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Postgres FD Implementation
Commit 9bb34281 authored by Tom Lane's avatar Tom Lane
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Rewrite the planner's handling of materialized plan types so that there is 

an explicit model of rescan costs being different from first-time costs.
The costing of Material nodes in particular now has some visible relationship
to the actual runtime behavior, where before it was essentially fantasy.
This also fixes up a couple of places where different materialized plan types
were treated differently for no very good reason (probably just oversights).

A couple of the regression tests are affected, because the planner now chooses
to put the other relation on the inside of a nestloop-with-materialize.
So far as I can see both changes are sane, and the planner is now more
consistently following the expectation that it should prefer to materialize
the smaller of two relations.

Per a recent discussion with Robert Haas.
parent 5f1b32dd
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Showing with 1034 additions and 921 deletions
src/backend/executor/execAmi.c
View file @ 9bb34281
...@@ -6,7 +6,7 @@ ...@@ -6,7 +6,7 @@
* Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California * Portions Copyright (c) 1994, Regents of the University of California
* *
* $PostgreSQL: pgsql/src/backend/executor/execAmi.c,v 1.103 2009/01/01 17:23:41 momjian Exp $ * $PostgreSQL: pgsql/src/backend/executor/execAmi.c,v 1.104 2009/09/12 22:12:03 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -496,3 +496,30 @@ IndexSupportsBackwardScan(Oid indexid) ...@@ -496,3 +496,30 @@ IndexSupportsBackwardScan(Oid indexid)
return result; return result;
} }
/*
* ExecMaterializesOutput - does a plan type materialize its output?
*
* Returns true if the plan node type is one that automatically materializes
* its output (typically by keeping it in a tuplestore). For such plans,
* a rescan without any parameter change will have zero startup cost and
* very low per-tuple cost.
*/
bool
ExecMaterializesOutput(NodeTag plantype)
{
switch (plantype)
{
case T_Material:
case T_FunctionScan:
case T_CteScan:
case T_WorkTableScan:
case T_Sort:
return true;
default:
break;
}
return false;
}
src/backend/optimizer/path/costsize.c
View file @ 9bb34281
...@@ -54,7 +54,7 @@ ...@@ -54,7 +54,7 @@
* Portions Copyright (c) 1994, Regents of the University of California * Portions Copyright (c) 1994, Regents of the University of California
* *
* IDENTIFICATION * IDENTIFICATION
* $PostgreSQL: pgsql/src/backend/optimizer/path/costsize.c,v 1.210 2009/07/11 04:09:33 tgl Exp $ * $PostgreSQL: pgsql/src/backend/optimizer/path/costsize.c,v 1.211 2009/09/12 22:12:03 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -63,6 +63,7 @@ ...@@ -63,6 +63,7 @@
#include <math.h> #include <math.h>
#include "executor/executor.h"
#include "executor/nodeHash.h" #include "executor/nodeHash.h"
#include "miscadmin.h" #include "miscadmin.h"
#include "nodes/nodeFuncs.h" #include "nodes/nodeFuncs.h"
...@@ -119,6 +120,8 @@ typedef struct ...@@ -119,6 +120,8 @@ typedef struct
static MergeScanSelCache *cached_scansel(PlannerInfo *root, static MergeScanSelCache *cached_scansel(PlannerInfo *root,
RestrictInfo *rinfo, RestrictInfo *rinfo,
PathKey *pathkey); PathKey *pathkey);
static void cost_rescan(PlannerInfo *root, Path *path,
Cost *rescan_startup_cost, Cost *rescan_total_cost);
static bool cost_qual_eval_walker(Node *node, cost_qual_eval_context *context); static bool cost_qual_eval_walker(Node *node, cost_qual_eval_context *context);
static bool adjust_semi_join(PlannerInfo *root, JoinPath *path, static bool adjust_semi_join(PlannerInfo *root, JoinPath *path,
SpecialJoinInfo *sjinfo, SpecialJoinInfo *sjinfo,
...@@ -895,15 +898,26 @@ cost_functionscan(Path *path, PlannerInfo *root, RelOptInfo *baserel) ...@@ -895,15 +898,26 @@ cost_functionscan(Path *path, PlannerInfo *root, RelOptInfo *baserel)
rte = planner_rt_fetch(baserel->relid, root); rte = planner_rt_fetch(baserel->relid, root);
Assert(rte->rtekind == RTE_FUNCTION); Assert(rte->rtekind == RTE_FUNCTION);
/* Estimate costs of executing the function expression */ /*
* Estimate costs of executing the function expression.
*
* Currently, nodeFunctionscan.c always executes the function to
* completion before returning any rows, and caches the results in a
* tuplestore. So the function eval cost is all startup cost, and
* per-row costs are minimal.
*
* XXX in principle we ought to charge tuplestore spill costs if the
* number of rows is large. However, given how phony our rowcount
* estimates for functions tend to be, there's not a lot of point
* in that refinement right now.
*/
cost_qual_eval_node(&exprcost, rte->funcexpr, root); cost_qual_eval_node(&exprcost, rte->funcexpr, root);
startup_cost += exprcost.startup; startup_cost += exprcost.startup + exprcost.per_tuple;
cpu_per_tuple = exprcost.per_tuple;
/* Add scanning CPU costs */ /* Add scanning CPU costs */
startup_cost += baserel->baserestrictcost.startup; startup_cost += baserel->baserestrictcost.startup;
cpu_per_tuple += cpu_tuple_cost + baserel->baserestrictcost.per_tuple; cpu_per_tuple = cpu_tuple_cost + baserel->baserestrictcost.per_tuple;
run_cost += cpu_per_tuple * baserel->tuples; run_cost += cpu_per_tuple * baserel->tuples;
path->startup_cost = startup_cost; path->startup_cost = startup_cost;
...@@ -1176,41 +1190,44 @@ sort_exceeds_work_mem(Sort *sort) ...@@ -1176,41 +1190,44 @@ sort_exceeds_work_mem(Sort *sort)
* *
* If the total volume of data to materialize exceeds work_mem, we will need * If the total volume of data to materialize exceeds work_mem, we will need
* to write it to disk, so the cost is much higher in that case. * to write it to disk, so the cost is much higher in that case.
*
* Note that here we are estimating the costs for the first scan of the
* relation, so the materialization is all overhead --- any savings will
* occur only on rescan, which is estimated in cost_rescan.
*/ */
void void
cost_material(Path *path, cost_material(Path *path,
Cost input_cost, double tuples, int width) Cost input_startup_cost, Cost input_total_cost,
double tuples, int width)
{ {
Cost startup_cost = input_cost; Cost startup_cost = input_startup_cost;
Cost run_cost = 0; Cost run_cost = input_total_cost - input_startup_cost;
double nbytes = relation_byte_size(tuples, width); double nbytes = relation_byte_size(tuples, width);
long work_mem_bytes = work_mem * 1024L; long work_mem_bytes = work_mem * 1024L;
/* disk costs */ /*
* Whether spilling or not, charge 2x cpu_tuple_cost per tuple to reflect
* bookkeeping overhead. (This rate must be more than cpu_tuple_cost;
* if it is exactly the same then there will be a cost tie between
* nestloop with A outer, materialized B inner and nestloop with B outer,
* materialized A inner. The extra cost ensures we'll prefer
* materializing the smaller rel.)
*/
run_cost += 2 * cpu_tuple_cost * tuples;
/*
* If we will spill to disk, charge at the rate of seq_page_cost per page.
* This cost is assumed to be evenly spread through the plan run phase,
* which isn't exactly accurate but our cost model doesn't allow for
* nonuniform costs within the run phase.
*/
if (nbytes > work_mem_bytes) if (nbytes > work_mem_bytes)
{ {
double npages = ceil(nbytes / BLCKSZ); double npages = ceil(nbytes / BLCKSZ);
/* We'll write during startup and read during retrieval */
startup_cost += seq_page_cost * npages;
run_cost += seq_page_cost * npages; run_cost += seq_page_cost * npages;
} }
/*
* Charge a very small amount per inserted tuple, to reflect bookkeeping
* costs. We use cpu_tuple_cost/10 for this. This is needed to break the
* tie that would otherwise exist between nestloop with A outer,
* materialized B inner and nestloop with B outer, materialized A inner.
* The extra cost ensures we'll prefer materializing the smaller rel.
*/
startup_cost += cpu_tuple_cost * 0.1 * tuples;
/*
* Also charge a small amount per extracted tuple. We use cpu_tuple_cost
* so that it doesn't appear worthwhile to materialize a bare seqscan.
*/
run_cost += cpu_tuple_cost * tuples;
path->startup_cost = startup_cost; path->startup_cost = startup_cost;
path->total_cost = startup_cost + run_cost; path->total_cost = startup_cost + run_cost;
} }
...@@ -1400,7 +1417,10 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo) ...@@ -1400,7 +1417,10 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
Path *inner_path = path->innerjoinpath; Path *inner_path = path->innerjoinpath;
Cost startup_cost = 0; Cost startup_cost = 0;
Cost run_cost = 0; Cost run_cost = 0;
Cost inner_rescan_start_cost;
Cost inner_rescan_total_cost;
Cost inner_run_cost; Cost inner_run_cost;
Cost inner_rescan_run_cost;
Cost cpu_per_tuple; Cost cpu_per_tuple;
QualCost restrict_qual_cost; QualCost restrict_qual_cost;
double outer_path_rows = PATH_ROWS(outer_path); double outer_path_rows = PATH_ROWS(outer_path);
...@@ -1413,32 +1433,26 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo) ...@@ -1413,32 +1433,26 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
if (!enable_nestloop) if (!enable_nestloop)
startup_cost += disable_cost; startup_cost += disable_cost;
/* estimate costs to rescan the inner relation */
cost_rescan(root, inner_path,
&inner_rescan_start_cost,
&inner_rescan_total_cost);
/* cost of source data */ /* cost of source data */
/* /*
* NOTE: clearly, we must pay both outer and inner paths' startup_cost * NOTE: clearly, we must pay both outer and inner paths' startup_cost
* before we can start returning tuples, so the join's startup cost is * before we can start returning tuples, so the join's startup cost is
* their sum. What's not so clear is whether the inner path's * their sum. We'll also pay the inner path's rescan startup cost
* startup_cost must be paid again on each rescan of the inner path. This * multiple times.
* is not true if the inner path is materialized or is a hashjoin, but
* probably is true otherwise.
