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.

diff --git a/src/backend/executor/execAmi.c b/src/backend/executor/execAmi.c
index cd23d8d8b64efe2b6afecbf45da4ae24e169b464..51923c436ad8b4852d80cd81de356a5b4432981c 100644 (file)
--- a/src/backend/executor/execAmi.c
+++ b/src/backend/executor/execAmi.c
@@ -6,7 +6,7 @@
  * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
  * 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)
 
    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;
+}

diff --git a/src/backend/optimizer/path/costsize.c b/src/backend/optimizer/path/costsize.c
index 1ede488c13b13f910b0d676f6935c9cfeaf9afc6..6acc5ae34b0a4bfacb2227ed87f2ad0ac18fd321 100644 (file)
--- a/src/backend/optimizer/path/costsize.c
+++ b/src/backend/optimizer/path/costsize.c
@@ -54,7 +54,7 @@
  * Portions Copyright (c) 1994, Regents of the University of California
  *
  * 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 @@
 
 #include 
 
+#include "executor/executor.h"
 #include "executor/nodeHash.h"
 #include "miscadmin.h"
 #include "nodes/nodeFuncs.h"
@@ -119,6 +120,8 @@ typedef struct
 static MergeScanSelCache *cached_scansel(PlannerInfo *root,
               RestrictInfo *rinfo,
               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 adjust_semi_join(PlannerInfo *root, JoinPath *path,
                 SpecialJoinInfo *sjinfo,
@@ -895,15 +898,26 @@ cost_functionscan(Path *path, PlannerInfo *root, RelOptInfo *baserel)
    rte = planner_rt_fetch(baserel->relid, root);
    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);
 
-   startup_cost += exprcost.startup;
-   cpu_per_tuple = exprcost.per_tuple;
+   startup_cost += exprcost.startup + exprcost.per_tuple;
 
    /* Add scanning CPU costs */
    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;
 
    path->startup_cost = startup_cost;
@@ -1176,41 +1190,44 @@ sort_exceeds_work_mem(Sort *sort)
  *
  * 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.
+ *
+ * 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
 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        run_cost = 0;
+   Cost        startup_cost = input_startup_cost;
+   Cost        run_cost = input_total_cost - input_startup_cost;
    double      nbytes = relation_byte_size(tuples, width);
    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)
    {
        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;
    }
 
-   /*
-    * 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->total_cost = startup_cost + run_cost;
 }
@@ -1400,7 +1417,10 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
    Path       *inner_path = path->innerjoinpath;
    Cost        startup_cost = 0;
    Cost        run_cost = 0;
+   Cost        inner_rescan_start_cost;
+   Cost        inner_rescan_total_cost;
    Cost        inner_run_cost;
+   Cost        inner_rescan_run_cost;
    Cost        cpu_per_tuple;
    QualCost    restrict_qual_cost;
    double      outer_path_rows = PATH_ROWS(outer_path);
@@ -1413,32 +1433,26 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
    if (!enable_nestloop)
        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 */
 
    /*
     * 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
-    * their sum.  What's not so clear is whether the inner path's
-    * startup_cost must be paid again on each rescan of the inner path. This
-    * is not true if the inner path is materialized or is a hashjoin, but
-    * probably is true otherwise.
+    * their sum.  We'll also pay the inner path's rescan startup cost
+    * multiple times.
     */
    startup_cost += outer_path->startup_cost + inner_path->startup_cost;
    run_cost += outer_path->total_cost - outer_path->startup_cost;
-   if (IsA(inner_path, MaterialPath) ||
-       IsA(inner_path, HashPath))
-   {
-       /* 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;
-   }
+   if (outer_path_rows > 1)
+       run_cost += (outer_path_rows - 1) * inner_rescan_start_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,
                         &outer_match_frac,
@@ -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
         * clamp inner_scan_frac to at most 1.0; but since match_count is at
         * 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);
        inner_scan_frac = 2.0 / (match_count + 1.0);
 
-       /* Add inner run cost for outer tuples having matches */
-       run_cost += outer_matched_rows * inner_run_cost * inner_scan_frac;
+       /* Add inner run cost for additional outer tuples having matches */
+       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!) */
        ntuples = outer_matched_rows * inner_path_rows * inner_scan_frac;
@@ -1479,13 +1503,16 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
        if (indexed_join_quals)
        {
            run_cost += (outer_path_rows - outer_matched_rows) *
-               inner_run_cost / inner_path_rows;
-           /* We won't be evaluating any quals at all for these rows */
+               inner_rescan_run_cost / inner_path_rows;
+           /*
+            * We won't be evaluating any quals at all for these rows,
+            * so don't add them to ntuples.
+            */
        }
        else
        {
            run_cost += (outer_path_rows - outer_matched_rows) *
-               inner_run_cost;
+               inner_rescan_run_cost;
            ntuples += (outer_path_rows - outer_matched_rows) *
                inner_path_rows;
        }
@@ -1493,7 +1520,9 @@ cost_nestloop(NestPath *path, PlannerInfo *root, SpecialJoinInfo *sjinfo)
    else
    {
        /* 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!) */
        ntuples = outer_path_rows * inner_path_rows;
@@ -2190,13 +2219,13 @@ cost_subplan(PlannerInfo *root, SubPlan *subplan, Plan *plan)
 
        /*
         * Also account for subplan's startup cost. If the subplan is
-        * uncorrelated or undirect correlated, AND its topmost node is a Sort
-        * or Material node, assume that we'll only need to pay its startup
-        * cost once; otherwise assume we pay the startup cost every time.
+        * uncorrelated or undirect correlated, AND its topmost node is one
+        * that materializes its output, assume that we'll only need to pay
+        * its startup cost once; otherwise assume we pay the startup cost
+        * every time.
         */
        if (subplan->parParam == NIL &&
-           (IsA(plan, Sort) ||
-            IsA(plan, Material)))
+           ExecMaterializesOutput(nodeTag(plan)))
            sp_cost.startup += plan->startup_cost;
        else
            sp_cost.per_tuple += plan->startup_cost;
@@ -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
  *     Estimate the CPU costs of evaluating a WHERE clause.

diff --git a/src/backend/optimizer/path/joinpath.c b/src/backend/optimizer/path/joinpath.c
index bc0831933e354e333de9903a489ffbb7ae446896..269c4824b6ac0b08601cb4b2eaa0734b764bcfab 100644 (file)
--- a/src/backend/optimizer/path/joinpath.c
+++ b/src/backend/optimizer/path/joinpath.c
@@ -8,7 +8,7 @@
  *
  *
  * 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 @@
 
