diff --git a/doc/src/sgml/perform.sgml b/doc/src/sgml/perform.sgml
index 4c150d50220579859a4820ee5f00405631e00d7c..6928f1d853e08ab0ab4af965b6c8afa44f6ce7d9 100644
--- a/doc/src/sgml/perform.sgml
+++ b/doc/src/sgml/perform.sgml
@@ -1,5 +1,5 @@
<!--
-$Header: /cvsroot/pgsql/doc/src/sgml/perform.sgml,v 1.23 2003/01/12 18:42:59 tgl Exp $
+$Header: /cvsroot/pgsql/doc/src/sgml/perform.sgml,v 1.24 2003/01/25 23:10:27 tgl Exp $
-->
<chapter id="performance-tips">
@@ -591,53 +591,93 @@ SELECT * FROM a LEFT JOIN (b JOIN c ON (b.ref = c.id)) ON (a.id = b.id);
</para>
<para>
- The <productname>PostgreSQL</productname> query planner treats all
- explicit <literal>JOIN</> syntaxes as constraining the join order, even though
- it is not logically necessary to make such a constraint for inner
- joins. Therefore, although all of these queries give the same result:
+ Explicit inner join syntax (<literal>INNER JOIN</>, <literal>CROSS
+ JOIN</>, or unadorned <literal>JOIN</>) is semantically the same as
+ listing the input relations in <literal>FROM</>, so it does not need to
+ constrain the join order. But it is possible to instruct the
+ <productname>PostgreSQL</productname> query planner to treat
+ explicit inner <literal>JOIN</>s as constraining the join order anyway.
+ For example, these three queries are logically equivalent:
<programlisting>
SELECT * FROM a, b, c WHERE a.id = b.id AND b.ref = c.id;
SELECT * FROM a CROSS JOIN b CROSS JOIN c WHERE a.id = b.id AND b.ref = c.id;
SELECT * FROM a JOIN (b JOIN c ON (b.ref = c.id)) ON (a.id = b.id);
</programlisting>
+ But if we tell the planner to honor the <literal>JOIN</> order,
the second and third take less time to plan than the first. This effect
is not worth worrying about for only three tables, but it can be a
lifesaver with many tables.
</para>
+ <para>
+ To force the planner to follow the <literal>JOIN</> order for inner joins,
+ set the <varname>JOIN_COLLAPSE_LIMIT</> run-time parameter to 1.
+ (Other possible values are discussed below.)
+ </para>
+
<para>
You do not need to constrain the join order completely in order to
- cut search time, because it's OK to use <literal>JOIN</> operators in a plain
- <literal>FROM</> list. For example,
+ cut search time, because it's OK to use <literal>JOIN</> operators
+ within items of a plain <literal>FROM</> list. For example, consider
<programlisting>
SELECT * FROM a CROSS JOIN b, c, d, e WHERE ...;
</programlisting>
+ With <varname>JOIN_COLLAPSE_LIMIT</> = 1, this
forces the planner to join A to B before joining them to other tables,
but doesn't constrain its choices otherwise. In this example, the
number of possible join orders is reduced by a factor of 5.
</para>
<para>
- If you have a mix of outer and inner joins in a complex query, you
- might not want to constrain the planner's search for a good ordering
- of inner joins inside an outer join. You can't do that directly in the
- <literal>JOIN</> syntax, but you can get around the syntactic limitation by using
- subselects. For example,
+ Constraining the planner's search in this way is a useful technique
+ both for reducing planning time and for directing the planner to a
+ good query plan. If the planner chooses a bad join order by default,
+ you can force it to choose a better order via <literal>JOIN</> syntax
+ --- assuming that you know of a better order, that is. Experimentation
+ is recommended.