*/ */
startup_cost += outer_path->startup_cost + inner_path->startup_cost; startup_cost += outer_path->startup_cost + inner_path->startup_cost;
run_cost += outer_path->total_cost - outer_path->startup_cost; run_cost += outer_path->total_cost - outer_path->startup_cost;
if (IsA(inner_path, MaterialPath) || if (outer_path_rows > 1)
IsA(inner_path, HashPath)) run_cost += (outer_path_rows - 1) * inner_rescan_start_cost;
{
/* charge only run cost for each iteration of inner path */
}
else
{
/*
* charge startup cost for each iteration of inner path, except we
* already charged the first startup_cost in our own startup
*/
run_cost += (outer_path_rows - 1) * inner_path->startup_cost;
}
inner_run_cost = inner_path->total_cost - inner_path->startup_cost; inner_run_cost = inner_path->total_cost - inner_path->startup_cost;
inner_rescan_run_cost = inner_rescan_total_cost - inner_rescan_start_cost;
if (adjust_semi_join(root, path, sjinfo, if (adjust_semi_join(root, path, sjinfo,
&outer_match_frac, &outer_match_frac,
...@@ -1458,12 +1472,22 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo) ...@@ -1458,12 +1472,22 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
* that fraction. (If we used a larger fuzz factor, we'd have to * that fraction. (If we used a larger fuzz factor, we'd have to
* clamp inner_scan_frac to at most 1.0; but since match_count is at * clamp inner_scan_frac to at most 1.0; but since match_count is at
* least 1, no such clamp is needed now.) * least 1, no such clamp is needed now.)
*
* A complicating factor is that rescans may be cheaper than first
* scans. If we never scan all the way to the end of the inner rel,
* it might be (depending on the plan type) that we'd never pay the
* whole inner first-scan run cost. However it is difficult to
* estimate whether that will happen, so be conservative and always
* charge the whole first-scan cost once.
*/ */
run_cost += inner_run_cost;
outer_matched_rows = rint(outer_path_rows * outer_match_frac); outer_matched_rows = rint(outer_path_rows * outer_match_frac);
inner_scan_frac = 2.0 / (match_count + 1.0); inner_scan_frac = 2.0 / (match_count + 1.0);
/* Add inner run cost for outer tuples having matches */ /* Add inner run cost for additional outer tuples having matches */
run_cost += outer_matched_rows * inner_run_cost * inner_scan_frac; if (outer_matched_rows > 1)
run_cost += (outer_matched_rows - 1) * inner_rescan_run_cost * inner_scan_frac;
/* Compute number of tuples processed (not number emitted!) */ /* Compute number of tuples processed (not number emitted!) */
ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac; ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac;
...@@ -1479,13 +1503,16 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo) ...@@ -1479,13 +1503,16 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
if (indexed_join_quals) if (indexed_join_quals)
{ {
run_cost += (outer_path_rows - outer_matched_rows) * run_cost += (outer_path_rows - outer_matched_rows) *
inner_run_cost / inner_path_rows; inner_rescan_run_cost / inner_path_rows;
/* We won't be evaluating any quals at all for these rows */ /*
* We won't be evaluating any quals at all for these rows,
* so don't add them to ntuples.
*/
} }
else else
{ {
run_cost += (outer_path_rows - outer_matched_rows) * run_cost += (outer_path_rows - outer_matched_rows) *
inner_run_cost; inner_rescan_run_cost;
ntuples += (outer_path_rows - outer_matched_rows) * ntuples += (outer_path_rows - outer_matched_rows) *
inner_path_rows; inner_path_rows;
} }
...@@ -1493,7 +1520,9 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo) ...@@ -1493,7 +1520,9 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
else else
{ {
/* Normal case; we'll scan whole input rel for each outer row */ /* Normal case; we'll scan whole input rel for each outer row */
run_cost += outer_path_rows * inner_run_cost; run_cost += inner_run_cost;
if (outer_path_rows > 1)
run_cost += (outer_path_rows - 1) * inner_rescan_run_cost;
/* Compute number of tuples processed (not number emitted!) */ /* Compute number of tuples processed (not number emitted!) */
ntuples = outer_path_rows * inner_path_rows; ntuples = outer_path_rows * inner_path_rows;
...@@ -2190,13 +2219,13 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan) ...@@ -2190,13 +2219,13 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
/* /*
* Also account for subplan's startup cost. If the subplan is * Also account for subplan's startup cost. If the subplan is
* uncorrelated or undirect correlated, AND its topmost node is a Sort * uncorrelated or undirect correlated, AND its topmost node is one
* or Material node, assume that we'll only need to pay its startup * that materializes its output, assume that we'll only need to pay
* cost once; otherwise assume we pay the startup cost every time. * its startup cost once; otherwise assume we pay the startup cost
* every time.
*/ */
if (subplan->parParam == NIL && if (subplan->parParam == NIL &&
(IsA(plan, Sort) || ExecMaterializesOutput(nodeTag(plan)))
IsA(plan, Material)))
sp_cost.startup += plan->startup_cost; sp_cost.startup += plan->startup_cost;
else else
sp_cost.per_tuple += plan->startup_cost; sp_cost.per_tuple += plan->startup_cost;
...@@ -2207,6 +2236,81 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan) ...@@ -2207,6 +2236,81 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
} }
/*
* cost_rescan
* Given a finished Path, estimate the costs of rescanning it after
* having done so the first time. For some Path types a rescan is
* cheaper than an original scan (if no parameters change), and this
* function embodies knowledge about that. The default is to return
* the same costs stored in the Path. (Note that the cost estimates
* actually stored in Paths are always for first scans.)
*
* This function is not currently intended to model effects such as rescans
* being cheaper due to disk block caching; what we are concerned with is
* plan types wherein the executor caches results explicitly, or doesn't
* redo startup calculations, etc.
*/
static void
cost_rescan(PlannerInfo *root, Path *path,
Cost *rescan_startup_cost, /* output parameters */
Cost *rescan_total_cost)
{
switch (path->pathtype)
{
case T_FunctionScan:
/*
* Currently, nodeFunctionscan.c always executes the function
* to completion before returning any rows, and caches the
* results in a tuplestore. So the function eval cost is
* all startup cost and isn't paid over again on rescans.
* However, all run costs will be paid over again.
*/
*rescan_startup_cost = 0;
*rescan_total_cost = path->total_cost - path->startup_cost;
break;
case T_HashJoin:
/*
* Assume that all of the startup cost represents hash table
* building, which we won't have to do over.
*/
*rescan_startup_cost = 0;
*rescan_total_cost = path->total_cost - path->startup_cost;
break;
case T_Material:
case T_CteScan:
case T_WorkTableScan:
case T_Sort:
{
/*
* These plan types materialize their final result in a
* tuplestore or tuplesort object. So the rescan cost is only
* cpu_tuple_cost per tuple, unless the result is large enough
* to spill to disk.
*/
Cost run_cost = cpu_tuple_cost * path->parent->rows;
double nbytes = relation_byte_size(path->parent->rows,
path->parent->width);
long work_mem_bytes = work_mem * 1024L;
if (nbytes > work_mem_bytes)
{
/* It will spill, so account for re-read cost */
double npages = ceil(nbytes / BLCKSZ);
run_cost += seq_page_cost * npages;
}
*rescan_startup_cost = 0;
*rescan_total_cost = run_cost;
}
break;
default:
*rescan_startup_cost = path->startup_cost;
*rescan_total_cost = path->total_cost;
break;
}
}
/* /*
* cost_qual_eval * cost_qual_eval
* Estimate the CPU costs of evaluating a WHERE clause. * Estimate the CPU costs of evaluating a WHERE clause.
......
src/backend/optimizer/path/joinpath.c
View file @ 9bb34281
...@@ -8,7 +8,7 @@ ...@@ -8,7 +8,7 @@
* *
* *
* IDENTIFICATION * IDENTIFICATION
* $PostgreSQL: pgsql/src/backend/optimizer/path/joinpath.c,v 1.122 2009/06/11 14:48:59 momjian Exp $ * $PostgreSQL: pgsql/src/backend/optimizer/path/joinpath.c,v 1.123 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -16,6 +16,7 @@ ...@@ -16,6 +16,7 @@
#include <math.h> #include <math.h>
#include "executor/executor.h"
#include "optimizer/cost.h" #include "optimizer/cost.h"
#include "optimizer/pathnode.h" #include "optimizer/pathnode.h"
#include "optimizer/paths.h" #include "optimizer/paths.h"
...@@ -405,18 +406,10 @@ match_unsorted_outer(PlannerInfo *root, ...@@ -405,18 +406,10 @@ match_unsorted_outer(PlannerInfo *root,
else if (nestjoinOK) else if (nestjoinOK)
{ {
/* /*
* If the cheapest inner path is a join or seqscan, we should consider * Consider materializing the cheapest inner path, unless it is one
* materializing it. (This is a heuristic: we could consider it * that materializes its output anyway.
* always, but for inner indexscans it's probably a waste of time.)
* Also skip it if the inner path materializes its output anyway.
*/ */
if (!(inner_cheapest_total->pathtype == T_IndexScan || if (!ExecMaterializesOutput(inner_cheapest_total->pathtype))
inner_cheapest_total->pathtype == T_BitmapHeapScan ||
inner_cheapest_total->pathtype == T_TidScan ||
inner_cheapest_total->pathtype == T_Material ||
inner_cheapest_total->pathtype == T_FunctionScan ||
inner_cheapest_total->pathtype == T_CteScan ||
inner_cheapest_total->pathtype == T_WorkTableScan))
matpath = (Path *) matpath = (Path *)
create_material_path(innerrel, inner_cheapest_total); create_material_path(innerrel, inner_cheapest_total);
......
src/backend/optimizer/plan/createplan.c
View file @ 9bb34281
...@@ -10,7 +10,7 @@ ...@@ -10,7 +10,7 @@
* *
* *
* IDENTIFICATION * IDENTIFICATION
* $PostgreSQL: pgsql/src/backend/optimizer/plan/createplan.c,v 1.261 2009/07/17 23:19:34 tgl Exp $ * $PostgreSQL: pgsql/src/backend/optimizer/plan/createplan.c,v 1.262 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -3266,6 +3266,7 @@ materialize_finished_plan(Plan *subplan) ...@@ -3266,6 +3266,7 @@ materialize_finished_plan(Plan *subplan)
/* Set cost data */ /* Set cost data */
cost_material(&matpath, cost_material(&matpath,
subplan->startup_cost,
subplan->total_cost, subplan->total_cost,
subplan->plan_rows, subplan->plan_rows,
subplan->plan_width); subplan->plan_width);
......