 #include 
 
+#include "executor/executor.h"
 #include "optimizer/cost.h"
 #include "optimizer/pathnode.h"
 #include "optimizer/paths.h"
@@ -405,18 +406,10 @@ match_unsorted_outer(PlannerInfo *root,
    else if (nestjoinOK)
    {
        /*
-        * If the cheapest inner path is a join or seqscan, we should consider
-        * materializing it.  (This is a heuristic: we could consider it
-        * always, but for inner indexscans it's probably a waste of time.)
-        * Also skip it if the inner path materializes its output anyway.
+        * Consider materializing the cheapest inner path, unless it is one
+        * that materializes its output anyway.
         */
-       if (!(inner_cheapest_total->pathtype == T_IndexScan ||
-             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))
+       if (!ExecMaterializesOutput(inner_cheapest_total->pathtype))
            matpath = (Path *)
                create_material_path(innerrel, inner_cheapest_total);
 

diff --git a/src/backend/optimizer/plan/createplan.c b/src/backend/optimizer/plan/createplan.c
index 3f211508a1fe096e68efe0c782510539927e28d3..ac9b96229a197227506f6631b789014561ffb949 100644 (file)
--- a/src/backend/optimizer/plan/createplan.c
+++ b/src/backend/optimizer/plan/createplan.c
@@ -10,7 +10,7 @@
  *
  *
  * 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)
 
    /* Set cost data */
    cost_material(&matpath,
+                 subplan->startup_cost,
                  subplan->total_cost,
                  subplan->plan_rows,
                  subplan->plan_width);

diff --git a/src/backend/optimizer/plan/subselect.c b/src/backend/optimizer/plan/subselect.c
index e56c0755d02af2d72f2bea6c2e2d081d994ed51e..78809474a3bd11f173bf6e5664f573503414960d 100644 (file)
--- a/src/backend/optimizer/plan/subselect.c
+++ b/src/backend/optimizer/plan/subselect.c
@@ -7,7 +7,7 @@
  * Portions Copyright (c) 1994, Regents of the University of California
  *
  * 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 @@
 
 #include "catalog/pg_operator.h"
 #include "catalog/pg_type.h"
+#include "executor/executor.h"
 #include "miscadmin.h"
 #include "nodes/makefuncs.h"
 #include "nodes/nodeFuncs.h"
@@ -564,33 +565,16 @@ build_subplan(PlannerInfo *root, Plan *plan, List *rtable,
            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
         * is pointless for a direct-correlated subplan, since we'd have to
         * 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.
         */
-       else if (splan->parParam == NIL)
-       {
-           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);
-       }
+       else if (splan->parParam == NIL &&
+                !ExecMaterializesOutput(nodeTag(plan)))
+           plan = materialize_finished_plan(plan);
 
        result = (Node *) splan;
        isInitPlan = false;

diff --git a/src/backend/optimizer/util/pathnode.c b/src/backend/optimizer/util/pathnode.c
index b0358cb112ee67c99ccfe6144af8edf4e20d7bcb..e2de24956a236d5a3482d878cd6c06df018f3d23 100644 (file)
--- a/src/backend/optimizer/util/pathnode.c
+++ b/src/backend/optimizer/util/pathnode.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *   $PostgreSQL: pgsql/src/backend/optimizer/util/pathnode.c,v 1.152 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)
    pathnode->subpath = subpath;
 
    cost_material(&pathnode->path,
+                 subpath->startup_cost,
                  subpath->total_cost,
                  rel->rows,
                  rel->width);
@@ -1424,7 +1425,8 @@ create_mergejoin_path(PlannerInfo *root,
         * cost_mergejoin will avoid choosing anyway).  Therefore
         * cost_material's cost estimate is bogus and we should charge just
         * 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->total_cost = inner_path->total_cost;

diff --git a/src/include/executor/executor.h b/src/include/executor/executor.h
index 2ad1e26b2a1f9e95d53f1d03fd99e56a15d8f963..c395eadc370c1b0b8956ac959f11ff66b411b7d6 100644 (file)
--- a/src/include/executor/executor.h
+++ b/src/include/executor/executor.h
@@ -7,7 +7,7 @@
  * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
  * 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);
 extern void ExecRestrPos(PlanState *node);
 extern bool ExecSupportsMarkRestore(NodeTag plantype);
 extern bool ExecSupportsBackwardScan(Plan *node);
+extern bool ExecMaterializesOutput(NodeTag plantype);
 
 /*
  * prototypes from functions in execCurrent.c

diff --git a/src/include/optimizer/cost.h b/src/include/optimizer/cost.h
index 343662f6b87da4016ac8caa5044b34aad0e13bec..f862979c0847baf971417e1ebf1cdc3ff7219549 100644 (file)
--- a/src/include/optimizer/cost.h
+++ b/src/include/optimizer/cost.h
@@ -7,7 +7,7 @@
  * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
  * 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,
          double limit_tuples);
 extern bool sort_exceeds_work_mem(Sort *sort);
 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,
         AggStrategy aggstrategy, int numAggs,
         int numGroupCols, double numGroups,

diff --git a/src/test/regress/expected/geometry.out b/src/test/regress/expected/geometry.out
index 6910e54ec661796d254902098346508c8776e61a..81237252eb77b3c0e09922f019cfbd4fb188d0d5 100644 (file)
--- a/src/test/regress/expected/geometry.out
+++ b/src/test/regress/expected/geometry.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (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)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (-0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-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)
 (20 rows)
 

diff --git a/src/test/regress/expected/geometry_1.out b/src/test/regress/expected/geometry_1.out
index 0e014925257aac965d074677696752a77fae412c..684ccd716838862eab6f8190803ebe126930050e 100644 (file)
--- a/src/test/regress/expected/geometry_1.out
+++ b/src/test/regress/expected/geometry_1.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (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)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-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)
 (20 rows)
 

diff --git a/src/test/regress/expected/geometry_2.out b/src/test/regress/expected/geometry_2.out
index 7787dab06185c6e79d9a6150651e2a6990f52946..658dba48aa50bd5c17d70d6eae0c8cb5cd152f6e 100644 (file)
--- a/src/test/regress/expected/geometry_2.out
+++ b/src/test/regress/expected/geometry_2.out
@@ -260,24 +260,24 @@ SELECT '' AS twenty, b.f1 / p.f1 AS rotation
  twenty |                               rotation                               
 --------+----------------------------------------------------------------------
         | (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)
-        | (0.12,-0.28),(0.04,-0.84)
-        | (0.26,-0.7),(0.1,-0.82)
-        | (0.12,-0.84),(0.12,-0.84)
         | (0.0651176557644,0),(0,-0.0483449262493)
-        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
-        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
-        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
         | (-0,0.0828402366864),(-0.201183431953,0)
-        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
-        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
-        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
         | (0.2,0),(0,0)
+        | (-0.1,-0.1),(-0.3,-0.3)
+        | (0.12,-0.28),(0.04,-0.84)
+        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
+        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
         | (0.3,0),(0.1,0)
+        | (-0.25,-0.25),(-0.25,-0.35)
+        | (0.26,-0.7),(0.1,-0.82)
+        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
+        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
         | (0.3,0.05),(0.25,0)
+        | (-0.3,-0.3),(-0.3,-0.3)
+        | (0.12,-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)
 (20 rows)
 