+ </para>
+
+ <para>
+ A closely related issue that affects planning time is collapsing of
+ sub-SELECTs into their parent query. For example, consider
+<programlisting>
+SELECT *
+FROM x, y,
+ (SELECT * FROM a, b, c WHERE something) AS ss
+WHERE somethingelse
+</programlisting>
+ This situation might arise from use of a view that contains a join;
+ the view's SELECT rule will be inserted in place of the view reference,
+ yielding a query much like the above. Normally, the planner will try
+ to collapse the sub-query into the parent, yielding
<programlisting>
-SELECT * FROM d LEFT JOIN
- (SELECT * FROM a, b, c WHERE ...) AS ss
- ON (...);
+SELECT * FROM x, y, a, b, c WHERE something AND somethingelse
</programlisting>
- Here, joining to D must be the last step in the query plan, but the
- planner is free to consider various join orders for A, B, and C.
+ This usually results in a better plan than planning the sub-query
+ separately. (For example, the outer WHERE conditions might be such that
+ joining X to A first eliminates many rows of A, thus avoiding the need to
+ form the full logical output of the sub-select.) But at the same time,
+ we have increased the planning time; here, we have a five-way join
+ problem replacing two separate three-way join problems. Because of the
+ exponential growth of the number of possibilities, this makes a big
+ difference. The planner tries to avoid getting stuck in huge join search
+ problems by not collapsing a sub-query if more than
+ <varname>FROM_COLLAPSE_LIMIT</> FROM-items would result in the parent
+ query. You can trade off planning time against quality of plan by
+ adjusting this run-time parameter up or down.
</para>
<para>
- Constraining the planner's search in this way is a useful technique
- both for reducing planning time and for directing the planner to a
- good query plan. If the planner chooses a bad join order by default,
- you can force it to choose a better order via <literal>JOIN</> syntax --- assuming
- that you know of a better order, that is. Experimentation is recommended.
+ <varname>FROM_COLLAPSE_LIMIT</> and <varname>JOIN_COLLAPSE_LIMIT</>
+ are similarly named because they do almost the same thing: one controls
+ when the planner will <quote>flatten out</> sub-SELECTs, and the
+ other controls when it will flatten out explicit inner JOINs. Typically
+ you would either set <varname>JOIN_COLLAPSE_LIMIT</> equal to
+ <varname>FROM_COLLAPSE_LIMIT</> (so that explicit JOINs and sub-SELECTs
+ act similarly) or set <varname>JOIN_COLLAPSE_LIMIT</> to 1 (if you want
+ to control join order with explicit JOINs). But you might set them
+ differently if you are trying to fine-tune the tradeoff between planning
+ time and run time.
</para>
</sect1>
diff --git a/doc/src/sgml/release.sgml b/doc/src/sgml/release.sgml
index 18d71f5866b64d67a2f0a6fae382d34dfd1d5b95..daccd63da77244bc1a1f1b8e464ff1f6b86c0f10 100644
--- a/doc/src/sgml/release.sgml
+++ b/doc/src/sgml/release.sgml
@@ -1,5 +1,5 @@
<!--
-$Header: /cvsroot/pgsql/doc/src/sgml/release.sgml,v 1.180 2003/01/23 23:38:51 petere Exp $
+$Header: /cvsroot/pgsql/doc/src/sgml/release.sgml,v 1.181 2003/01/25 23:10:27 tgl Exp $
-->
<appendix id="release">
@@ -24,6 +24,7 @@ CDATA means the content is "SGML-free", so you can write without
worries about funny characters.
-->
<literallayout><![CDATA[
+Explicit JOINs no longer constrain query plan, unless JOIN_COLLAPSE_LIMIT = 1
Performance of "foo IN (SELECT ...)" queries has been considerably improved
FETCH 0 now re-fetches cursor's current row, per SQL spec
Revised executor state representation; plan trees are read-only to executor now
diff --git a/doc/src/sgml/runtime.sgml b/doc/src/sgml/runtime.sgml
index 34321cae52d16760057ffc2a70cf2828a3fe6c3e..cf8a648ba84bf5e6d4a5fa676d315e7be5dc78d3 100644
--- a/doc/src/sgml/runtime.sgml
+++ b/doc/src/sgml/runtime.sgml
@@ -1,5 +1,5 @@
<!--
-$Header: /cvsroot/pgsql/doc/src/sgml/runtime.sgml,v 1.166 2003/01/11 05:04:14 momjian Exp $
+$Header: /cvsroot/pgsql/doc/src/sgml/runtime.sgml,v 1.167 2003/01/25 23:10:27 tgl Exp $
-->
<Chapter Id="runtime">
@@ -773,6 +773,19 @@ env PGOPTIONS='-c geqo=off' psql
</listitem>
</varlistentry>
+ <varlistentry>
+ <term><varname>FROM_COLLAPSE_LIMIT</varname> (<type>integer</type>)</term>
+ <listitem>
+ <para>
+ The planner will merge sub-queries into upper queries if the resulting
+ FROM list would have no more than this many items. Smaller values
+ reduce planning time but may yield inferior query plans.