src/backend/optimizer/plan/subselect.c
View file @ 9bb34281
...@@ -7,7 +7,7 @@ ...@@ -7,7 +7,7 @@
* Portions Copyright (c) 1994, Regents of the University of California * Portions Copyright (c) 1994, Regents of the University of California
* *
* IDENTIFICATION * IDENTIFICATION
* $PostgreSQL: pgsql/src/backend/optimizer/plan/subselect.c,v 1.152 2009/07/16 06:33:43 petere Exp $ * $PostgreSQL: pgsql/src/backend/optimizer/plan/subselect.c,v 1.153 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -15,6 +15,7 @@ ...@@ -15,6 +15,7 @@
#include "catalog/pg_operator.h" #include "catalog/pg_operator.h"
#include "catalog/pg_type.h" #include "catalog/pg_type.h"
#include "executor/executor.h"
#include "miscadmin.h" #include "miscadmin.h"
#include "nodes/makefuncs.h" #include "nodes/makefuncs.h"
#include "nodes/nodeFuncs.h" #include "nodes/nodeFuncs.h"
...@@ -564,33 +565,16 @@ build_subplan(PlannerInfo *root, Plan *plan, List *rtable, ...@@ -564,33 +565,16 @@ build_subplan(PlannerInfo *root, Plan *plan, List *rtable,
splan->useHashTable = true; splan->useHashTable = true;
/* /*
* Otherwise, we have the option to tack a MATERIAL node onto the top * Otherwise, we have the option to tack a Material node onto the top
* of the subplan, to reduce the cost of reading it repeatedly. This * of the subplan, to reduce the cost of reading it repeatedly. This
* is pointless for a direct-correlated subplan, since we'd have to * is pointless for a direct-correlated subplan, since we'd have to
* recompute its results each time anyway. For uncorrelated/undirect * recompute its results each time anyway. For uncorrelated/undirect
* correlated subplans, we add MATERIAL unless the subplan's top plan * correlated subplans, we add Material unless the subplan's top plan
* node would materialize its output anyway. * node would materialize its output anyway.
*/ */
else if (splan->parParam == NIL) else if (splan->parParam == NIL &&
{ !ExecMaterializesOutput(nodeTag(plan)))
bool use_material;
switch (nodeTag(plan))
{
case T_Material:
case T_FunctionScan:
case T_CteScan:
case T_WorkTableScan:
case T_Sort:
use_material = false;
break;
default:
use_material = true;
break;
}
if (use_material)
plan = materialize_finished_plan(plan); plan = materialize_finished_plan(plan);
}
result = (Node *) splan; result = (Node *) splan;
isInitPlan = false; isInitPlan = false;
......
src/backend/optimizer/util/pathnode.c
View file @ 9bb34281
...@@ -8,7 +8,7 @@ ...@@ -8,7 +8,7 @@
* *
* *
* IDENTIFICATION * IDENTIFICATION
* $PostgreSQL: pgsql/src/backend/optimizer/util/pathnode.c,v 1.152 2009/06/11 14:48:59 momjian Exp $ * $PostgreSQL: pgsql/src/backend/optimizer/util/pathnode.c,v 1.153 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -711,6 +711,7 @@ create_material_path(RelOptInfo *rel, Path *subpath) ...@@ -711,6 +711,7 @@ create_material_path(RelOptInfo *rel, Path *subpath)
pathnode->subpath = subpath; pathnode->subpath = subpath;
cost_material(&pathnode->path, cost_material(&pathnode->path,
subpath->startup_cost,
subpath->total_cost, subpath->total_cost,
rel->rows, rel->rows,
rel->width); rel->width);
...@@ -1424,7 +1425,8 @@ create_mergejoin_path(PlannerInfo *root, ...@@ -1424,7 +1425,8 @@ create_mergejoin_path(PlannerInfo *root,
* cost_mergejoin will avoid choosing anyway). Therefore * cost_mergejoin will avoid choosing anyway). Therefore
* cost_material's cost estimate is bogus and we should charge just * cost_material's cost estimate is bogus and we should charge just
* cpu_tuple_cost per tuple. (Keep this estimate in sync with similar * cpu_tuple_cost per tuple. (Keep this estimate in sync with similar
* ones in cost_mergejoin and create_mergejoin_plan.) * ones in cost_mergejoin and create_mergejoin_plan; also see
* cost_rescan.)
*/ */
mpath->startup_cost = inner_path->startup_cost; mpath->startup_cost = inner_path->startup_cost;
mpath->total_cost = inner_path->total_cost; mpath->total_cost = inner_path->total_cost;
......
src/include/executor/executor.h
View file @ 9bb34281
...@@ -7,7 +7,7 @@ ...@@ -7,7 +7,7 @@
* Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California * Portions Copyright (c) 1994, Regents of the University of California
* *
* $PostgreSQL: pgsql/src/include/executor/executor.h,v 1.158 2009/07/29 20:56:20 tgl Exp $ * $PostgreSQL: pgsql/src/include/executor/executor.h,v 1.159 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -83,6 +83,7 @@ extern void ExecMarkPos(PlanState *node); ...@@ -83,6 +83,7 @@ extern void ExecMarkPos(PlanState *node);
extern void ExecRestrPos(PlanState *node); extern void ExecRestrPos(PlanState *node);
extern bool ExecSupportsMarkRestore(NodeTag plantype); extern bool ExecSupportsMarkRestore(NodeTag plantype);
extern bool ExecSupportsBackwardScan(Plan *node); extern bool ExecSupportsBackwardScan(Plan *node);
extern bool ExecMaterializesOutput(NodeTag plantype);
/* /*
* prototypes from functions in execCurrent.c * prototypes from functions in execCurrent.c
......
src/include/optimizer/cost.h
View file @ 9bb34281
...@@ -7,7 +7,7 @@ ...@@ -7,7 +7,7 @@
* Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California * Portions Copyright (c) 1994, Regents of the University of California
* *
* $PostgreSQL: pgsql/src/include/optimizer/cost.h,v 1.97 2009/06/11 14:49:11 momjian Exp $ * $PostgreSQL: pgsql/src/include/optimizer/cost.h,v 1.98 2009/09/12 22:12:04 tgl Exp $
* *
*------------------------------------------------------------------------- *-------------------------------------------------------------------------
*/ */
...@@ -86,7 +86,8 @@ extern void cost_sort(Path *path, PlannerInfo *root, ...@@ -86,7 +86,8 @@ extern void cost_sort(Path *path, PlannerInfo *root,
double limit_tuples); double limit_tuples);
extern bool sort_exceeds_work_mem(Sort *sort); extern bool sort_exceeds_work_mem(Sort *sort);
extern void cost_material(Path *path, extern void cost_material(Path *path,
Cost input_cost, double tuples, int width); Cost input_startup_cost, Cost input_total_cost,
double tuples, int width);
extern void cost_agg(Path *path, PlannerInfo *root, extern void cost_agg(Path *path, PlannerInfo *root,
AggStrategy aggstrategy, int numAggs, AggStrategy aggstrategy, int numAggs,
int numGroupCols, double numGroups, int numGroupCols, double numGroups,
......
src/test/regress/expected/geometry.out
View file @ 9bb34281
...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation ...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
twenty | rotation twenty | rotation
--------+---------------------------------------------------------------------- --------+----------------------------------------------------------------------
| (0,-0),(-0.2,-0.2) | (0,-0),(-0.2,-0.2)
| (-0.1,-0.1),(-0.3,-0.3)
| (-0.25,-0.25),(-0.25,-0.35)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.08,-0),(0,-0.56) | (0.08,-0),(0,-0.56)
| (0.12,-0.28),(0.04,-0.84)
| (0.26,-0.7),(0.1,-0.82)
| (0.12,-0.84),(0.12,-0.84)
| (0.0651176557644,0),(0,-0.0483449262493) | (0.0651176557644,0),(0,-0.0483449262493)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (-0,0.0828402366864),(-0.201183431953,0) | (-0,0.0828402366864),(-0.201183431953,0)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.2,0),(0,0) | (0.2,0),(0,0)
| (-0.1,-0.1),(-0.3,-0.3)
| (0.12,-0.28),(0.04,-0.84)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (0.3,0),(0.1,0) | (0.3,0),(0.1,0)
| (-0.25,-0.25),(-0.25,-0.35)
| (0.26,-0.7),(0.1,-0.82)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (0.3,0.05),(0.25,0) | (0.3,0.05),(0.25,0)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.12,-0.84),(0.12,-0.84)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.3,0),(0.3,0) | (0.3,0),(0.3,0)
(20 rows) (20 rows)
......
src/test/regress/expected/geometry_1.out
View file @ 9bb34281
...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation ...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
twenty | rotation twenty | rotation
--------+---------------------------------------------------------------------- --------+----------------------------------------------------------------------
| (0,0),(-0.2,-0.2) | (0,0),(-0.2,-0.2)
| (-0.1,-0.1),(-0.3,-0.3)
| (-0.25,-0.25),(-0.25,-0.35)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.08,0),(0,-0.56) | (0.08,0),(0,-0.56)
| (0.12,-0.28),(0.04,-0.84)
| (0.26,-0.7),(0.1,-0.82)
| (0.12,-0.84),(0.12,-0.84)
| (0.0651176557644,0),(0,-0.0483449262493) | (0.0651176557644,0),(0,-0.0483449262493)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (0,0.0828402366864),(-0.201183431953,0) | (0,0.0828402366864),(-0.201183431953,0)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.2,0),(0,0) | (0.2,0),(0,0)
| (-0.1,-0.1),(-0.3,-0.3)
| (0.12,-0.28),(0.04,-0.84)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (0.3,0),(0.1,0) | (0.3,0),(0.1,0)
| (-0.25,-0.25),(-0.25,-0.35)
| (0.26,-0.7),(0.1,-0.82)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (0.3,0.05),(0.25,0) | (0.3,0.05),(0.25,0)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.12,-0.84),(0.12,-0.84)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.3,0),(0.3,0) | (0.3,0),(0.3,0)
(20 rows) (20 rows)
......
