 8 | eight | 2 | 2 | 1 | -1
+ | 8 | 8 | eight | 2 | 2 | 2 | 2
+ | 8 | 8 | eight | 2 | 2 | 3 | -3
+ | 8 | 8 | eight | 2 | 2 | 2 | 4
+ | 8 | 8 | eight | 2 | 2 | 5 | -5
+ | 8 | 8 | eight | 2 | 2 | 5 | -5
+ | 8 | 8 | eight | 2 | 2 | 0 |
+ | 8 | 8 | eight | 2 | 2 | |
+ | 8 | 8 | eight | 2 | 2 | | 0
+ | 8 | 8 | eight | 3 | -3 | 1 | -1
+ | 8 | 8 | eight | 3 | -3 | 2 | 2
+ | 8 | 8 | eight | 3 | -3 | 3 | -3
+ | 8 | 8 | eight | 3 | -3 | 2 | 4
+ | 8 | 8 | eight | 3 | -3 | 5 | -5
+ | 8 | 8 | eight | 3 | -3 | 5 | -5
+ | 8 | 8 | eight | 3 | -3 | 0 |
| 8 | 8 | eight | 3 | -3 | |
+ | 8 | 8 | eight | 3 | -3 | | 0
+ | 8 | 8 | eight | 2 | 4 | 1 | -1
+ | 8 | 8 | eight | 2 | 4 | 2 | 2
+ | 8 | 8 | eight | 2 | 4 | 3 | -3
+ | 8 | 8 | eight | 2 | 4 | 2 | 4
+ | 8 | 8 | eight | 2 | 4 | 5 | -5
+ | 8 | 8 | eight | 2 | 4 | 5 | -5
+ | 8 | 8 | eight | 2 | 4 | 0 |
+ | 8 | 8 | eight | 2 | 4 | |
+ | 8 | 8 | eight | 2 | 4 | | 0
+ | 8 | 8 | eight | 5 | -5 | 1 | -1
+ | 8 | 8 | eight | 5 | -5 | 2 | 2
+ | 8 | 8 | eight | 5 | -5 | 3 | -3
+ | 8 | 8 | eight | 5 | -5 | 2 | 4
+ | 8 | 8 | eight | 5 | -5 | 5 | -5
+ | 8 | 8 | eight | 5 | -5 | 5 | -5
+ | 8 | 8 | eight | 5 | -5 | 0 |
+ | 8 | 8 | eight | 5 | -5 | |
+ | 8 | 8 | eight | 5 | -5 | | 0
+ | 8 | 8 | eight | 5 | -5 | 1 | -1
+ | 8 | 8 | eight | 5 | -5 | 2 | 2
+ | 8 | 8 | eight | 5 | -5 | 3 | -3
+ | 8 | 8 | eight | 5 | -5 | 2 | 4
+ | 8 | 8 | eight | 5 | -5 | 5 | -5
+ | 8 | 8 | eight | 5 | -5 | 5 | -5
+ | 8 | 8 | eight | 5 | -5 | 0 |
+ | 8 | 8 | eight | 5 | -5 | |
+ | 8 | 8 | eight | 5 | -5 | | 0
+ | 8 | 8 | eight | 0 | | 1 | -1
+ | 8 | 8 | eight | 0 | | 2 | 2
+ | 8 | 8 | eight | 0 | | 3 | -3
+ | 8 | 8 | eight | 0 | | 2 | 4
+ | 8 | 8 | eight | 0 | | 5 | -5
+ | 8 | 8 | eight | 0 | | 5 | -5
+ | 8 | 8 | eight | 0 | | 0 |
+ | 8 | 8 | eight | 0 | | |
+ | 8 | 8 | eight | 0 | | | 0
+ | 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
+ | 8 | 8 | eight | | 0 | 1 | -1
+ | 8 | 8 | eight | | 0 | 2 | 2
+ | 8 | 8 | eight | | 0 | 3 | -3
+ | 8 | 8 | eight | | 0 | 2 | 4
+ | 8 | 8 | eight | | 0 | 5 | -5
+ | 8 | 8 | eight | | 0 | 5 | -5
+ | 8 | 8 | eight | | 0 | 0 |
+ | 8 | 8 | eight | | 0 | |
+ | 8 | 8 | eight | | 0 | | 0
+ | 0 | | zero | 1 | -1 | 1 | -1
+ | 0 | | zero | 1 | -1 | 2 | 2
+ | 0 | | zero | 1 | -1 | 3 | -3
+ | 0 | | zero | 1 | -1 | 2 | 4
+ | 0 | | zero | 1 | -1 | 5 | -5
+ | 0 | | zero | 1 | -1 | 5 | -5