+ The default is 8. It is usually wise to keep this less than
+ <literal>GEQO_THRESHOLD</>.
+ </para>
+ </listitem>
+ </varlistentry>
+
<varlistentry>
<indexterm>
<primary>genetic query optimization</primary>
@@ -826,12 +839,27 @@ env PGOPTIONS='-c geqo=off' psql
<listitem>
<para>
Use genetic query optimization to plan queries with at least
- this many <literal>FROM</> items involved. (Note that a
+ this many <literal>FROM</> items involved. (Note that an outer
<literal>JOIN</> construct counts as only one <literal>FROM</>
item.) The default is 11. For simpler queries it is usually best
- to use the deterministic, exhaustive planner. This parameter
- also controls how hard the optimizer will try to merge subquery
- <literal>FROM</literal> clauses into the upper query.
+ to use the deterministic, exhaustive planner, but for queries with
+ many tables the deterministic planner takes too long.
+ </para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><varname>JOIN_COLLAPSE_LIMIT</varname> (<type>integer</type>)</term>
+ <listitem>
+ <para>
+ The planner will flatten explicit inner <literal>JOIN</> constructs
+ into lists of <literal>FROM</> items whenever a list of no more than
+ this many items would result. Usually this is set the same as
+ <literal>FROM_COLLAPSE_LIMIT</>. Setting it to 1 prevents any
+ flattening of inner <literal>JOIN</>s, allowing explicit
+ <literal>JOIN</> syntax to be used to control the join order.
+ Intermediate values might be useful to trade off planning time
+ against quality of plan.
</para>
</listitem>
</varlistentry>
@@ -1842,8 +1870,8 @@ dynamic_library_path = '/usr/local/lib/postgresql:/home/my_project/lib:$libdir'
server. The default is 64. Each buffer is typically 8192
bytes. This must be greater than 16, as well as at least twice
the value of <varname>MAX_CONNECTIONS</varname>; however, a
- higher value can often improve performance on modern
- machines. Values of at least a few thousand are recommended
+ higher value can often improve performance.
+ Values of a few thousand are recommended
for production installations. This option can only be set at
server start.
</para>
@@ -1878,15 +1906,17 @@ dynamic_library_path = '/usr/local/lib/postgresql:/home/my_project/lib:$libdir'
<listitem>
<para>
Specifies the amount of memory to be used by internal sorts and
- hashes before switching to temporary disk files. The value is
+ hash tables before switching to temporary disk files. The value is
specified in kilobytes, and defaults to 1024 kilobytes (1 MB).
- Note that for a complex query, several sorts might be running in
- parallel, and each one will be allowed to use as much memory as
- this value specifies before it starts to put data into temporary
+ Note that for a complex query, several sorts or hashes might be
+ running in parallel; each one will be allowed to use as much memory
+ as this value specifies before it starts to put data into temporary
files. Also, each running backend could be doing one or more
sorts simultaneously, so the total memory used could be many
times the value of <varname>SORT_MEM</varname>. Sorts are used
by <literal>ORDER BY</>, merge joins, and <command>CREATE INDEX</>.
+ Hash tables are used in hash joins, hash-based aggregation, and
+ hash-based processing of <literal>IN</> sub-selects.