src/test/regress/expected/geometry_2.out
View file @ 9bb34281
...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation ...@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
twenty | rotation twenty | rotation
--------+---------------------------------------------------------------------- --------+----------------------------------------------------------------------
| (0,-0),(-0.2,-0.2) | (0,-0),(-0.2,-0.2)
| (-0.1,-0.1),(-0.3,-0.3)
| (-0.25,-0.25),(-0.25,-0.35)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.08,-0),(0,-0.56) | (0.08,-0),(0,-0.56)
| (0.12,-0.28),(0.04,-0.84)
| (0.26,-0.7),(0.1,-0.82)
| (0.12,-0.84),(0.12,-0.84)
| (0.0651176557644,0),(0,-0.0483449262493) | (0.0651176557644,0),(0,-0.0483449262493)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (-0,0.0828402366864),(-0.201183431953,0) | (-0,0.0828402366864),(-0.201183431953,0)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.2,0),(0,0) | (0.2,0),(0,0)
| (-0.1,-0.1),(-0.3,-0.3)
| (0.12,-0.28),(0.04,-0.84)
| (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
| (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
| (0.3,0),(0.1,0) | (0.3,0),(0.1,0)
| (-0.25,-0.25),(-0.25,-0.35)
| (0.26,-0.7),(0.1,-0.82)
| (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
| (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
| (0.3,0.05),(0.25,0) | (0.3,0.05),(0.25,0)
| (-0.3,-0.3),(-0.3,-0.3)
| (0.12,-0.84),(0.12,-0.84)
| (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
| (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
| (0.3,0),(0.3,0) | (0.3,0),(0.3,0)
(20 rows) (20 rows)
......
src/test/regress/expected/join.out
View file @ 9bb34281
...@@ -662,895 +662,895 @@ SELECT '' AS "xxx", * ...@@ -662,895 +662,895 @@ SELECT '' AS "xxx", *
xxx | i | j | t | i | k | i | k xxx | i | j | t | i | k | i | k
-----+---+---+-------+---+----+---+---- -----+---+---+-------+---+----+---+----
| 1 | 4 | one | 1 | -1 | 1 | -1 | 1 | 4 | one | 1 | -1 | 1 | -1
| 2 | 3 | two | 1 | -1 | 1 | -1 | 1 | 4 | one | 2 | 2 | 1 | -1
| 3 | 2 | three | 1 | -1 | 1 | -1 | 1 | 4 | one | 3 | -3 | 1 | -1
| 4 | 1 | four | 1 | -1 | 1 | -1 | 1 | 4 | one | 2 | 4 | 1 | -1
| 5 | 0 | five | 1 | -1 | 1 | -1 | 1 | 4 | one | 5 | -5 | 1 | -1
| 6 | 6 | six | 1 | -1 | 1 | -1 | 1 | 4 | one | 5 | -5 | 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 | 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 | 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 | 1 | 4 | one | | 0 | 1 | -1
| 2 | 3 | two | 1 | -1 | 1 | -1
| 2 | 3 | two | 2 | 2 | 1 | -1
| 2 | 3 | two | 3 | -3 | 1 | -1
| 2 | 3 | two | 2 | 4 | 1 | -1
| 2 | 3 | two | 5 | -5 | 1 | -1
| 2 | 3 | two | 5 | -5 | 1 | -1
| 2 | 3 | two | 0 | | 1 | -1
| 2 | 3 | two | | | 1 | -1
| 2 | 3 | two | | 0 | 1 | -1 | 2 | 3 | two | | 0 | 1 | -1
| 3 | 2 | three | 1 | -1 | 1 | -1
| 3 | 2 | three | 2 | 2 | 1 | -1
| 3 | 2 | three | 3 | -3 | 1 | -1
| 3 | 2 | three | 2 | 4 | 1 | -1
| 3 | 2 | three | 5 | -5 | 1 | -1
| 3 | 2 | three | 5 | -5 | 1 | -1
| 3 | 2 | three | 0 | | 1 | -1
| 3 | 2 | three | | | 1 | -1
| 3 | 2 | three | | 0 | 1 | -1 | 3 | 2 | three | | 0 | 1 | -1
| 4 | 1 | four | 1 | -1 | 1 | -1
| 4 | 1 | four | 2 | 2 | 1 | -1
| 4 | 1 | four | 3 | -3 | 1 | -1
| 4 | 1 | four | 2 | 4 | 1 | -1
| 4 | 1 | four | 5 | -5 | 1 | -1
| 4 | 1 | four | 5 | -5 | 1 | -1
| 4 | 1 | four | 0 | | 1 | -1
| 4 | 1 | four | | | 1 | -1
| 4 | 1 | four | | 0 | 1 | -1 | 4 | 1 | four | | 0 | 1 | -1
| 5 | 0 | five | 1 | -1 | 1 | -1
| 5 | 0 | five | 2 | 2 | 1 | -1
| 5 | 0 | five | 3 | -3 | 1 | -1
| 5 | 0 | five | 2 | 4 | 1 | -1
| 5 | 0 | five | 5 | -5 | 1 | -1
| 5 | 0 | five | 5 | -5 | 1 | -1
| 5 | 0 | five | 0 | | 1 | -1
| 5 | 0 | five | | | 1 | -1
| 5 | 0 | five | | 0 | 1 | -1 | 5 | 0 | five | | 0 | 1 | -1
| 6 | 6 | six | 1 | -1 | 1 | -1
| 6 | 6 | six | 2 | 2 | 1 | -1
| 6 | 6 | six | 3 | -3 | 1 | -1
| 6 | 6 | six | 2 | 4 | 1 | -1
| 6 | 6 | six | 5 | -5 | 1 | -1
| 6 | 6 | six | 5 | -5 | 1 | -1
| 6 | 6 | six | 0 | | 1 | -1
| 6 | 6 | six | | | 1 | -1
| 6 | 6 | six | | 0 | 1 | -1 | 6 | 6 | six | | 0 | 1 | -1
| 7 | 7 | seven | 1 | -1 | 1 | -1
| 7 | 7 | seven | 2 | 2 | 1 | -1
| 7 | 7 | seven | 3 | -3 | 1 | -1
| 7 | 7 | seven | 2 | 4 | 1 | -1
| 7 | 7 | seven | 5 | -5 | 1 | -1
| 7 | 7 | seven | 5 | -5 | 1 | -1
| 7 | 7 | seven | 0 | | 1 | -1
| 7 | 7 | seven | | | 1 | -1
| 7 | 7 | seven | | 0 | 1 | -1 | 7 | 7 | seven | | 0 | 1 | -1
| 8 | 8 | eight | 1 | -1 | 1 | -1
| 8 | 8 | eight | 2 | 2 | 1 | -1
| 8 | 8 | eight | 3 | -3 | 1 | -1
| 8 | 8 | eight | 2 | 4 | 1 | -1
| 8 | 8 | eight | 5 | -5 | 1 | -1
| 8 | 8 | eight | 5 | -5 | 1 | -1
| 8 | 8 | eight | 0 | | 1 | -1
| 8 | 8 | eight | | | 1 | -1
| 8 | 8 | eight | | 0 | 1 | -1 | 8 | 8 | eight | | 0 | 1 | -1
| 0 | | zero | 1 | -1 | 1 | -1
| 0 | | zero | 2 | 2 | 1 | -1
| 0 | | zero | 3 | -3 | 1 | -1
| 0 | | zero | 2 | 4 | 1 | -1
| 0 | | zero | 5 | -5 | 1 | -1
| 0 | | zero | 5 | -5 | 1 | -1
| 0 | | zero | 0 | | 1 | -1
| 0 | | zero | | | 1 | -1
| 0 | | zero | | 0 | 1 | -1 | 0 | | zero | | 0 | 1 | -1
| | | null | 1 | -1 | 1 | -1
| | | null | 2 | 2 | 1 | -1
| | | null | 3 | -3 | 1 | -1
| | | null | 2 | 4 | 1 | -1
| | | null | 5 | -5 | 1 | -1
| | | null | 5 | -5 | 1 | -1
| | | null | 0 | | 1 | -1
| | | null | | | 1 | -1
| | | null | | 0 | 1 | -1 | | | null | | 0 | 1 | -1
| | 0 | zero | 1 | -1 | 1 | -1
| | 0 | zero | 2 | 2 | 1 | -1
| | 0 | zero | 3 | -3 | 1 | -1
| | 0 | zero | 2 | 4 | 1 | -1
| | 0 | zero | 5 | -5 | 1 | -1
| | 0 | zero | 5 | -5 | 1 | -1
| | 0 | zero | 0 | | 1 | -1
| | 0 | zero | | | 1 | -1
| | 0 | zero | | 0 | 1 | -1 | | 0 | zero | | 0 | 1 | -1
| 1 | 4 | one | 1 | -1 | 2 | 2
| 1 | 4 | one | 2 | 2 | 2 | 2
| 1 | 4 | one | 3 | -3 | 2 | 2
| 1 | 4 | one | 2 | 4 | 2 | 2
| 1 | 4 | one | 5 | -5 | 2 | 2
| 1 | 4 | one | 5 | -5 | 2 | 2
| 1 | 4 | one | 0 | | 2 | 2
| 1 | 4 | one | | | 2 | 2
| 1 | 4 | one | | 0 | 2 | 2 | 1 | 4 | one | | 0 | 2 | 2