+ | 0 | | zero | 1 | -1 | 0 |
+ | 0 | | zero | 1 | -1 | |
+ | 0 | | zero | 1 | -1 | | 0
+ | 0 | | zero | 2 | 2 | 1 | -1
+ | 0 | | zero | 2 | 2 | 2 | 2
+ | 0 | | zero | 2 | 2 | 3 | -3
+ | 0 | | zero | 2 | 2 | 2 | 4
+ | 0 | | zero | 2 | 2 | 5 | -5
+ | 0 | | zero | 2 | 2 | 5 | -5
+ | 0 | | zero | 2 | 2 | 0 |
+ | 0 | | zero | 2 | 2 | |
+ | 0 | | zero | 2 | 2 | | 0
+ | 0 | | zero | 3 | -3 | 1 | -1
+ | 0 | | zero | 3 | -3 | 2 | 2
+ | 0 | | zero | 3 | -3 | 3 | -3
+ | 0 | | zero | 3 | -3 | 2 | 4
+ | 0 | | zero | 3 | -3 | 5 | -5
+ | 0 | | zero | 3 | -3 | 5 | -5
+ | 0 | | zero | 3 | -3 | 0 |
| 0 | | zero | 3 | -3 | |
- | | | 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 |
+ | 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
+ | | | null | 1 | -1 | 1 | -1
+ | | | null | 1 | -1 | 2 | 2
+ | | | null | 1 | -1 | 3 | -3
+ | | | null | 1 | -1 | 2 | 4
+ | | | null | 1 | -1 | 5 | -5
+ | | | null | 1 | -1 | 5 | -5
+ | | | null | 1 | -1 | 0 |
+ | | | null | 1 | -1 | |
+ | | | null | 1 | -1 | | 0
+ | | | null | 2 | 2 | 1 | -1
+ | | | null | 2 | 2 | 2 | 2
+ | | | null | 2 | 2 | 3 | -3
+ | | | null | 2 | 2 | 2 | 4
+ | | | null | 2 | 2 | 5 | -5
+ | | | null | 2 | 2 | 5 | -5
+ | | | null | 2 | 2 | 0 |
+ | | | null | 2 | 2 | |
+ | | | null | 2 | 2 | | 0
+ | | | null | 3 | -3 | 1 | -1
+ | | | null | 3 | -3 | 2 | 2
+ | | | null | 3 | -3 | 3 | -3
+ | | | null | 3 | -3 | 2 | 4
+ | | | null | 3 | -3 | 5 | -5
+ | | | null | 3 | -3 | 5 | -5
+ | | | null | 3 | -3 | 0 |
+ | | | null | 3 | -3 | |
+ | | | null | 3 | -3 | | 0
+ | | | null | 2 | 4 | 1 | -1
+ | | | null | 2 | 4 | 2 | 2
+ | | | null | 2 | 4 | 3 | -3
+ | | | null | 2 | 4 | 2 | 4
+ | | | null | 2 | 4 | 5 | -5
+ | | | null | 2 | 4 | 5 | -5
| | | null | 2 | 4 | 0 |
+ | | | null | 2 | 4 | |
+ | | | null | 2 | 4 | | 0
+ | | | null | 5 | -5 | 1 | -1
+ | | | null | 5 | -5 | 2 | 2
+ | | | null | 5 | -5 | 3 | -3
+ | | | null | 5 | -5 | 2 | 4
+ | | | null | 5 | -5 | 5 | -5
+ | | | null | 5 | -5 | 5 | -5
+ | | | null | 5 | -5 | 0 |
+ | | | null | 5 | -5 | |
+ | | | null | 5 | -5 | | 0
+ | | | null | 5 | -5 | 1 | -1
+ | | | null | 5 | -5 | 2 | 2
+ | | | null | 5 | -5 | 3 | -3
+ | | | null | 5 | -5 | 2 | 4
+ | | | null | 5 | -5 | 5 | -5
+ | | | null | 5 | -5 | 5 | -5
+ | | | null | 5 | -5 | 0 |
+ | | | null | 5 | -5 | |
+ | | | null | 5 | -5 | | 0
+ | | | null | 0 | | 1 | -1