</para>
</listitem>
</varlistentry>
diff --git a/src/backend/optimizer/path/allpaths.c b/src/backend/optimizer/path/allpaths.c
index f85144b8184d4da2bec50d1bd84eda48650fb299..6c40a16e32a779265adddbd90040ebfc53464968 100644
--- a/src/backend/optimizer/path/allpaths.c
+++ b/src/backend/optimizer/path/allpaths.c
@@ -8,7 +8,7 @@
*
*
* IDENTIFICATION
- * $Header: /cvsroot/pgsql/src/backend/optimizer/path/allpaths.c,v 1.94 2003/01/20 18:54:49 tgl Exp $
+ * $Header: /cvsroot/pgsql/src/backend/optimizer/path/allpaths.c,v 1.95 2003/01/25 23:10:27 tgl Exp $
*
*-------------------------------------------------------------------------
*/
@@ -30,8 +30,9 @@
#include "rewrite/rewriteManip.h"
-bool enable_geqo = true;
-int geqo_rels = DEFAULT_GEQO_RELS;
+/* These parameters are set by GUC */
+bool enable_geqo = false; /* just in case GUC doesn't set it */
+int geqo_threshold;
static void set_base_rel_pathlists(Query *root);
@@ -422,7 +423,7 @@ make_fromexpr_rel(Query *root, FromExpr *from)
* Consider the different orders in which we could join the rels,
* using either GEQO or regular optimizer.
*/
- if (enable_geqo && levels_needed >= geqo_rels)
+ if (enable_geqo && levels_needed >= geqo_threshold)
return geqo(root, levels_needed, initial_rels);
else
return make_one_rel_by_joins(root, levels_needed, initial_rels);
diff --git a/src/backend/optimizer/plan/planner.c b/src/backend/optimizer/plan/planner.c
index 388380f8843bbdfd1fdf948708a4dfeabc67850a..1b481ccbd25c633715d8c169d3db9c8aa20bfca2 100644
--- a/src/backend/optimizer/plan/planner.c
+++ b/src/backend/optimizer/plan/planner.c
@@ -8,7 +8,7 @@
*
*
* IDENTIFICATION
- * $Header: /cvsroot/pgsql/src/backend/optimizer/plan/planner.c,v 1.141 2003/01/20 18:54:52 tgl Exp $
+ * $Header: /cvsroot/pgsql/src/backend/optimizer/plan/planner.c,v 1.142 2003/01/25 23:10:27 tgl Exp $
*
*-------------------------------------------------------------------------
*/
@@ -166,12 +166,6 @@ subquery_planner(Query *parse, double tuple_fraction)
parse->jointree = (FromExpr *)
pull_up_subqueries(parse, (Node *) parse->jointree, false);
- /*
- * If so, we may have created opportunities to simplify the jointree.
- */
- parse->jointree = (FromExpr *)
- preprocess_jointree(parse, (Node *) parse->jointree);
-
/*
* Detect whether any rangetable entries are RTE_JOIN kind; if not,
* we can avoid the expense of doing flatten_join_alias_vars().
@@ -246,6 +240,16 @@ subquery_planner(Query *parse, double tuple_fraction)
}
parse->havingQual = (Node *) newHaving;
+ /*
+ * See if we can simplify the jointree; opportunities for this may come
+ * from having pulled up subqueries, or from flattening explicit JOIN
+ * syntax. We must do this after flattening JOIN alias variables, since
+ * eliminating explicit JOIN nodes from the jointree will cause
+ * get_relids_for_join() to fail.