diff --git a/src/test/regress/expected/join.out b/src/test/regress/expected/join.out
index dd9bf9c43f0d59713e885f00d511d57744798e55..0dc3e56960374cbbe326d10decf961c9281a82f5 100644 (file)
--- a/src/test/regress/expected/join.out
+++ b/src/test/regress/expected/join.out
@@ -662,895 +662,895 @@ SELECT '' AS "xxx", *
  xxx | i | j |   t   | i | k  | i | k  
 -----+---+---+-------+---+----+---+----
      | 1 | 4 | one   | 1 | -1 | 1 | -1
-     | 2 | 3 | two   | 1 | -1 | 1 | -1
-     | 3 | 2 | three | 1 | -1 | 1 | -1
-     | 4 | 1 | four  | 1 | -1 | 1 | -1
-     | 5 | 0 | five  | 1 | -1 | 1 | -1
-     | 6 | 6 | six   | 1 | -1 | 1 | -1
-     | 7 | 7 | seven | 1 | -1 | 1 | -1
-     | 8 | 8 | eight | 1 | -1 | 1 | -1
-     | 0 |   | zero  | 1 | -1 | 1 | -1
-     |   |   | null  | 1 | -1 | 1 | -1
-     |   | 0 | zero  | 1 | -1 | 1 | -1
-     | 1 | 4 | one   | 1 | -1 | 2 |  2
-     | 2 | 3 | two   | 1 | -1 | 2 |  2
-     | 3 | 2 | three | 1 | -1 | 2 |  2
-     | 4 | 1 | four  | 1 | -1 | 2 |  2
-     | 5 | 0 | five  | 1 | -1 | 2 |  2
-     | 6 | 6 | six   | 1 | -1 | 2 |  2
-     | 7 | 7 | seven | 1 | -1 | 2 |  2
-     | 8 | 8 | eight | 1 | -1 | 2 |  2
-     | 0 |   | zero  | 1 | -1 | 2 |  2
-     |   |   | null  | 1 | -1 | 2 |  2
-     |   | 0 | zero  | 1 | -1 | 2 |  2
-     | 1 | 4 | one   | 1 | -1 | 3 | -3
-     | 2 | 3 | two   | 1 | -1 | 3 | -3
-     | 3 | 2 | three | 1 | -1 | 3 | -3
-     | 4 | 1 | four  | 1 | -1 | 3 | -3
-     | 5 | 0 | five  | 1 | -1 | 3 | -3
-     | 6 | 6 | six   | 1 | -1 | 3 | -3
-     | 7 | 7 | seven | 1 | -1 | 3 | -3
-     | 8 | 8 | eight | 1 | -1 | 3 | -3
-     | 0 |   | zero  | 1 | -1 | 3 | -3
-     |   |   | null  | 1 | -1 | 3 | -3
-     |   | 0 | zero  | 1 | -1 | 3 | -3
-     | 1 | 4 | one   | 1 | -1 | 2 |  4
-     | 2 | 3 | two   | 1 | -1 | 2 |  4
-     | 3 | 2 | three | 1 | -1 | 2 |  4
-     | 4 | 1 | four  | 1 | -1 | 2 |  4
-     | 5 | 0 | five  | 1 | -1 | 2 |  4
-     | 6 | 6 | six   | 1 | -1 | 2 |  4
-     | 7 | 7 | seven | 1 | -1 | 2 |  4
-     | 8 | 8 | eight | 1 | -1 | 2 |  4
-     | 0 |   | zero  | 1 | -1 | 2 |  4
-     |   |   | null  | 1 | -1 | 2 |  4
-     |   | 0 | zero  | 1 | -1 | 2 |  4
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 5 | -5
-     | 2 | 3 | two   | 1 | -1 | 5 | -5
-     | 3 | 2 | three | 1 | -1 | 5 | -5
-     | 4 | 1 | four  | 1 | -1 | 5 | -5
-     | 5 | 0 | five  | 1 | -1 | 5 | -5
-     | 6 | 6 | six   | 1 | -1 | 5 | -5
-     | 7 | 7 | seven | 1 | -1 | 5 | -5
-     | 8 | 8 | eight | 1 | -1 | 5 | -5
-     | 0 |   | zero  | 1 | -1 | 5 | -5
-     |   |   | null  | 1 | -1 | 5 | -5
-     |   | 0 | zero  | 1 | -1 | 5 | -5
-     | 1 | 4 | one   | 1 | -1 | 0 |   
-     | 2 | 3 | two   | 1 | -1 | 0 |   
-     | 3 | 2 | three | 1 | -1 | 0 |   
-     | 4 | 1 | four  | 1 | -1 | 0 |   
-     | 5 | 0 | five  | 1 | -1 | 0 |   
-     | 6 | 6 | six   | 1 | -1 | 0 |   
-     | 7 | 7 | seven | 1 | -1 | 0 |   
-     | 8 | 8 | eight | 1 | -1 | 0 |   
-     | 0 |   | zero  | 1 | -1 | 0 |   
-     |   |   | null  | 1 | -1 | 0 |   
-     |   | 0 | zero  | 1 | -1 | 0 |   
-     | 1 | 4 | one   | 1 | -1 |   |   
-     | 2 | 3 | two   | 1 | -1 |   |   
-     | 3 | 2 | three | 1 | -1 |   |   
-     | 4 | 1 | four  | 1 | -1 |   |   
-     | 5 | 0 | five  | 1 | -1 |   |   
-     | 6 | 6 | six   | 1 | -1 |   |   
-     | 7 | 7 | seven | 1 | -1 |   |   
-     | 8 | 8 | eight | 1 | -1 |   |   
-     | 0 |   | zero  | 1 | -1 |   |   
-     |   |   | null  | 1 | -1 |   |   
-     |   | 0 | zero  | 1 | -1 |   |   
-     | 1 | 4 | one   | 1 | -1 |   |  0
-     | 2 | 3 | two   | 1 | -1 |   |  0
-     | 3 | 2 | three | 1 | -1 |   |  0
-     | 4 | 1 | four  | 1 | -1 |   |  0
-     | 5 | 0 | five  | 1 | -1 |   |  0
-     | 6 | 6 | six   | 1 | -1 |   |  0
-     | 7 | 7 | seven | 1 | -1 |   |  0
-     | 8 | 8 | eight | 1 | -1 |   |  0
-     | 0 |   | zero  | 1 | -1 |   |  0
-     |   |   | null  | 1 | -1 |   |  0
-     |   | 0 | zero  | 1 | -1 |   |  0
-     | 1 | 4 | one   | 2 |  2 | 1 | -1
-     | 2 | 3 | two   | 2 |  2 | 1 | -1
-     | 3 | 2 | three | 2 |  2 | 1 | -1
-     | 4 | 1 | four  | 2 |  2 | 1 | -1
-     | 5 | 0 | five  | 2 |  2 | 1 | -1
-     | 6 | 6 | six   | 2 |  2 | 1 | -1
-     | 7 | 7 | seven | 2 |  2 | 1 | -1
-     | 8 | 8 | eight | 2 |  2 | 1 | -1
-     | 0 |   | zero  | 2 |  2 | 1 | -1
-     |   |   | null  | 2 |  2 | 1 | -1
-     |   | 0 | zero  | 2 |  2 | 1 | -1
-     | 1 | 4 | one   | 2 |  2 | 2 |  2
-     | 2 | 3 | two   | 2 |  2 | 2 |  2