| 2 | 3 | two | 1 | -1 | 2 | 2
| 2 | 3 | two | 2 | 2 | 2 | 2
| 2 | 3 | two | 3 | -3 | 2 | 2
| 2 | 3 | two | 2 | 4 | 2 | 2
| 2 | 3 | two | 5 | -5 | 2 | 2
| 2 | 3 | two | 5 | -5 | 2 | 2
| 2 | 3 | two | 0 | | 2 | 2
| 2 | 3 | two | | | 2 | 2
| 2 | 3 | two | | 0 | 2 | 2 | 2 | 3 | two | | 0 | 2 | 2
| 3 | 2 | three | 1 | -1 | 2 | 2
| 3 | 2 | three | 2 | 2 | 2 | 2
| 3 | 2 | three | 3 | -3 | 2 | 2
| 3 | 2 | three | 2 | 4 | 2 | 2
| 3 | 2 | three | 5 | -5 | 2 | 2
| 3 | 2 | three | 5 | -5 | 2 | 2
| 3 | 2 | three | 0 | | 2 | 2
| 3 | 2 | three | | | 2 | 2
| 3 | 2 | three | | 0 | 2 | 2 | 3 | 2 | three | | 0 | 2 | 2
| 4 | 1 | four | 1 | -1 | 2 | 2
| 4 | 1 | four | 2 | 2 | 2 | 2
| 4 | 1 | four | 3 | -3 | 2 | 2
| 4 | 1 | four | 2 | 4 | 2 | 2
| 4 | 1 | four | 5 | -5 | 2 | 2
| 4 | 1 | four | 5 | -5 | 2 | 2
| 4 | 1 | four | 0 | | 2 | 2
| 4 | 1 | four | | | 2 | 2
| 4 | 1 | four | | 0 | 2 | 2 | 4 | 1 | four | | 0 | 2 | 2
| 5 | 0 | five | 1 | -1 | 2 | 2
| 5 | 0 | five | 2 | 2 | 2 | 2
| 5 | 0 | five | 3 | -3 | 2 | 2
| 5 | 0 | five | 2 | 4 | 2 | 2
| 5 | 0 | five | 5 | -5 | 2 | 2
| 5 | 0 | five | 5 | -5 | 2 | 2
| 5 | 0 | five | 0 | | 2 | 2
| 5 | 0 | five | | | 2 | 2
| 5 | 0 | five | | 0 | 2 | 2 | 5 | 0 | five | | 0 | 2 | 2
| 6 | 6 | six | 1 | -1 | 2 | 2
| 6 | 6 | six | 2 | 2 | 2 | 2
| 6 | 6 | six | 3 | -3 | 2 | 2
| 6 | 6 | six | 2 | 4 | 2 | 2
| 6 | 6 | six | 5 | -5 | 2 | 2
| 6 | 6 | six | 5 | -5 | 2 | 2
| 6 | 6 | six | 0 | | 2 | 2
| 6 | 6 | six | | | 2 | 2
| 6 | 6 | six | | 0 | 2 | 2 | 6 | 6 | six | | 0 | 2 | 2
| 7 | 7 | seven | 1 | -1 | 2 | 2
| 7 | 7 | seven | 2 | 2 | 2 | 2
| 7 | 7 | seven | 3 | -3 | 2 | 2
| 7 | 7 | seven | 2 | 4 | 2 | 2
| 7 | 7 | seven | 5 | -5 | 2 | 2
| 7 | 7 | seven | 5 | -5 | 2 | 2
| 7 | 7 | seven | 0 | | 2 | 2
| 7 | 7 | seven | | | 2 | 2
| 7 | 7 | seven | | 0 | 2 | 2 | 7 | 7 | seven | | 0 | 2 | 2
| 8 | 8 | eight | 1 | -1 | 2 | 2
| 8 | 8 | eight | 2 | 2 | 2 | 2
| 8 | 8 | eight | 3 | -3 | 2 | 2
| 8 | 8 | eight | 2 | 4 | 2 | 2
| 8 | 8 | eight | 5 | -5 | 2 | 2
| 8 | 8 | eight | 5 | -5 | 2 | 2
| 8 | 8 | eight | 0 | | 2 | 2
| 8 | 8 | eight | | | 2 | 2
| 8 | 8 | eight | | 0 | 2 | 2 | 8 | 8 | eight | | 0 | 2 | 2
| 0 | | zero | 1 | -1 | 2 | 2
| 0 | | zero | 2 | 2 | 2 | 2
| 0 | | zero | 3 | -3 | 2 | 2
| 0 | | zero | 2 | 4 | 2 | 2
| 0 | | zero | 5 | -5 | 2 | 2
| 0 | | zero | 5 | -5 | 2 | 2
| 0 | | zero | 0 | | 2 | 2
| 0 | | zero | | | 2 | 2
| 0 | | zero | | 0 | 2 | 2 | 0 | | zero | | 0 | 2 | 2
| | | null | 1 | -1 | 2 | 2
| | | null | 2 | 2 | 2 | 2
| | | null | 3 | -3 | 2 | 2
| | | null | 2 | 4 | 2 | 2
| | | null | 5 | -5 | 2 | 2
| | | null | 5 | -5 | 2 | 2
| | | null | 0 | | 2 | 2
| | | null | | | 2 | 2
| | | null | | 0 | 2 | 2 | | | null | | 0 | 2 | 2
| | 0 | zero | 1 | -1 | 2 | 2
| | 0 | zero | 2 | 2 | 2 | 2
| | 0 | zero | 3 | -3 | 2 | 2
| | 0 | zero | 2 | 4 | 2 | 2
| | 0 | zero | 5 | -5 | 2 | 2
| | 0 | zero | 5 | -5 | 2 | 2
| | 0 | zero | 0 | | 2 | 2
| | 0 | zero | | | 2 | 2
| | 0 | zero | | 0 | 2 | 2 | | 0 | zero | | 0 | 2 | 2
| 1 | 4 | one | 1 | -1 | 3 | -3
| 1 | 4 | one | 2 | 2 | 3 | -3
| 1 | 4 | one | 3 | -3 | 3 | -3
| 1 | 4 | one | 2 | 4 | 3 | -3
| 1 | 4 | one | 5 | -5 | 3 | -3
| 1 | 4 | one | 5 | -5 | 3 | -3
| 1 | 4 | one | 0 | | 3 | -3
| 1 | 4 | one | | | 3 | -3
| 1 | 4 | one | | 0 | 3 | -3 | 1 | 4 | one | | 0 | 3 | -3
| 2 | 3 | two | 1 | -1 | 3 | -3
| 2 | 3 | two | 2 | 2 | 3 | -3
| 2 | 3 | two | 3 | -3 | 3 | -3
| 2 | 3 | two | 2 | 4 | 3 | -3
| 2 | 3 | two | 5 | -5 | 3 | -3
| 2 | 3 | two | 5 | -5 | 3 | -3
| 2 | 3 | two | 0 | | 3 | -3
| 2 | 3 | two | | | 3 | -3
| 2 | 3 | two | | 0 | 3 | -3 | 2 | 3 | two | | 0 | 3 | -3
| 3 | 2 | three | 1 | -1 | 3 | -3
| 3 | 2 | three | 2 | 2 | 3 | -3
| 3 | 2 | three | 3 | -3 | 3 | -3
| 3 | 2 | three | 2 | 4 | 3 | -3
| 3 | 2 | three | 5 | -5 | 3 | -3
| 3 | 2 | three | 5 | -5 | 3 | -3
| 3 | 2 | three | 0 | | 3 | -3
| 3 | 2 | three | | | 3 | -3
| 3 | 2 | three | | 0 | 3 | -3 | 3 | 2 | three | | 0 | 3 | -3
| 4 | 1 | four | 1 | -1 | 3 | -3
| 4 | 1 | four | 2 | 2 | 3 | -3
| 4 | 1 | four | 3 | -3 | 3 | -3
| 4 | 1 | four | 2 | 4 | 3 | -3
| 4 | 1 | four | 5 | -5 | 3 | -3
| 4 | 1 | four | 5 | -5 | 3 | -3
| 4 | 1 | four | 0 | | 3 | -3
| 4 | 1 | four | | | 3 | -3
| 4 | 1 | four | | 0 | 3 | -3 | 4 | 1 | four | | 0 | 3 | -3
| 5 | 0 | five | 1 | -1 | 3 | -3
| 5 | 0 | five | 2 | 2 | 3 | -3
| 5 | 0 | five | 3 | -3 | 3 | -3
| 5 | 0 | five | 2 | 4 | 3 | -3
| 5 | 0 | five | 5 | -5 | 3 | -3
| 5 | 0 | five | 5 | -5 | 3 | -3
| 5 | 0 | five | 0 | | 3 | -3
| 5 | 0 | five | | | 3 | -3
| 5 | 0 | five | | 0 | 3 | -3 | 5 | 0 | five | | 0 | 3 | -3
| 6 | 6 | six | 1 | -1 | 3 | -3
| 6 | 6 | six | 2 | 2 | 3 | -3
| 6 | 6 | six | 3 | -3 | 3 | -3
| 6 | 6 | six | 2 | 4 | 3 | -3
| 6 | 6 | six | 5 | -5 | 3 | -3
| 6 | 6 | six | 5 | -5 | 3 | -3
| 6 | 6 | six | 0 | | 3 | -3
| 6 | 6 | six | | | 3 | -3
| 6 | 6 | six | | 0 | 3 | -3 | 6 | 6 | six | | 0 | 3 | -3
| 7 | 7 | seven | 1 | -1 | 3 | -3
| 7 | 7 | seven | 2 | 2 | 3 | -3
| 7 | 7 | seven | 3 | -3 | 3 | -3
| 7 | 7 | seven | 2 | 4 | 3 | -3
| 7 | 7 | seven | 5 | -5 | 3 | -3
| 7 | 7 | seven | 5 | -5 | 3 | -3
| 7 | 7 | seven | 0 | | 3 | -3
| 7 | 7 | seven | | | 3 | -3
| 7 | 7 | seven | | 0 | 3 | -3 | 7 | 7 | seven | | 0 | 3 | -3
| 8 | 8 | eight | 1 | -1 | 3 | -3
| 8 | 8 | eight | 2 | 2 | 3 | -3
| 8 | 8 | eight | 3 | -3 | 3 | -3
| 8 | 8 | eight | 2 | 4 | 3 | -3
| 8 | 8 | eight | 5 | -5 | 3 | -3
| 8 | 8 | eight | 5 | -5 | 3 | -3
| 8 | 8 | eight | 0 | | 3 | -3
| 8 | 8 | eight | | | 3 | -3
| 8 | 8 | eight | | 0 | 3 | -3 | 8 | 8 | eight | | 0 | 3 | -3
| 0 | | zero | 1 | -1 | 3 | -3
| 0 | | zero | 2 | 2 | 3 | -3
| 0 | | zero | 3 | -3 | 3 | -3
| 0 | | zero | 2 | 4 | 3 | -3
| 0 | | zero | 5 | -5 | 3 | -3
| 0 | | zero | 5 | -5 | 3 | -3
| 0 | | zero | 0 | | 3 | -3
| 0 | | zero | | | 3 | -3
| 0 | | zero | | 0 | 3 | -3 | 0 | | zero | | 0 | 3 | -3
| | | null | 1 | -1 | 3 | -3
| | | null | 2 | 2 | 3 | -3
| | | null | 3 | -3 | 3 | -3