+ */
+ parse->jointree = (FromExpr *)
+ preprocess_jointree(parse, (Node *) parse->jointree);
+
/*
* Do the main planning. If we have an inherited target relation,
* that needs special processing, else go straight to
diff --git a/src/backend/optimizer/prep/prepjointree.c b/src/backend/optimizer/prep/prepjointree.c
index 083528c0490d2a60f55b8cbaaf8ddd6ac819a533..68fbb1e1f53eb4fea4ef17f209a69c3bb706f6e0 100644
--- a/src/backend/optimizer/prep/prepjointree.c
+++ b/src/backend/optimizer/prep/prepjointree.c
@@ -9,14 +9,13 @@
*
*
* IDENTIFICATION
- * $Header: /cvsroot/pgsql/src/backend/optimizer/prep/prepjointree.c,v 1.1 2003/01/20 18:54:54 tgl Exp $
+ * $Header: /cvsroot/pgsql/src/backend/optimizer/prep/prepjointree.c,v 1.2 2003/01/25 23:10:27 tgl Exp $
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include "optimizer/clauses.h"
-#include "optimizer/paths.h"
#include "optimizer/prep.h"
#include "optimizer/subselect.h"
#include "optimizer/var.h"
@@ -24,6 +23,11 @@
#include "rewrite/rewriteManip.h"
+/* These parameters are set by GUC */
+int from_collapse_limit;
+int join_collapse_limit;
+
+
static bool is_simple_subquery(Query *subquery);
static bool has_nullable_targetlist(Query *subquery);
static void resolvenew_in_jointree(Node *jtnode, int varno, List *subtlist);
@@ -467,7 +471,16 @@ resolvenew_in_jointree(Node *jtnode, int varno, List *subtlist)
* case we can consider collapsing the two FromExprs into one. This is
* an optional conversion, since the planner will work correctly either
* way. But we may find a better plan (at the cost of more planning time)
- * if we merge the two nodes.
+ * if we merge the two nodes, creating a single join search space out of
+ * two. To allow the user to trade off planning time against plan quality,
+ * we provide a control parameter from_collapse_limit that limits the size
+ * of the join search space that can be created this way.
+ *
+ * We also consider flattening explicit inner JOINs into FromExprs (which
+ * will in turn allow them to be merged into parent FromExprs). The tradeoffs
+ * here are the same as for flattening FromExprs, but we use a different
+ * control parameter so that the user can use explicit JOINs to control the
+ * join order even when they are inner JOINs.
*
* NOTE: don't try to do this in the same jointree scan that does subquery
* pullup! Since we're changing the jointree structure here, that wouldn't
@@ -492,7 +505,7 @@ preprocess_jointree(Query *parse, Node *jtnode)
{
Node *child = (Node *) lfirst(l);
- /* Recursively simplify the child... */
+ /* Recursively simplify this child... */
child = preprocess_jointree(parse, child);
/* Now, is it a FromExpr? */
if (child && IsA(child, FromExpr))
@@ -500,21 +513,25 @@ preprocess_jointree(Query *parse, Node *jtnode)
/*
* Yes, so do we want to merge it into parent? Always do
* so if child has just one element (since that doesn't
- * make the parent's list any longer). Otherwise we have
- * to be careful about the increase in planning time
- * caused by combining the two join search spaces into
- * one. Our heuristic is to merge if the merge will
- * produce a join list no longer than GEQO_RELS/2.
- * (Perhaps need an additional user parameter?)
+ * make the parent's list any longer). Otherwise merge if
+ * the resulting join list would be no longer than
+ * from_collapse_limit.
*/
FromExpr *subf = (FromExpr *) child;
int childlen = length(subf->fromlist);
int myothers = length(newlist) + length(lnext(l));
- if (childlen <= 1 || (childlen + myothers) <= geqo_rels / 2)
+ if (childlen <= 1 ||
+ (childlen + myothers) <= from_collapse_limit)
{
newlist = nconc(newlist, subf->fromlist);
- f->quals = make_and_qual(subf->quals, f->quals);
+ /*
+ * By now, the quals have been converted to implicit-AND
+ * lists, so we just need to join the lists. NOTE: we
+ * put the pulled-up quals first.
+ */
+ f->quals = (Node *) nconc((List *) subf->quals,
+ (List *) f->quals);
}
else
newlist = lappend(newlist, child);
@@ -528,9 +545,64 @@ preprocess_jointree(Query *parse, Node *jtnode)
{
JoinExpr *j = (JoinExpr *) jtnode;
- /* Can't usefully change the JoinExpr, but recurse on children */
+ /* Recursively simplify the children... */
j->larg = preprocess_jointree(parse, j->larg);
j->rarg = preprocess_jointree(parse, j->rarg);
+ /*
+ * If it is an outer join, we must not flatten it. An inner join
+ * is semantically equivalent to a FromExpr; we convert it to one,
+ * allowing it to be flattened into its parent, if the resulting
+ * FromExpr would have no more than join_collapse_limit members.