-     | 3 | 2 | three | 2 |  2 | 2 |  2
-     | 4 | 1 | four  | 2 |  2 | 2 |  2
-     | 5 | 0 | five  | 2 |  2 | 2 |  2
-     | 6 | 6 | six   | 2 |  2 | 2 |  2
-     | 7 | 7 | seven | 2 |  2 | 2 |  2
-     | 8 | 8 | eight | 2 |  2 | 2 |  2
-     | 0 |   | zero  | 2 |  2 | 2 |  2
-     |   |   | null  | 2 |  2 | 2 |  2
-     |   | 0 | zero  | 2 |  2 | 2 |  2
-     | 1 | 4 | one   | 2 |  2 | 3 | -3
-     | 2 | 3 | two   | 2 |  2 | 3 | -3
-     | 3 | 2 | three | 2 |  2 | 3 | -3
-     | 4 | 1 | four  | 2 |  2 | 3 | -3
-     | 5 | 0 | five  | 2 |  2 | 3 | -3
-     | 6 | 6 | six   | 2 |  2 | 3 | -3
-     | 7 | 7 | seven | 2 |  2 | 3 | -3
-     | 8 | 8 | eight | 2 |  2 | 3 | -3
-     | 0 |   | zero  | 2 |  2 | 3 | -3
-     |   |   | null  | 2 |  2 | 3 | -3
-     |   | 0 | zero  | 2 |  2 | 3 | -3
-     | 1 | 4 | one   | 2 |  2 | 2 |  4
-     | 2 | 3 | two   | 2 |  2 | 2 |  4
-     | 3 | 2 | three | 2 |  2 | 2 |  4
-     | 4 | 1 | four  | 2 |  2 | 2 |  4
-     | 5 | 0 | five  | 2 |  2 | 2 |  4
-     | 6 | 6 | six   | 2 |  2 | 2 |  4
-     | 7 | 7 | seven | 2 |  2 | 2 |  4
-     | 8 | 8 | eight | 2 |  2 | 2 |  4
-     | 0 |   | zero  | 2 |  2 | 2 |  4
-     |   |   | null  | 2 |  2 | 2 |  4
-     |   | 0 | zero  | 2 |  2 | 2 |  4
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 5 | -5
-     | 2 | 3 | two   | 2 |  2 | 5 | -5
-     | 3 | 2 | three | 2 |  2 | 5 | -5
-     | 4 | 1 | four  | 2 |  2 | 5 | -5
-     | 5 | 0 | five  | 2 |  2 | 5 | -5
-     | 6 | 6 | six   | 2 |  2 | 5 | -5
-     | 7 | 7 | seven | 2 |  2 | 5 | -5
-     | 8 | 8 | eight | 2 |  2 | 5 | -5
-     | 0 |   | zero  | 2 |  2 | 5 | -5
-     |   |   | null  | 2 |  2 | 5 | -5
-     |   | 0 | zero  | 2 |  2 | 5 | -5
-     | 1 | 4 | one   | 2 |  2 | 0 |   
-     | 2 | 3 | two   | 2 |  2 | 0 |   
-     | 3 | 2 | three | 2 |  2 | 0 |   
-     | 4 | 1 | four  | 2 |  2 | 0 |   
-     | 5 | 0 | five  | 2 |  2 | 0 |   
-     | 6 | 6 | six   | 2 |  2 | 0 |   
-     | 7 | 7 | seven | 2 |  2 | 0 |   
-     | 8 | 8 | eight | 2 |  2 | 0 |   
-     | 0 |   | zero  | 2 |  2 | 0 |   
-     |   |   | null  | 2 |  2 | 0 |   
-     |   | 0 | zero  | 2 |  2 | 0 |   
-     | 1 | 4 | one   | 2 |  2 |   |   
-     | 2 | 3 | two   | 2 |  2 |   |   
-     | 3 | 2 | three | 2 |  2 |   |   
-     | 4 | 1 | four  | 2 |  2 |   |   
-     | 5 | 0 | five  | 2 |  2 |   |   
-     | 6 | 6 | six   | 2 |  2 |   |   
-     | 7 | 7 | seven | 2 |  2 |   |   
-     | 8 | 8 | eight | 2 |  2 |   |   
-     | 0 |   | zero  | 2 |  2 |   |   
-     |   |   | null  | 2 |  2 |   |   
-     |   | 0 | zero  | 2 |  2 |   |   
-     | 1 | 4 | one   | 2 |  2 |   |  0
-     | 2 | 3 | two   | 2 |  2 |   |  0
-     | 3 | 2 | three | 2 |  2 |   |  0
-     | 4 | 1 | four  | 2 |  2 |   |  0
-     | 5 | 0 | five  | 2 |  2 |   |  0
-     | 6 | 6 | six   | 2 |  2 |   |  0
-     | 7 | 7 | seven | 2 |  2 |   |  0
-     | 8 | 8 | eight | 2 |  2 |   |  0
-     | 0 |   | zero  | 2 |  2 |   |  0
-     |   |   | null  | 2 |  2 |   |  0
-     |   | 0 | zero  | 2 |  2 |   |  0
-     | 1 | 4 | one   | 3 | -3 | 1 | -1
-     | 2 | 3 | two   | 3 | -3 | 1 | -1
-     | 3 | 2 | three | 3 | -3 | 1 | -1
-     | 4 | 1 | four  | 3 | -3 | 1 | -1
-     | 5 | 0 | five  | 3 | -3 | 1 | -1
-     | 6 | 6 | six   | 3 | -3 | 1 | -1
-     | 7 | 7 | seven | 3 | -3 | 1 | -1
-     | 8 | 8 | eight | 3 | -3 | 1 | -1
-     | 0 |   | zero  | 3 | -3 | 1 | -1
-     |   |   | null  | 3 | -3 | 1 | -1
-     |   | 0 | zero  | 3 | -3 | 1 | -1
-     | 1 | 4 | one   | 3 | -3 | 2 |  2
-     | 2 | 3 | two   | 3 | -3 | 2 |  2
-     | 3 | 2 | three | 3 | -3 | 2 |  2
-     | 4 | 1 | four  | 3 | -3 | 2 |  2
-     | 5 | 0 | five  | 3 | -3 | 2 |  2
-     | 6 | 6 | six   | 3 | -3 | 2 |  2
-     | 7 | 7 | seven | 3 | -3 | 2 |  2
-     | 8 | 8 | eight | 3 | -3 | 2 |  2
-     | 0 |   | zero  | 3 | -3 | 2 |  2
-     |   |   | null  | 3 | -3 | 2 |  2
-     |   | 0 | zero  | 3 | -3 | 2 |  2
-     | 1 | 4 | one   | 3 | -3 | 3 | -3
-     | 2 | 3 | two   | 3 | -3 | 3 | -3
-     | 3 | 2 | three | 3 | -3 | 3 | -3
-     | 4 | 1 | four  | 3 | -3 | 3 | -3
-     | 5 | 0 | five  | 3 | -3 | 3 | -3
-     | 6 | 6 | six   | 3 | -3 | 3 | -3
-     | 7 | 7 | seven | 3 | -3 | 3 | -3
-     | 8 | 8 | eight | 3 | -3 | 3 | -3
-     | 0 |   | zero  | 3 | -3 | 3 | -3
-     |   |   | null  | 3 | -3 | 3 | -3
-     |   | 0 | zero  | 3 | -3 | 3 | -3
-     | 1 | 4 | one   | 3 | -3 | 2 |  4
-     | 2 | 3 | two   | 3 | -3 | 2 |  4
-     | 3 | 2 | three | 3 | -3 | 2 |  4
-     | 4 | 1 | four  | 3 | -3 | 2 |  4