| | | null | 2 | 4 | 3 | -3
| | | null | 5 | -5 | 3 | -3
| | | null | 5 | -5 | 3 | -3
| | | null | 0 | | 3 | -3
| | | null | | | 3 | -3
| | | null | | 0 | 3 | -3 | | | null | | 0 | 3 | -3
| | 0 | zero | 1 | -1 | 3 | -3
| | 0 | zero | 2 | 2 | 3 | -3
| | 0 | zero | 3 | -3 | 3 | -3
| | 0 | zero | 2 | 4 | 3 | -3
| | 0 | zero | 5 | -5 | 3 | -3
| | 0 | zero | 5 | -5 | 3 | -3
| | 0 | zero | 0 | | 3 | -3
| | 0 | zero | | | 3 | -3
| | 0 | zero | | 0 | 3 | -3 | | 0 | zero | | 0 | 3 | -3
| 1 | 4 | one | 1 | -1 | 2 | 4
| 1 | 4 | one | 2 | 2 | 2 | 4
| 1 | 4 | one | 3 | -3 | 2 | 4
| 1 | 4 | one | 2 | 4 | 2 | 4
| 1 | 4 | one | 5 | -5 | 2 | 4
| 1 | 4 | one | 5 | -5 | 2 | 4
| 1 | 4 | one | 0 | | 2 | 4
| 1 | 4 | one | | | 2 | 4
| 1 | 4 | one | | 0 | 2 | 4 | 1 | 4 | one | | 0 | 2 | 4
| 2 | 3 | two | 1 | -1 | 2 | 4
| 2 | 3 | two | 2 | 2 | 2 | 4
| 2 | 3 | two | 3 | -3 | 2 | 4
| 2 | 3 | two | 2 | 4 | 2 | 4
| 2 | 3 | two | 5 | -5 | 2 | 4
| 2 | 3 | two | 5 | -5 | 2 | 4
| 2 | 3 | two | 0 | | 2 | 4
| 2 | 3 | two | | | 2 | 4
| 2 | 3 | two | | 0 | 2 | 4 | 2 | 3 | two | | 0 | 2 | 4
| 3 | 2 | three | 1 | -1 | 2 | 4
| 3 | 2 | three | 2 | 2 | 2 | 4
| 3 | 2 | three | 3 | -3 | 2 | 4
| 3 | 2 | three | 2 | 4 | 2 | 4
| 3 | 2 | three | 5 | -5 | 2 | 4
| 3 | 2 | three | 5 | -5 | 2 | 4
| 3 | 2 | three | 0 | | 2 | 4
| 3 | 2 | three | | | 2 | 4
| 3 | 2 | three | | 0 | 2 | 4 | 3 | 2 | three | | 0 | 2 | 4
| 4 | 1 | four | 1 | -1 | 2 | 4
| 4 | 1 | four | 2 | 2 | 2 | 4
| 4 | 1 | four | 3 | -3 | 2 | 4
| 4 | 1 | four | 2 | 4 | 2 | 4
| 4 | 1 | four | 5 | -5 | 2 | 4
| 4 | 1 | four | 5 | -5 | 2 | 4
| 4 | 1 | four | 0 | | 2 | 4
| 4 | 1 | four | | | 2 | 4
| 4 | 1 | four | | 0 | 2 | 4 | 4 | 1 | four | | 0 | 2 | 4
| 5 | 0 | five | 1 | -1 | 2 | 4
| 5 | 0 | five | 2 | 2 | 2 | 4
| 5 | 0 | five | 3 | -3 | 2 | 4
| 5 | 0 | five | 2 | 4 | 2 | 4
| 5 | 0 | five | 5 | -5 | 2 | 4
| 5 | 0 | five | 5 | -5 | 2 | 4
| 5 | 0 | five | 0 | | 2 | 4
| 5 | 0 | five | | | 2 | 4
| 5 | 0 | five | | 0 | 2 | 4 | 5 | 0 | five | | 0 | 2 | 4
| 6 | 6 | six | 1 | -1 | 2 | 4
| 6 | 6 | six | 2 | 2 | 2 | 4
| 6 | 6 | six | 3 | -3 | 2 | 4
| 6 | 6 | six | 2 | 4 | 2 | 4
| 6 | 6 | six | 5 | -5 | 2 | 4
| 6 | 6 | six | 5 | -5 | 2 | 4
| 6 | 6 | six | 0 | | 2 | 4
| 6 | 6 | six | | | 2 | 4
| 6 | 6 | six | | 0 | 2 | 4 | 6 | 6 | six | | 0 | 2 | 4
| 7 | 7 | seven | 1 | -1 | 2 | 4
| 7 | 7 | seven | 2 | 2 | 2 | 4
| 7 | 7 | seven | 3 | -3 | 2 | 4
| 7 | 7 | seven | 2 | 4 | 2 | 4
| 7 | 7 | seven | 5 | -5 | 2 | 4
| 7 | 7 | seven | 5 | -5 | 2 | 4
| 7 | 7 | seven | 0 | | 2 | 4
| 7 | 7 | seven | | | 2 | 4
| 7 | 7 | seven | | 0 | 2 | 4 | 7 | 7 | seven | | 0 | 2 | 4
| 8 | 8 | eight | 1 | -1 | 2 | 4
| 8 | 8 | eight | 2 | 2 | 2 | 4
| 8 | 8 | eight | 3 | -3 | 2 | 4
| 8 | 8 | eight | 2 | 4 | 2 | 4
| 8 | 8 | eight | 5 | -5 | 2 | 4
| 8 | 8 | eight | 5 | -5 | 2 | 4
| 8 | 8 | eight | 0 | | 2 | 4
| 8 | 8 | eight | | | 2 | 4
| 8 | 8 | eight | | 0 | 2 | 4 | 8 | 8 | eight | | 0 | 2 | 4
| 0 | | zero | 1 | -1 | 2 | 4
| 0 | | zero | 2 | 2 | 2 | 4
| 0 | | zero | 3 | -3 | 2 | 4
| 0 | | zero | 2 | 4 | 2 | 4
| 0 | | zero | 5 | -5 | 2 | 4
| 0 | | zero | 5 | -5 | 2 | 4
| 0 | | zero | 0 | | 2 | 4
| 0 | | zero | | | 2 | 4
| 0 | | zero | | 0 | 2 | 4 | 0 | | zero | | 0 | 2 | 4
| | | null | 1 | -1 | 2 | 4
| | | null | 2 | 2 | 2 | 4
| | | null | 3 | -3 | 2 | 4
| | | null | 2 | 4 | 2 | 4
| | | null | 5 | -5 | 2 | 4
| | | null | 5 | -5 | 2 | 4
| | | null | 0 | | 2 | 4
| | | null | | | 2 | 4
| | | null | | 0 | 2 | 4 | | | null | | 0 | 2 | 4
| | 0 | zero | 1 | -1 | 2 | 4
| | 0 | zero | 2 | 2 | 2 | 4
| | 0 | zero | 3 | -3 | 2 | 4
| | 0 | zero | 2 | 4 | 2 | 4
| | 0 | zero | 5 | -5 | 2 | 4
| | 0 | zero | 5 | -5 | 2 | 4
| | 0 | zero | 0 | | 2 | 4
| | 0 | zero | | | 2 | 4
| | 0 | zero | | 0 | 2 | 4 | | 0 | zero | | 0 | 2 | 4
| 1 | 4 | one | 1 | -1 | 5 | -5
| 1 | 4 | one | 2 | 2 | 5 | -5
| 1 | 4 | one | 3 | -3 | 5 | -5
| 1 | 4 | one | 2 | 4 | 5 | -5
| 1 | 4 | one | 5 | -5 | 5 | -5
| 1 | 4 | one | 5 | -5 | 5 | -5
| 1 | 4 | one | 0 | | 5 | -5
| 1 | 4 | one | | | 5 | -5
| 1 | 4 | one | | 0 | 5 | -5 | 1 | 4 | one | | 0 | 5 | -5
| 2 | 3 | two | 1 | -1 | 5 | -5
| 2 | 3 | two | 2 | 2 | 5 | -5
| 2 | 3 | two | 3 | -3 | 5 | -5
| 2 | 3 | two | 2 | 4 | 5 | -5
| 2 | 3 | two | 5 | -5 | 5 | -5
| 2 | 3 | two | 5 | -5 | 5 | -5
| 2 | 3 | two | 0 | | 5 | -5
| 2 | 3 | two | | | 5 | -5
| 2 | 3 | two | | 0 | 5 | -5 | 2 | 3 | two | | 0 | 5 | -5
| 3 | 2 | three | 1 | -1 | 5 | -5
| 3 | 2 | three | 2 | 2 | 5 | -5
| 3 | 2 | three | 3 | -3 | 5 | -5
| 3 | 2 | three | 2 | 4 | 5 | -5
| 3 | 2 | three | 5 | -5 | 5 | -5
| 3 | 2 | three | 5 | -5 | 5 | -5
| 3 | 2 | three | 0 | | 5 | -5
| 3 | 2 | three | | | 5 | -5
| 3 | 2 | three | | 0 | 5 | -5 | 3 | 2 | three | | 0 | 5 | -5
| 4 | 1 | four | 1 | -1 | 5 | -5
| 4 | 1 | four | 2 | 2 | 5 | -5
| 4 | 1 | four | 3 | -3 | 5 | -5
| 4 | 1 | four | 2 | 4 | 5 | -5
| 4 | 1 | four | 5 | -5 | 5 | -5
| 4 | 1 | four | 5 | -5 | 5 | -5
| 4 | 1 | four | 0 | | 5 | -5
| 4 | 1 | four | | | 5 | -5
| 4 | 1 | four | | 0 | 5 | -5 | 4 | 1 | four | | 0 | 5 | -5
| 5 | 0 | five | 1 | -1 | 5 | -5
| 5 | 0 | five | 2 | 2 | 5 | -5
| 5 | 0 | five | 3 | -3 | 5 | -5
| 5 | 0 | five | 2 | 4 | 5 | -5
| 5 | 0 | five | 5 | -5 | 5 | -5
| 5 | 0 | five | 5 | -5 | 5 | -5
| 5 | 0 | five | 0 | | 5 | -5
| 5 | 0 | five | | | 5 | -5
| 5 | 0 | five | | 0 | 5 | -5 | 5 | 0 | five | | 0 | 5 | -5
| 6 | 6 | six | 1 | -1 | 5 | -5
| 6 | 6 | six | 2 | 2 | 5 | -5
| 6 | 6 | six | 3 | -3 | 5 | -5
| 6 | 6 | six | 2 | 4 | 5 | -5
| 6 | 6 | six | 5 | -5 | 5 | -5
| 6 | 6 | six | 5 | -5 | 5 | -5
| 6 | 6 | six | 0 | | 5 | -5
| 6 | 6 | six | | | 5 | -5
| 6 | 6 | six | | 0 | 5 | -5 | 6 | 6 | six | | 0 | 5 | -5
| 7 | 7 | seven | 1 | -1 | 5 | -5
| 7 | 7 | seven | 2 | 2 | 5 | -5
| 7 | 7 | seven | 3 | -3 | 5 | -5
| 7 | 7 | seven | 2 | 4 | 5 | -5
| 7 | 7 | seven | 5 | -5 | 5 | -5
| 7 | 7 | seven | 5 | -5 | 5 | -5
| 7 | 7 | seven | 0 | | 5 | -5