+ */
+ if (j->jointype == JOIN_INNER && join_collapse_limit > 1)
+ {
+ int leftlen,
+ rightlen;
+
+ if (j->larg && IsA(j->larg, FromExpr))
+ leftlen = length(((FromExpr *) j->larg)->fromlist);
+ else
+ leftlen = 1;
+ if (j->rarg && IsA(j->rarg, FromExpr))
+ rightlen = length(((FromExpr *) j->rarg)->fromlist);
+ else
+ rightlen = 1;
+ if ((leftlen + rightlen) <= join_collapse_limit)
+ {
+ FromExpr *f = makeNode(FromExpr);
+
+ f->fromlist = NIL;
+ f->quals = NULL;
+
+ if (j->larg && IsA(j->larg, FromExpr))
+ {
+ FromExpr *subf = (FromExpr *) j->larg;
+
+ f->fromlist = subf->fromlist;
+ f->quals = subf->quals;
+ }
+ else
+ f->fromlist = makeList1(j->larg);
+
+ if (j->rarg && IsA(j->rarg, FromExpr))
+ {
+ FromExpr *subf = (FromExpr *) j->rarg;
+
+ f->fromlist = nconc(f->fromlist,
+ subf->fromlist);
+ f->quals = (Node *) nconc((List *) f->quals,
+ (List *) subf->quals);
+ }
+ else
+ f->fromlist = lappend(f->fromlist, j->rarg);
+
+ /* pulled-up quals first */
+ f->quals = (Node *) nconc((List *) f->quals,
+ (List *) j->quals);
+
+ return (Node *) f;
+ }
+ }
}
else
elog(ERROR, "preprocess_jointree: unexpected node type %d",
@@ -615,6 +687,9 @@ get_relids_in_jointree(Node *jtnode)
/*
* get_relids_for_join: get list of base RT indexes making up a join
+ *
+ * NB: this will not work reliably after preprocess_jointree() is run,
+ * since that may eliminate join nodes from the jointree.
*/
List *
get_relids_for_join(Query *parse, int joinrelid)
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 471d895ea72dab384a46e2fbfe6f9d73d9b897b7..9b726dcfe329525ea09b743c0c4ca22e5b32ad57 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -5,7 +5,7 @@
* command, configuration file, and command line options.
* See src/backend/utils/misc/README for more information.
*
- * $Header: /cvsroot/pgsql/src/backend/utils/misc/guc.c,v 1.110 2003/01/10 22:03:29 petere Exp $
+ * $Header: /cvsroot/pgsql/src/backend/utils/misc/guc.c,v 1.111 2003/01/25 23:10:27 tgl Exp $
*
* Copyright 2000 by PostgreSQL Global Development Group
* Written by Peter Eisentraut <peter_e@gmx.net>.
@@ -37,7 +37,7 @@
#include "optimizer/cost.h"
#include "optimizer/geqo.h"
#include "optimizer/paths.h"
-#include "optimizer/planmain.h"
+#include "optimizer/prep.h"
#include "parser/parse_expr.h"
#include "storage/fd.h"
#include "storage/freespace.h"
@@ -539,8 +539,16 @@ static struct config_int
10, 1, 1000, NULL, NULL
},
{
- {"geqo_threshold", PGC_USERSET}, &geqo_rels,
- DEFAULT_GEQO_RELS, 2, INT_MAX, NULL, NULL
+ {"from_collapse_limit", PGC_USERSET}, &from_collapse_limit,
+ 8, 1, INT_MAX, NULL, NULL
+ },
+ {
+ {"join_collapse_limit", PGC_USERSET}, &join_collapse_limit,
+ 8, 1, INT_MAX, NULL, NULL
+ },
+ {
+ {"geqo_threshold", PGC_USERSET}, &geqo_threshold,
+ 11, 2, INT_MAX, NULL, NULL
},
{
{"geqo_pool_size", PGC_USERSET}, &Geqo_pool_size,
diff --git a/src/backend/utils/misc/postgresql.conf.sample b/src/backend/utils/misc/postgresql.conf.sample
index 41750b9e22957612de9fb0f9973d473ebb3ee710..515eec9acaec661dec71575f784d3980cc70663a 100644