-     | 5 | 0 | five  | 3 | -3 | 2 |  4
-     | 6 | 6 | six   | 3 | -3 | 2 |  4
-     | 7 | 7 | seven | 3 | -3 | 2 |  4
-     | 8 | 8 | eight | 3 | -3 | 2 |  4
-     | 0 |   | zero  | 3 | -3 | 2 |  4
-     |   |   | null  | 3 | -3 | 2 |  4
-     |   | 0 | zero  | 3 | -3 | 2 |  4
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 5 | -5
-     | 2 | 3 | two   | 3 | -3 | 5 | -5
-     | 3 | 2 | three | 3 | -3 | 5 | -5
-     | 4 | 1 | four  | 3 | -3 | 5 | -5
-     | 5 | 0 | five  | 3 | -3 | 5 | -5
-     | 6 | 6 | six   | 3 | -3 | 5 | -5
-     | 7 | 7 | seven | 3 | -3 | 5 | -5
-     | 8 | 8 | eight | 3 | -3 | 5 | -5
-     | 0 |   | zero  | 3 | -3 | 5 | -5
-     |   |   | null  | 3 | -3 | 5 | -5
-     |   | 0 | zero  | 3 | -3 | 5 | -5
-     | 1 | 4 | one   | 3 | -3 | 0 |   
-     | 2 | 3 | two   | 3 | -3 | 0 |   
-     | 3 | 2 | three | 3 | -3 | 0 |   
-     | 4 | 1 | four  | 3 | -3 | 0 |   
-     | 5 | 0 | five  | 3 | -3 | 0 |   
-     | 6 | 6 | six   | 3 | -3 | 0 |   
-     | 7 | 7 | seven | 3 | -3 | 0 |   
-     | 8 | 8 | eight | 3 | -3 | 0 |   
-     | 0 |   | zero  | 3 | -3 | 0 |   
-     |   |   | null  | 3 | -3 | 0 |   
-     |   | 0 | zero  | 3 | -3 | 0 |   
-     | 1 | 4 | one   | 3 | -3 |   |   
-     | 2 | 3 | two   | 3 | -3 |   |   
-     | 3 | 2 | three | 3 | -3 |   |   
-     | 4 | 1 | four  | 3 | -3 |   |   
-     | 5 | 0 | five  | 3 | -3 |   |   
-     | 6 | 6 | six   | 3 | -3 |   |   
-     | 7 | 7 | seven | 3 | -3 |   |   
-     | 8 | 8 | eight | 3 | -3 |   |   
-     | 0 |   | zero  | 3 | -3 |   |   
-     |   |   | null  | 3 | -3 |   |   
-     |   | 0 | zero  | 3 | -3 |   |   
-     | 1 | 4 | one   | 3 | -3 |   |  0
-     | 2 | 3 | two   | 3 | -3 |   |  0
-     | 3 | 2 | three | 3 | -3 |   |  0
-     | 4 | 1 | four  | 3 | -3 |   |  0
-     | 5 | 0 | five  | 3 | -3 |   |  0
-     | 6 | 6 | six   | 3 | -3 |   |  0
-     | 7 | 7 | seven | 3 | -3 |   |  0
-     | 8 | 8 | eight | 3 | -3 |   |  0
-     | 0 |   | zero  | 3 | -3 |   |  0
-     |   |   | null  | 3 | -3 |   |  0
-     |   | 0 | zero  | 3 | -3 |   |  0
-     | 1 | 4 | one   | 2 |  4 | 1 | -1
-     | 2 | 3 | two   | 2 |  4 | 1 | -1
-     | 3 | 2 | three | 2 |  4 | 1 | -1
-     | 4 | 1 | four  | 2 |  4 | 1 | -1
-     | 5 | 0 | five  | 2 |  4 | 1 | -1
-     | 6 | 6 | six   | 2 |  4 | 1 | -1
-     | 7 | 7 | seven | 2 |  4 | 1 | -1
-     | 8 | 8 | eight | 2 |  4 | 1 | -1
-     | 0 |   | zero  | 2 |  4 | 1 | -1
-     |   |   | null  | 2 |  4 | 1 | -1
-     |   | 0 | zero  | 2 |  4 | 1 | -1
-     | 1 | 4 | one   | 2 |  4 | 2 |  2
-     | 2 | 3 | two   | 2 |  4 | 2 |  2
-     | 3 | 2 | three | 2 |  4 | 2 |  2
-     | 4 | 1 | four  | 2 |  4 | 2 |  2
-     | 5 | 0 | five  | 2 |  4 | 2 |  2
-     | 6 | 6 | six   | 2 |  4 | 2 |  2
-     | 7 | 7 | seven | 2 |  4 | 2 |  2
-     | 8 | 8 | eight | 2 |  4 | 2 |  2
-     | 0 |   | zero  | 2 |  4 | 2 |  2
-     |   |   | null  | 2 |  4 | 2 |  2
-     |   | 0 | zero  | 2 |  4 | 2 |  2
-     | 1 | 4 | one   | 2 |  4 | 3 | -3
-     | 2 | 3 | two   | 2 |  4 | 3 | -3
-     | 3 | 2 | three | 2 |  4 | 3 | -3
-     | 4 | 1 | four  | 2 |  4 | 3 | -3
-     | 5 | 0 | five  | 2 |  4 | 3 | -3
-     | 6 | 6 | six   | 2 |  4 | 3 | -3
-     | 7 | 7 | seven | 2 |  4 | 3 | -3
-     | 8 | 8 | eight | 2 |  4 | 3 | -3
-     | 0 |   | zero  | 2 |  4 | 3 | -3
-     |   |   | null  | 2 |  4 | 3 | -3
-     |   | 0 | zero  | 2 |  4 | 3 | -3
-     | 1 | 4 | one   | 2 |  4 | 2 |  4
-     | 2 | 3 | two   | 2 |  4 | 2 |  4
-     | 3 | 2 | three | 2 |  4 | 2 |  4
-     | 4 | 1 | four  | 2 |  4 | 2 |  4
-     | 5 | 0 | five  | 2 |  4 | 2 |  4
-     | 6 | 6 | six   | 2 |  4 | 2 |  4
-     | 7 | 7 | seven | 2 |  4 | 2 |  4
-     | 8 | 8 | eight | 2 |  4 | 2 |  4
-     | 0 |   | zero  | 2 |  4 | 2 |  4
-     |   |   | null  | 2 |  4 | 2 |  4
-     |   | 0 | zero  | 2 |  4 | 2 |  4
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 5 | -5
-     | 2 | 3 | two   | 2 |  4 | 5 | -5
-     | 3 | 2 | three | 2 |  4 | 5 | -5
-     | 4 | 1 | four  | 2 |  4 | 5 | -5
-     | 5 | 0 | five  | 2 |  4 | 5 | -5
-     | 6 | 6 | six   | 2 |  4 | 5 | -5
-     | 7 | 7 | seven | 2 |  4 | 5 | -5
-     | 8 | 8 | eight | 2 |  4 | 5 | -5
-     | 0 |   | zero  | 2 |  4 | 5 | -5
-     |   |   | null  | 2 |  4 | 5 | -5
-     |   | 0 | zero  | 2 |  4 | 5 | -5
-     | 1 | 4 | one   | 2 |  4 | 0 |   
-     | 2 | 3 | two   | 2 |  4 | 0 |   
-     | 3 | 2 | three | 2 |  4 | 0 |   
-     | 4 | 1 | four  | 2 |  4 | 0 |   
-     | 5 | 0 | five  | 2 |  4 | 0 |   