+ | | | null | 0 | | 2 | 2
+ | | | null | 0 | | 3 | -3
+ | | | null | 0 | | 2 | 4
+ | | | null | 0 | | 5 | -5
+ | | | null | 0 | | 5 | -5
+ | | | null | 0 | | 0 |
+ | | | null | 0 | | |
+ | | | null | 0 | | | 0
+ | | | null | | | 1 | -1
+ | | | null | | | 2 | 2
+ | | | null | | | 3 | -3
+ | | | null | | | 2 | 4
+ | | | null | | | 5 | -5
+ | | | null | | | 5 | -5
+ | | | null | | | 0 |
+ | | | null | | | |
+ | | | null | | | | 0
+ | | | null | | 0 | 1 | -1
+ | | | null | | 0 | 2 | 2
+ | | | null | | 0 | 3 | -3
+ | | | null | | 0 | 2 | 4
+ | | | null | | 0 | 5 | -5
+ | | | null | | 0 | 5 | -5
+ | | | null | | 0 | 0 |
+ | | | null | | 0 | |
+ | | | null | | 0 | | 0
+ | | 0 | zero | 1 | -1 | 1 | -1
+ | | 0 | zero | 1 | -1 | 2 | 2
+ | | 0 | zero | 1 | -1 | 3 | -3
+ | | 0 | zero | 1 | -1 | 2 | 4
+ | | 0 | zero | 1 | -1 | 5 | -5
+ | | 0 | zero | 1 | -1 | 5 | -5
+ | | 0 | zero | 1 | -1 | 0 |
+ | | 0 | zero | 1 | -1 | |
+ | | 0 | zero | 1 | -1 | | 0
+ | | 0 | zero | 2 | 2 | 1 | -1
+ | | 0 | zero | 2 | 2 | 2 | 2
+ | | 0 | zero | 2 | 2 | 3 | -3
+ | | 0 | zero | 2 | 2 | 2 | 4
+ | | 0 | zero | 2 | 2 | 5 | -5
+ | | 0 | zero | 2 | 2 | 5 | -5
+ | | 0 | zero | 2 | 2 | 0 |
+ | | 0 | zero | 2 | 2 | |
+ | | 0 | zero | 2 | 2 | | 0
+ | | 0 | zero | 3 | -3 | 1 | -1
+ | | 0 | zero | 3 | -3 | 2 | 2
+ | | 0 | zero | 3 | -3 | 3 | -3
+ | | 0 | zero | 3 | -3 | 2 | 4
+ | | 0 | zero | 3 | -3 | 5 | -5
+ | | 0 | zero | 3 | -3 | 5 | -5
+ | | 0 | zero | 3 | -3 | 0 |
+ | | 0 | zero | 3 | -3 | |
+ | | 0 | zero | 3 | -3 | | 0
+ | | 0 | zero | 2 | 4 | 1 | -1
+ | | 0 | zero | 2 | 4 | 2 | 2
+ | | 0 | zero | 2 | 4 | 3 | -3
+ | | 0 | zero | 2 | 4 | 2 | 4
+ | | 0 | zero | 2 | 4 | 5 | -5
+ | | 0 | zero | 2 | 4 | 5 | -5
| | 0 | zero | 2 | 4 | 0 |
- | 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)
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
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", *
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
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)
--
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)
--
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)
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)
+++ /dev/null
---
--- 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;
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)
projects / postgresql / commitdiff