| 7 | 7 | seven | | | 5 | -5
| 7 | 7 | seven | | 0 | 5 | -5 | 7 | 7 | seven | | 0 | 5 | -5
| 8 | 8 | eight | 1 | -1 | 5 | -5
| 8 | 8 | eight | 2 | 2 | 5 | -5
| 8 | 8 | eight | 3 | -3 | 5 | -5
| 8 | 8 | eight | 2 | 4 | 5 | -5
| 8 | 8 | eight | 5 | -5 | 5 | -5
| 8 | 8 | eight | 5 | -5 | 5 | -5
| 8 | 8 | eight | 0 | | 5 | -5
| 8 | 8 | eight | | | 5 | -5
| 8 | 8 | eight | | 0 | 5 | -5 | 8 | 8 | eight | | 0 | 5 | -5
| 0 | | zero | 1 | -1 | 5 | -5
| 0 | | zero | 2 | 2 | 5 | -5
| 0 | | zero | 3 | -3 | 5 | -5
| 0 | | zero | 2 | 4 | 5 | -5
| 0 | | zero | 5 | -5 | 5 | -5
| 0 | | zero | 5 | -5 | 5 | -5
| 0 | | zero | 0 | | 5 | -5
| 0 | | zero | | | 5 | -5
| 0 | | zero | | 0 | 5 | -5 | 0 | | zero | | 0 | 5 | -5
| | | null | 1 | -1 | 5 | -5
| | | null | 2 | 2 | 5 | -5
| | | null | 3 | -3 | 5 | -5
| | | null | 2 | 4 | 5 | -5
| | | null | 5 | -5 | 5 | -5
| | | null | 5 | -5 | 5 | -5
| | | null | 0 | | 5 | -5
| | | null | | | 5 | -5
| | | null | | 0 | 5 | -5 | | | null | | 0 | 5 | -5
| | 0 | zero | 1 | -1 | 5 | -5
| | 0 | zero | 2 | 2 | 5 | -5
| | 0 | zero | 3 | -3 | 5 | -5
| | 0 | zero | 2 | 4 | 5 | -5
| | 0 | zero | 5 | -5 | 5 | -5
| | 0 | zero | 5 | -5 | 5 | -5
| | 0 | zero | 0 | | 5 | -5
| | 0 | zero | | | 5 | -5
| | 0 | zero | | 0 | 5 | -5 | | 0 | zero | | 0 | 5 | -5
| 1 | 4 | one | 1 | -1 | 5 | -5
| 1 | 4 | one | 2 | 2 | 5 | -5
| 1 | 4 | one | 3 | -3 | 5 | -5
| 1 | 4 | one | 2 | 4 | 5 | -5
| 1 | 4 | one | 5 | -5 | 5 | -5
| 1 | 4 | one | 5 | -5 | 5 | -5
| 1 | 4 | one | 0 | | 5 | -5
| 1 | 4 | one | | | 5 | -5
| 1 | 4 | one | | 0 | 5 | -5 | 1 | 4 | one | | 0 | 5 | -5
| 2 | 3 | two | 1 | -1 | 5 | -5
| 2 | 3 | two | 2 | 2 | 5 | -5
| 2 | 3 | two | 3 | -3 | 5 | -5
| 2 | 3 | two | 2 | 4 | 5 | -5
| 2 | 3 | two | 5 | -5 | 5 | -5
| 2 | 3 | two | 5 | -5 | 5 | -5
| 2 | 3 | two | 0 | | 5 | -5
| 2 | 3 | two | | | 5 | -5
| 2 | 3 | two | | 0 | 5 | -5 | 2 | 3 | two | | 0 | 5 | -5
| 3 | 2 | three | 1 | -1 | 5 | -5
| 3 | 2 | three | 2 | 2 | 5 | -5
| 3 | 2 | three | 3 | -3 | 5 | -5
| 3 | 2 | three | 2 | 4 | 5 | -5
| 3 | 2 | three | 5 | -5 | 5 | -5
| 3 | 2 | three | 5 | -5 | 5 | -5
| 3 | 2 | three | 0 | | 5 | -5
| 3 | 2 | three | | | 5 | -5
| 3 | 2 | three | | 0 | 5 | -5 | 3 | 2 | three | | 0 | 5 | -5
| 4 | 1 | four | 1 | -1 | 5 | -5
| 4 | 1 | four | 2 | 2 | 5 | -5
| 4 | 1 | four | 3 | -3 | 5 | -5
| 4 | 1 | four | 2 | 4 | 5 | -5
| 4 | 1 | four | 5 | -5 | 5 | -5
| 4 | 1 | four | 5 | -5 | 5 | -5
| 4 | 1 | four | 0 | | 5 | -5
| 4 | 1 | four | | | 5 | -5
| 4 | 1 | four | | 0 | 5 | -5 | 4 | 1 | four | | 0 | 5 | -5
| 5 | 0 | five | 1 | -1 | 5 | -5
| 5 | 0 | five | 2 | 2 | 5 | -5
| 5 | 0 | five | 3 | -3 | 5 | -5
| 5 | 0 | five | 2 | 4 | 5 | -5
| 5 | 0 | five | 5 | -5 | 5 | -5
| 5 | 0 | five | 5 | -5 | 5 | -5
| 5 | 0 | five | 0 | | 5 | -5
| 5 | 0 | five | | | 5 | -5
| 5 | 0 | five | | 0 | 5 | -5 | 5 | 0 | five | | 0 | 5 | -5
| 6 | 6 | six | 1 | -1 | 5 | -5
| 6 | 6 | six | 2 | 2 | 5 | -5
| 6 | 6 | six | 3 | -3 | 5 | -5
| 6 | 6 | six | 2 | 4 | 5 | -5
| 6 | 6 | six | 5 | -5 | 5 | -5
| 6 | 6 | six | 5 | -5 | 5 | -5
| 6 | 6 | six | 0 | | 5 | -5
| 6 | 6 | six | | | 5 | -5
| 6 | 6 | six | | 0 | 5 | -5 | 6 | 6 | six | | 0 | 5 | -5
| 7 | 7 | seven | 1 | -1 | 5 | -5
| 7 | 7 | seven | 2 | 2 | 5 | -5
| 7 | 7 | seven | 3 | -3 | 5 | -5
| 7 | 7 | seven | 2 | 4 | 5 | -5
| 7 | 7 | seven | 5 | -5 | 5 | -5
| 7 | 7 | seven | 5 | -5 | 5 | -5
| 7 | 7 | seven | 0 | | 5 | -5
| 7 | 7 | seven | | | 5 | -5
| 7 | 7 | seven | | 0 | 5 | -5 | 7 | 7 | seven | | 0 | 5 | -5
| 8 | 8 | eight | 1 | -1 | 5 | -5
| 8 | 8 | eight | 2 | 2 | 5 | -5
| 8 | 8 | eight | 3 | -3 | 5 | -5
| 8 | 8 | eight | 2 | 4 | 5 | -5
| 8 | 8 | eight | 5 | -5 | 5 | -5
| 8 | 8 | eight | 5 | -5 | 5 | -5
| 8 | 8 | eight | 0 | | 5 | -5
| 8 | 8 | eight | | | 5 | -5
| 8 | 8 | eight | | 0 | 5 | -5 | 8 | 8 | eight | | 0 | 5 | -5
| 0 | | zero | 1 | -1 | 5 | -5
| 0 | | zero | 2 | 2 | 5 | -5
| 0 | | zero | 3 | -3 | 5 | -5
| 0 | | zero | 2 | 4 | 5 | -5
| 0 | | zero | 5 | -5 | 5 | -5
| 0 | | zero | 5 | -5 | 5 | -5
| 0 | | zero | 0 | | 5 | -5
| 0 | | zero | | | 5 | -5
| 0 | | zero | | 0 | 5 | -5 | 0 | | zero | | 0 | 5 | -5
| | | null | 1 | -1 | 5 | -5
| | | null | 2 | 2 | 5 | -5
| | | null | 3 | -3 | 5 | -5
| | | null | 2 | 4 | 5 | -5
| | | null | 5 | -5 | 5 | -5
| | | null | 5 | -5 | 5 | -5
| | | null | 0 | | 5 | -5
| | | null | | | 5 | -5
| | | null | | 0 | 5 | -5 | | | null | | 0 | 5 | -5
| | 0 | zero | 1 | -1 | 5 | -5
| | 0 | zero | 2 | 2 | 5 | -5
| | 0 | zero | 3 | -3 | 5 | -5
| | 0 | zero | 2 | 4 | 5 | -5
| | 0 | zero | 5 | -5 | 5 | -5
| | 0 | zero | 5 | -5 | 5 | -5
| | 0 | zero | 0 | | 5 | -5
| | 0 | zero | | | 5 | -5
| | 0 | zero | | 0 | 5 | -5 | | 0 | zero | | 0 | 5 | -5
| 1 | 4 | one | 1 | -1 | 0 |
| 1 | 4 | one | 2 | 2 | 0 |
| 1 | 4 | one | 3 | -3 | 0 |
| 1 | 4 | one | 2 | 4 | 0 |
| 1 | 4 | one | 5 | -5 | 0 |
| 1 | 4 | one | 5 | -5 | 0 |
| 1 | 4 | one | 0 | | 0 |
| 1 | 4 | one | | | 0 |
| 1 | 4 | one | | 0 | 0 | | 1 | 4 | one | | 0 | 0 |
| 2 | 3 | two | 1 | -1 | 0 |
| 2 | 3 | two | 2 | 2 | 0 |
| 2 | 3 | two | 3 | -3 | 0 |
| 2 | 3 | two | 2 | 4 | 0 |
| 2 | 3 | two | 5 | -5 | 0 |
| 2 | 3 | two | 5 | -5 | 0 |
| 2 | 3 | two | 0 | | 0 |
| 2 | 3 | two | | | 0 |
| 2 | 3 | two | | 0 | 0 | | 2 | 3 | two | | 0 | 0 |
| 3 | 2 | three | 1 | -1 | 0 |
| 3 | 2 | three | 2 | 2 | 0 |
| 3 | 2 | three | 3 | -3 | 0 |
| 3 | 2 | three | 2 | 4 | 0 |
| 3 | 2 | three | 5 | -5 | 0 |
| 3 | 2 | three | 5 | -5 | 0 |
| 3 | 2 | three | 0 | | 0 |
| 3 | 2 | three | | | 0 |
| 3 | 2 | three | | 0 | 0 | | 3 | 2 | three | | 0 | 0 |
| 4 | 1 | four | 1 | -1 | 0 |
| 4 | 1 | four | 2 | 2 | 0 |
| 4 | 1 | four | 3 | -3 | 0 |
| 4 | 1 | four | 2 | 4 | 0 |
| 4 | 1 | four | 5 | -5 | 0 |
| 4 | 1 | four | 5 | -5 | 0 |
| 4 | 1 | four | 0 | | 0 |
| 4 | 1 | four | | | 0 |
| 4 | 1 | four | | 0 | 0 | | 4 | 1 | four | | 0 | 0 |
| 5 | 0 | five | 1 | -1 | 0 |
| 5 | 0 | five | 2 | 2 | 0 |