-     | 6 | 6 | six   | 2 |  4 | 0 |   
-     | 7 | 7 | seven | 2 |  4 | 0 |   
-     | 8 | 8 | eight | 2 |  4 | 0 |   
-     | 0 |   | zero  | 2 |  4 | 0 |   
-     |   |   | null  | 2 |  4 | 0 |   
-     |   | 0 | zero  | 2 |  4 | 0 |   
-     | 1 | 4 | one   | 2 |  4 |   |   
-     | 2 | 3 | two   | 2 |  4 |   |   
-     | 3 | 2 | three | 2 |  4 |   |   
-     | 4 | 1 | four  | 2 |  4 |   |   
-     | 5 | 0 | five  | 2 |  4 |   |   
-     | 6 | 6 | six   | 2 |  4 |   |   
-     | 7 | 7 | seven | 2 |  4 |   |   
-     | 8 | 8 | eight | 2 |  4 |   |   
-     | 0 |   | zero  | 2 |  4 |   |   
-     |   |   | null  | 2 |  4 |   |   
-     |   | 0 | zero  | 2 |  4 |   |   
-     | 1 | 4 | one   | 2 |  4 |   |  0
-     | 2 | 3 | two   | 2 |  4 |   |  0
-     | 3 | 2 | three | 2 |  4 |   |  0
-     | 4 | 1 | four  | 2 |  4 |   |  0
-     | 5 | 0 | five  | 2 |  4 |   |  0
-     | 6 | 6 | six   | 2 |  4 |   |  0
-     | 7 | 7 | seven | 2 |  4 |   |  0
-     | 8 | 8 | eight | 2 |  4 |   |  0
-     | 0 |   | zero  | 2 |  4 |   |  0
-     |   |   | null  | 2 |  4 |   |  0
-     |   | 0 | zero  | 2 |  4 |   |  0
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
-     | 1 | 4 | one   | 5 | -5 | 1 | -1
-     | 2 | 3 | two   | 5 | -5 | 1 | -1
-     | 3 | 2 | three | 5 | -5 | 1 | -1
-     | 4 | 1 | four  | 5 | -5 | 1 | -1
-     | 5 | 0 | five  | 5 | -5 | 1 | -1
-     | 6 | 6 | six   | 5 | -5 | 1 | -1
-     | 7 | 7 | seven | 5 | -5 | 1 | -1
-     | 8 | 8 | eight | 5 | -5 | 1 | -1
-     | 0 |   | zero  | 5 | -5 | 1 | -1
-     |   |   | null  | 5 | -5 | 1 | -1
-     |   | 0 | zero  | 5 | -5 | 1 | -1
-     | 1 | 4 | one   | 5 | -5 | 2 |  2
-     | 2 | 3 | two   | 5 | -5 | 2 |  2
-     | 3 | 2 | three | 5 | -5 | 2 |  2
-     | 4 | 1 | four  | 5 | -5 | 2 |  2
-     | 5 | 0 | five  | 5 | -5 | 2 |  2
-     | 6 | 6 | six   | 5 | -5 | 2 |  2
-     | 7 | 7 | seven | 5 | -5 | 2 |  2
-     | 8 | 8 | eight | 5 | -5 | 2 |  2
-     | 0 |   | zero  | 5 | -5 | 2 |  2
-     |   |   | null  | 5 | -5 | 2 |  2
-     |   | 0 | zero  | 5 | -5 | 2 |  2
-     | 1 | 4 | one   | 5 | -5 | 3 | -3
-     | 2 | 3 | two   | 5 | -5 | 3 | -3
-     | 3 | 2 | three | 5 | -5 | 3 | -3
-     | 4 | 1 | four  | 5 | -5 | 3 | -3
-     | 5 | 0 | five  | 5 | -5 | 3 | -3
-     | 6 | 6 | six   | 5 | -5 | 3 | -3
-     | 7 | 7 | seven | 5 | -5 | 3 | -3
-     | 8 | 8 | eight | 5 | -5 | 3 | -3
-     | 0 |   | zero  | 5 | -5 | 3 | -3
-     |   |   | null  | 5 | -5 | 3 | -3
-     |   | 0 | zero  | 5 | -5 | 3 | -3
-     | 1 | 4 | one   | 5 | -5 | 2 |  4
-     | 2 | 3 | two   | 5 | -5 | 2 |  4
-     | 3 | 2 | three | 5 | -5 | 2 |  4
-     | 4 | 1 | four  | 5 | -5 | 2 |  4
-     | 5 | 0 | five  | 5 | -5 | 2 |  4
-     | 6 | 6 | six   | 5 | -5 | 2 |  4
-     | 7 | 7 | seven | 5 | -5 | 2 |  4
-     | 8 | 8 | eight | 5 | -5 | 2 |  4
-     | 0 |   | zero  | 5 | -5 | 2 |  4
-     |   |   | null  | 5 | -5 | 2 |  4
-     |   | 0 | zero  | 5 | -5 | 2 |  4
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 5 | -5
-     | 2 | 3 | two   | 5 | -5 | 5 | -5
-     | 3 | 2 | three | 5 | -5 | 5 | -5
-     | 4 | 1 | four  | 5 | -5 | 5 | -5
-     | 5 | 0 | five  | 5 | -5 | 5 | -5
-     | 6 | 6 | six   | 5 | -5 | 5 | -5
-     | 7 | 7 | seven | 5 | -5 | 5 | -5
-     | 8 | 8 | eight | 5 | -5 | 5 | -5
-     | 0 |   | zero  | 5 | -5 | 5 | -5
-     |   |   | null  | 5 | -5 | 5 | -5
-     |   | 0 | zero  | 5 | -5 | 5 | -5
-     | 1 | 4 | one   | 5 | -5 | 0 |   
-     | 2 | 3 | two   | 5 | -5 | 0 |   
-     | 3 | 2 | three | 5 | -5 | 0 |   
-     | 4 | 1 | four  | 5 | -5 | 0 |   
-     | 5 | 0 | five  | 5 | -5 | 0 |   
-     | 6 | 6 | six   | 5 | -5 | 0 |   
-     | 7 | 7 | seven | 5 | -5 | 0 |   
-     | 8 | 8 | eight | 5 | -5 | 0 |   
-     | 0 |   | zero  | 5 | -5 | 0 |   
-     |   |   | null  | 5 | -5 | 0 |   
-     |   | 0 | zero  | 5 | -5 | 0 |   
-     | 1 | 4 | one   | 5 | -5 |   |   
-     | 2 | 3 | two   | 5 | -5 |   |   
-     | 3 | 2 | three | 5 | -5 |   |   
-     | 4 | 1 | four  | 5 | -5 |   |   
-     | 5 | 0 | five  | 5 | -5 |   |   
-     | 6 | 6 | six   | 5 | -5 |   |   
-     | 7 | 7 | seven | 5 | -5 |   |   
-     | 8 | 8 | eight | 5 | -5 |   |   
-     | 0 |   | zero  | 5 | -5 |   |   
-     |   |   | null  | 5 | -5 |   |   
-     |   | 0 | zero  | 5 | -5 |   |   
-     | 1 | 4 | one   | 5 | -5 |   |  0
-     | 2 | 3 | two   | 5 | -5 |   |  0
-     | 3 | 2 | three | 5 | -5 |   |  0
-     | 4 | 1 | four  | 5 | -5 |   |  0
-     | 5 | 0 | five  | 5 | -5 |   |  0