--- a/src/backend/utils/misc/postgresql.conf.sample
+++ b/src/backend/utils/misc/postgresql.conf.sample
@@ -94,6 +94,9 @@
#cpu_index_tuple_cost = 0.001 # (same)
#cpu_operator_cost = 0.0025 # (same)
+#from_collapse_limit = 8
+#join_collapse_limit = 8 # 1 disables collapsing of explicit JOINs
+
#default_statistics_target = 10 # range 1-1000
#
diff --git a/src/bin/psql/tab-complete.c b/src/bin/psql/tab-complete.c
index e6972537536dc5fe3fbf86bacd1e1677333a5470..efebd2f6b6fe2f114f0882f8296d52ab95497bd9 100644
--- a/src/bin/psql/tab-complete.c
+++ b/src/bin/psql/tab-complete.c
@@ -3,7 +3,7 @@
*
* Copyright 2000-2002 by PostgreSQL Global Development Group
*
- * $Header: /cvsroot/pgsql/src/bin/psql/tab-complete.c,v 1.71 2003/01/10 22:03:30 petere Exp $
+ * $Header: /cvsroot/pgsql/src/bin/psql/tab-complete.c,v 1.72 2003/01/25 23:10:30 tgl Exp $
*/
/*----------------------------------------------------------------------
@@ -252,6 +252,7 @@ psql_completion(char *text, int start, int end)
"explain_pretty_print",
"extra_float_digits",
"fixbtree",
+ "from_collapse_limit",
"fsync",
"geqo",
"geqo_effort",
@@ -260,6 +261,7 @@ psql_completion(char *text, int start, int end)
"geqo_random_seed",
"geqo_selection_bias",
"geqo_threshold",
+ "join_collapse_limit",
"log_hostname",
"krb_server_keyfile",
"lc_messages",
diff --git a/src/include/optimizer/paths.h b/src/include/optimizer/paths.h
index 76285bac408c63d53bde46e517fd935f2ac7b304..8b4f701744ed6408870be9fb3edd2f1557a0326c 100644
--- a/src/include/optimizer/paths.h
+++ b/src/include/optimizer/paths.h
@@ -8,7 +8,7 @@
* Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
- * $Id: paths.h,v 1.64 2003/01/24 03:58:43 tgl Exp $
+ * $Id: paths.h,v 1.65 2003/01/25 23:10:30 tgl Exp $
*
*-------------------------------------------------------------------------
*/
@@ -18,16 +18,11 @@
#include "nodes/relation.h"
-/* default GEQO threshold (default value for geqo_rels) */
-/* If you change this, update backend/utils/misc/postgresql.sample.conf */
-#define DEFAULT_GEQO_RELS 11
-
-
/*
* allpaths.c
*/
extern bool enable_geqo;
-extern int geqo_rels;
+extern int geqo_threshold;
extern RelOptInfo *make_one_rel(Query *root);
extern RelOptInfo *make_fromexpr_rel(Query *root, FromExpr *from);
diff --git a/src/include/optimizer/prep.h b/src/include/optimizer/prep.h
index 17ecb4d593ff3090b02a3e1b536a3e5115744319..458539a817444371f0cf785a5f764cb67e4fb553 100644
--- a/src/include/optimizer/prep.h
+++ b/src/include/optimizer/prep.h
@@ -7,7 +7,7 @@
* Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
- * $Id: prep.h,v 1.34 2003/01/20 18:55:05 tgl Exp $
+ * $Id: prep.h,v 1.35 2003/01/25 23:10:30 tgl Exp $
*
*-------------------------------------------------------------------------
*/
@@ -20,6 +20,9 @@
/*
* prototypes for prepjointree.c
*/
+extern int from_collapse_limit;
+extern int join_collapse_limit;
+
extern Node *pull_up_IN_clauses(Query *parse, Node *node);
extern Node *pull_up_subqueries(Query *parse, Node *jtnode,
bool below_outer_join);
diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index 6e1a21a03e168876325c623a3c3fbe870215e6f2..e04a90e07211ffe99a10a57bec97867f5d3d567b 100644
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -660,895 +660,895 @@ SELECT '' AS "xxx", *
xxx | i | j | t | i | k | i | k
-----+---+---+-------+---+----+---+----
| 1 | 4 | one | 1 | -1 | 1 | -1
- | 1 | 4 | one | 1 | -1 | 2 | 2
- | 1 | 4 | one | 1 | -1 | 3 | -3
- | 1 | 4 | one | 1 | -1 | 2 | 4
- | 1 | 4 | one | 1 | -1 | 5 | -5
- | 1 | 4 | one | 1 | -1 | 5 | -5
- | 1 | 4 | one | 1 | -1 | 0 |
- | 1 | 4 | one | 1 | -1 | |
- | 1 | 4 | one | 1 | -1 | | 0
- | 1 | 4 | one | 2 | 2 | 1 | -1
- | 1 | 4 | one | 2 | 2 | 2 | 2
- | 1 | 4 | one | 2 | 2 | 3 | -3
- | 1 | 4 | one | 2 | 2 | 2 | 4
- | 1 | 4 | one | 2 | 2 | 5 | -5
- | 1 | 4 | one | 2 | 2 | 5 | -5
- | 1 | 4 | one | 2 | 2 | 0 |
- | 1 | 4 | one | 2 | 2 | |
- | 1 | 4 | one | 2 | 2 | | 0
- | 1 | 4 | one | 3 | -3 | 1 | -1
- | 1 | 4 | one | 3 | -3 | 2 | 2
- | 1 | 4 | one | 3 | -3 | 3 | -3
- | 1 | 4 | one | 3 | -3 | 2 | 4
- | 1 | 4 | one | 3 | -3 | 5 | -5
- | 1 | 4 | one | 3 | -3 | 5 | -5
- | 1 | 4 | one | 3 | -3 | 0 |
- | 1 | 4 | one | 3 | -3 | |
- | 1 | 4 | one | 3 | -3 | | 0
- | 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
+ | 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
- | 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 |
- | 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
+ | 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 | |
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+ | | | null | | | 5 | -5
| | 0 | zero | | | 5 | -5
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+ | 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
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+ | | | null | | | | 0
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+ | | | null | | 0 | 2 | 4
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+ | 5 | 0 | five | | 0 | 5 | -5
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+ | 0 | | zero | | 0 | 5 | -5
+ | | | null | | 0 | 5 | -5
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+ | 0 | | zero | | 0 | 5 | -5
+ | | | null | | 0 | 5 | -5
| | 0 | zero | | 0 | 5 | -5
+ | 1 | 4 | one | | 0 | 0 |
+ | 2 | 3 | two | | 0 | 0 |
+ | 3 | 2 | three | | 0 | 0 |
+ | 4 | 1 | four | | 0 | 0 |
+ | 5 | 0 | five | | 0 | 0 |
+ | 6 | 6 | six | | 0 | 0 |
+ | 7 | 7 | seven | | 0 | 0 |
+ | 8 | 8 | eight | | 0 | 0 |
+ | 0 | | zero | | 0 | 0 |
+ | | | null | | 0 | 0 |
| | 0 | zero | | 0 | 0 |
+ | 1 | 4 | one | | 0 | |
+ | 2 | 3 | two | | 0 | |
+ | 3 | 2 | three | | 0 | |
+ | 4 | 1 | four | | 0 | |
+ | 5 | 0 | five | | 0 | |
+ | 6 | 6 | six | | 0 | |
+ | 7 | 7 | seven | | 0 | |
+ | 8 | 8 | eight | | 0 | |
+ | 0 | | zero | | 0 | |
+ | | | null | | 0 | |
| | 0 | zero | | 0 | |
+ | 1 | 4 | one | | 0 | | 0
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+ | 3 | 2 | three | | 0 | | 0
+ | 4 | 1 | four | | 0 | | 0
+ | 5 | 0 | five | | 0 | | 0
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+ | 8 | 8 | eight | | 0 | | 0
+ | 0 | | zero | | 0 | | 0
+ | | | null | | 0 | | 0
| | 0 | zero | | 0 | | 0
(891 rows)