| 5 | 0 | five | 3 | -3 | 0 |
| 5 | 0 | five | 2 | 4 | 0 |
| 5 | 0 | five | 5 | -5 | 0 |
| 5 | 0 | five | 5 | -5 | 0 |
| 5 | 0 | five | 0 | | 0 |
| 5 | 0 | five | | | 0 |
| 5 | 0 | five | | 0 | 0 | | 5 | 0 | five | | 0 | 0 |
| 6 | 6 | six | 1 | -1 | 0 |
| 6 | 6 | six | 2 | 2 | 0 |
| 6 | 6 | six | 3 | -3 | 0 |
| 6 | 6 | six | 2 | 4 | 0 |
| 6 | 6 | six | 5 | -5 | 0 |
| 6 | 6 | six | 5 | -5 | 0 |
| 6 | 6 | six | 0 | | 0 |
| 6 | 6 | six | | | 0 |
| 6 | 6 | six | | 0 | 0 | | 6 | 6 | six | | 0 | 0 |
| 7 | 7 | seven | 1 | -1 | 0 |
| 7 | 7 | seven | 2 | 2 | 0 |
| 7 | 7 | seven | 3 | -3 | 0 |
| 7 | 7 | seven | 2 | 4 | 0 |
| 7 | 7 | seven | 5 | -5 | 0 |
| 7 | 7 | seven | 5 | -5 | 0 |
| 7 | 7 | seven | 0 | | 0 |
| 7 | 7 | seven | | | 0 |
| 7 | 7 | seven | | 0 | 0 | | 7 | 7 | seven | | 0 | 0 |
| 8 | 8 | eight | 1 | -1 | 0 |
| 8 | 8 | eight | 2 | 2 | 0 |
| 8 | 8 | eight | 3 | -3 | 0 |
| 8 | 8 | eight | 2 | 4 | 0 |
| 8 | 8 | eight | 5 | -5 | 0 |
| 8 | 8 | eight | 5 | -5 | 0 |
| 8 | 8 | eight | 0 | | 0 |
| 8 | 8 | eight | | | 0 |
| 8 | 8 | eight | | 0 | 0 | | 8 | 8 | eight | | 0 | 0 |
| 0 | | zero | 1 | -1 | 0 |
| 0 | | zero | 2 | 2 | 0 |
| 0 | | zero | 3 | -3 | 0 |
| 0 | | zero | 2 | 4 | 0 |
| 0 | | zero | 5 | -5 | 0 |
| 0 | | zero | 5 | -5 | 0 |
| 0 | | zero | 0 | | 0 |
| 0 | | zero | | | 0 |
| 0 | | zero | | 0 | 0 | | 0 | | zero | | 0 | 0 |
| | | null | 1 | -1 | 0 |
| | | null | 2 | 2 | 0 |
| | | null | 3 | -3 | 0 |
| | | null | 2 | 4 | 0 |
| | | null | 5 | -5 | 0 |
| | | null | 5 | -5 | 0 |
| | | null | 0 | | 0 |
| | | null | | | 0 |
| | | null | | 0 | 0 | | | | null | | 0 | 0 |
| | 0 | zero | 1 | -1 | 0 |
| | 0 | zero | 2 | 2 | 0 |
| | 0 | zero | 3 | -3 | 0 |
| | 0 | zero | 2 | 4 | 0 |
| | 0 | zero | 5 | -5 | 0 |
| | 0 | zero | 5 | -5 | 0 |
| | 0 | zero | 0 | | 0 |
| | 0 | zero | | | 0 |
| | 0 | zero | | 0 | 0 | | | 0 | zero | | 0 | 0 |
| 1 | 4 | one | 1 | -1 | |
| 1 | 4 | one | 2 | 2 | |
| 1 | 4 | one | 3 | -3 | |
| 1 | 4 | one | 2 | 4 | |
| 1 | 4 | one | 5 | -5 | |
| 1 | 4 | one | 5 | -5 | |
| 1 | 4 | one | 0 | | |
| 1 | 4 | one | | | |
| 1 | 4 | one | | 0 | | | 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 | | | 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 | | | 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 | | | 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 | | | 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 | | | 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 | | | 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 | | | 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 | | | 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 | | | | | 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 | | | | 0 | zero | | 0 | |
| 1 | 4 | one | 1 | -1 | | 0
| 1 | 4 | one | 2 | 2 | | 0
| 1 | 4 | one | 3 | -3 | | 0
| 1 | 4 | one | 2 | 4 | | 0
| 1 | 4 | one | 5 | -5 | | 0
| 1 | 4 | one | 5 | -5 | | 0
| 1 | 4 | one | 0 | | | 0
| 1 | 4 | one | | | | 0
| 1 | 4 | one | | 0 | | 0 | 1 | 4 | one | | 0 | | 0
| 2 | 3 | two | 1 | -1 | | 0
| 2 | 3 | two | 2 | 2 | | 0
| 2 | 3 | two | 3 | -3 | | 0
| 2 | 3 | two | 2 | 4 | | 0
| 2 | 3 | two | 5 | -5 | | 0
| 2 | 3 | two | 5 | -5 | | 0
| 2 | 3 | two | 0 | | | 0
| 2 | 3 | two | | | | 0
| 2 | 3 | two | | 0 | | 0 | 2 | 3 | two | | 0 | | 0
| 3 | 2 | three | 1 | -1 | | 0
| 3 | 2 | three | 2 | 2 | | 0
| 3 | 2 | three | 3 | -3 | | 0
| 3 | 2 | three | 2 | 4 | | 0
| 3 | 2 | three | 5 | -5 | | 0
| 3 | 2 | three | 5 | -5 | | 0
| 3 | 2 | three | 0 | | | 0
| 3 | 2 | three | | | | 0
| 3 | 2 | three | | 0 | | 0 | 3 | 2 | three | | 0 | | 0
| 4 | 1 | four | 1 | -1 | | 0
| 4 | 1 | four | 2 | 2 | | 0
| 4 | 1 | four | 3 | -3 | | 0
| 4 | 1 | four | 2 | 4 | | 0
| 4 | 1 | four | 5 | -5 | | 0
| 4 | 1 | four | 5 | -5 | | 0
| 4 | 1 | four | 0 | | | 0
| 4 | 1 | four | | | | 0
| 4 | 1 | four | | 0 | | 0 | 4 | 1 | four | | 0 | | 0
| 5 | 0 | five | 1 | -1 | | 0
| 5 | 0 | five | 2 | 2 | | 0
| 5 | 0 | five | 3 | -3 | | 0
| 5 | 0 | five | 2 | 4 | | 0
| 5 | 0 | five | 5 | -5 | | 0
| 5 | 0 | five | 5 | -5 | | 0
| 5 | 0 | five | 0 | | | 0
| 5 | 0 | five | | | | 0
| 5 | 0 | five | | 0 | | 0 | 5 | 0 | five | | 0 | | 0
| 6 | 6 | six | 1 | -1 | | 0
| 6 | 6 | six | 2 | 2 | | 0
| 6 | 6 | six | 3 | -3 | | 0
| 6 | 6 | six | 2 | 4 | | 0
| 6 | 6 | six | 5 | -5 | | 0
| 6 | 6 | six | 5 | -5 | | 0
| 6 | 6 | six | 0 | | | 0
| 6 | 6 | six | | | | 0
| 6 | 6 | six | | 0 | | 0 | 6 | 6 | six | | 0 | | 0
| 7 | 7 | seven | 1 | -1 | | 0
| 7 | 7 | seven | 2 | 2 | | 0
| 7 | 7 | seven | 3 | -3 | | 0
| 7 | 7 | seven | 2 | 4 | | 0
| 7 | 7 | seven | 5 | -5 | | 0
| 7 | 7 | seven | 5 | -5 | | 0
| 7 | 7 | seven | 0 | | | 0
| 7 | 7 | seven | | | | 0
| 7 | 7 | seven | | 0 | | 0 | 7 | 7 | seven | | 0 | | 0
| 8 | 8 | eight | 1 | -1 | | 0
| 8 | 8 | eight | 2 | 2 | | 0
| 8 | 8 | eight | 3 | -3 | | 0
| 8 | 8 | eight | 2 | 4 | | 0
| 8 | 8 | eight | 5 | -5 | | 0
| 8 | 8 | eight | 5 | -5 | | 0
| 8 | 8 | eight | 0 | | | 0
| 8 | 8 | eight | | | | 0
| 8 | 8 | eight | | 0 | | 0 | 8 | 8 | eight | | 0 | | 0
| 0 | | zero | 1 | -1 | | 0
| 0 | | zero | 2 | 2 | | 0
| 0 | | zero | 3 | -3 | | 0
| 0 | | zero | 2 | 4 | | 0
| 0 | | zero | 5 | -5 | | 0
| 0 | | zero | 5 | -5 | | 0
| 0 | | zero | 0 | | | 0
| 0 | | zero | | | | 0
| 0 | | zero | | 0 | | 0 | 0 | | zero | | 0 | | 0
| | | null | 1 | -1 | | 0
| | | null | 2 | 2 | | 0
| | | null | 3 | -3 | | 0
| | | null | 2 | 4 | | 0
| | | null | 5 | -5 | | 0
| | | null | 5 | -5 | | 0
| | | null | 0 | | | 0
| | | null | | | | 0
| | | null | | 0 | | 0 | | | null | | 0 | | 0
| | 0 | zero | 1 | -1 | | 0
| | 0 | zero | 2 | 2 | | 0
| | 0 | zero | 3 | -3 | | 0
| | 0 | zero | 2 | 4 | | 0
| | 0 | zero | 5 | -5 | | 0
| | 0 | zero | 5 | -5 | | 0
| | 0 | zero | 0 | | | 0
| | 0 | zero | | | | 0
| | 0 | zero | | 0 | | 0 | | 0 | zero | | 0 | | 0
(891 rows) (891 rows)
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