-     | 6 | 6 | six   | 5 | -5 |   |  0
-     | 7 | 7 | seven | 5 | -5 |   |  0
-     | 8 | 8 | eight | 5 | -5 |   |  0
-     | 0 |   | zero  | 5 | -5 |   |  0
-     |   |   | null  | 5 | -5 |   |  0
-     |   | 0 | zero  | 5 | -5 |   |  0
+     | 1 | 4 | one   | 2 |  2 | 1 | -1
+     | 1 | 4 | one   | 3 | -3 | 1 | -1
+     | 1 | 4 | one   | 2 |  4 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 1 | -1
+     | 1 | 4 | one   | 5 | -5 | 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
-     | 2 | 3 | two   |   |    | 1 | -1
-     | 3 | 2 | three |   |    | 1 | -1
-     | 4 | 1 | four  |   |    | 1 | -1
-     | 5 | 0 | five  |   |    | 1 | -1
-     | 6 | 6 | six   |   |    | 1 | -1
-     | 7 | 7 | seven |   |    | 1 | -1
-     | 8 | 8 | eight |   |    | 1 | -1
-     | 0 |   | zero  |   |    | 1 | -1
-     |   |   | null  |   |    | 1 | -1
-     |   | 0 | zero  |   |    | 1 | -1
-     | 1 | 4 | one   |   |    | 2 |  2
-     | 2 | 3 | two   |   |    | 2 |  2
-     | 3 | 2 | three |   |    | 2 |  2
-     | 4 | 1 | four  |   |    | 2 |  2
-     | 5 | 0 | five  |   |    | 2 |  2
-     | 6 | 6 | six   |   |    | 2 |  2
-     | 7 | 7 | seven |   |    | 2 |  2
-     | 8 | 8 | eight |   |    | 2 |  2
-     | 0 |   | zero  |   |    | 2 |  2
-     |   |   | null  |   |    | 2 |  2
-     |   | 0 | zero  |   |    | 2 |  2
-     | 1 | 4 | one   |   |    | 3 | -3
-     | 2 | 3 | two   |   |    | 3 | -3
-     | 3 | 2 | three |   |    | 3 | -3
-     | 4 | 1 | four  |   |    | 3 | -3
-     | 5 | 0 | five  |   |    | 3 | -3
-     | 6 | 6 | six   |   |    | 3 | -3
-     | 7 | 7 | seven |   |    | 3 | -3
-     | 8 | 8 | eight |   |    | 3 | -3
-     | 0 |   | zero  |   |    | 3 | -3
-     |   |   | null  |   |    | 3 | -3
-     |   | 0 | zero  |   |    | 3 | -3
-     | 1 | 4 | one   |   |    | 2 |  4
-     | 2 | 3 | two   |   |    | 2 |  4
-     | 3 | 2 | three |   |    | 2 |  4
-     | 4 | 1 | four  |   |    | 2 |  4
-     | 5 | 0 | five  |   |    | 2 |  4
-     | 6 | 6 | six   |   |    | 2 |  4
-     | 7 | 7 | seven |   |    | 2 |  4
-     | 8 | 8 | eight |   |    | 2 |  4
-     | 0 |   | zero  |   |    | 2 |  4
-     |   |   | null  |   |    | 2 |  4
-     |   | 0 | zero  |   |    | 2 |  4
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     | 1 | 4 | one   |   |    | 5 | -5
-     | 2 | 3 | two   |   |    | 5 | -5
-     | 3 | 2 | three |   |    | 5 | -5
-     | 4 | 1 | four  |   |    | 5 | -5
-     | 5 | 0 | five  |   |    | 5 | -5
-     | 6 | 6 | six   |   |    | 5 | -5
-     | 7 | 7 | seven |   |    | 5 | -5
-     | 8 | 8 | eight |   |    | 5 | -5
-     | 0 |   | zero  |   |    | 5 | -5
-     |   |   | null  |   |    | 5 | -5
-     |   | 0 | zero  |   |    | 5 | -5
-     | 1 | 4 | one   |   |    | 0 |   
-     | 2 | 3 | two   |   |    | 0 |   
-     | 3 | 2 | three |   |    | 0 |   
-     | 4 | 1 | four  |   |    | 0 |   
-     | 5 | 0 | five  |   |    | 0 |   
-     | 6 | 6 | six   |   |    | 0 |   
-     | 7 | 7 | seven |   |    | 0 |   
-     | 8 | 8 | eight |   |    | 0 |   
-     | 0 |   | zero  |   |    | 0 |   
-     |   |   | null  |   |    | 0 |   
-     |   | 0 | zero  |   |    | 0 |   
-     | 1 | 4 | one   |   |    |   |   
-     | 2 | 3 | two   |   |    |   |   
-     | 3 | 2 | three |   |    |   |   
-     | 4 | 1 | four  |   |    |   |   
-     | 5 | 0 | five  |   |    |   |   
-     | 6 | 6 | six   |   |    |   |   
-     | 7 | 7 | seven |   |    |   |   
-     | 8 | 8 | eight |   |    |   |   
-     | 0 |   | zero  |   |    |   |   
-     |   |   | null  |   |    |   |   
-     |   | 0 | zero  |   |    |   |   
-     | 1 | 4 | one   |   |    |   |  0
-     | 2 | 3 | two   |   |    |   |  0
-     | 3 | 2 | three |   |    |   |  0
-     | 4 | 1 | four  |   |    |   |  0
-     | 5 | 0 | five  |   |    |   |  0
-     | 6 | 6 | six   |   |    |   |  0
-     | 7 | 7 | seven |   |    |   |  0
-     | 8 | 8 | eight |   |    |   |  0
-     | 0 |   | zero  |   |    |   |  0
-     |   |   | null  |   |    |   |  0
-     |   | 0 | zero  |   |    |   |  0
      | 1 | 4 | one   |   |  0 | 1 | -1
+     | 2 | 3 | two   | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     |   |   | 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
+     |   | 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
+     | 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
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      | 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
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      | 2 | 3 | two   |   |  0 | 2 |  2
+     | 3 | 2 | three | 1 | -1 | 2 |  2
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+     | 3 | 2 | three | 5 | -5 | 2 |  2
+     | 3 | 2 | three | 0 |    | 2 |  2
+     | 3 | 2 | three |   |    | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     |   |   | 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
+     |   | 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
+     | 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
+     | 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
+     | 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
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+     | 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 |   
+     | 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 |   
+     | 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 |   
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      | 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 |   
+     | 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 |   
+     | 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 |   
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      | 0 |   | zero  |   |  0 | 0 |   
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+     |   |   | null  | 2 |  2 | 0 |   
+     |   |   | null  | 3 | -3 | 0 |   
+     |   |   | null  | 2 |  4 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
+     |   |   | null  | 5 | -5 | 0 |   
+     |   |   | null  | 0 |    | 0 |   
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      |   |   | null  |   |  0 | 0 |   
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+     |   | 0 | zero  | 3 | -3 | 0 |   
+     |   | 0 | zero  | 2 |  4 | 0 |   
+     |   | 0 | zero  | 5 | -5 | 0 |   
+     |   | 0 | zero  | 5 | -5 | 0 |   
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      |   | 0 | zero  |   |  0 | 0 |   
+     | 1 | 4 | one   | 1 | -1 |   |   
+     | 1 | 4 | one   | 2 |  2 |   |   
+     | 1 | 4 | one   | 3 | -3 |   |   
+     | 1 | 4 | one   | 2 |  4 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 1 | 4 | one   | 5 | -5 |   |   
+     | 1 | 4 | one   | 0 |    |   |   
+     | 1 | 4 | one   |   |    |   |   
      | 1 | 4 | one   |   |  0 |   |   
+     | 2 | 3 | two   | 1 | -1 |   |   
+     | 2 | 3 | two   | 2 |  2 |   |   
+     | 2 | 3 | two   | 3 | -3 |   |   
+     | 2 | 3 | two   | 2 |  4 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 2 | 3 | two   | 5 | -5 |   |   
+     | 2 | 3 | two   | 0 |    |   |   
+     | 2 | 3 | two   |   |    |   |   
      | 2 | 3 | two   |   |  0 |   |   
+     | 3 | 2 | three | 1 | -1 |   |   
+     | 3 | 2 | three | 2 |  2 |   |   
+     | 3 | 2 | three | 3 | -3 |   |   
+     | 3 | 2 | three | 2 |  4 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 3 | 2 | three | 5 | -5 |   |   
+     | 3 | 2 | three | 0 |    |   |   
+     | 3 | 2 | three |   |    |   |   
      | 3 | 2 | three |   |  0 |   |   
+     | 4 | 1 | four  | 1 | -1 |   |   
+     | 4 | 1 | four  | 2 |  2 |   |   
+     | 4 | 1 | four  | 3 | -3 |   |   
+     | 4 | 1 | four  | 2 |  4 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 4 | 1 | four  | 5 | -5 |   |   
+     | 4 | 1 | four  | 0 |    |   |   
+     | 4 | 1 | four  |   |    |   |   
      | 4 | 1 | four  |   |  0 |   |   
+     | 5 | 0 | five  | 1 | -1 |   |   
+     | 5 | 0 | five  | 2 |  2 |   |   
+     | 5 | 0 | five  | 3 | -3 |   |   
+     | 5 | 0 | five  | 2 |  4 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 5 | 0 | five  | 5 | -5 |   |   
+     | 5 | 0 | five  | 0 |    |   |   
+     | 5 | 0 | five  |   |    |   |   
      | 5 | 0 | five  |   |  0 |   |   
+     | 6 | 6 | six   | 1 | -1 |   |   
+     | 6 | 6 | six   | 2 |  2 |   |   
+     | 6 | 6 | six   | 3 | -3 |   |   
+     | 6 | 6 | six   | 2 |  4 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 6 | 6 | six   | 5 | -5 |   |   
+     | 6 | 6 | six   | 0 |    |   |   
+     | 6 | 6 | six   |   |    |   |   
      | 6 | 6 | six   |   |  0 |   |   
+     | 7 | 7 | seven | 1 | -1 |   |   
+     | 7 | 7 | seven | 2 |  2 |   |   
+     | 7 | 7 | seven | 3 | -3 |   |   
+     | 7 | 7 | seven | 2 |  4 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 7 | 7 | seven | 5 | -5 |   |   
+     | 7 | 7 | seven | 0 |    |   |   
+     | 7 | 7 | seven |   |    |   |   
      | 7 | 7 | seven |   |  0 |   |   
+     | 8 | 8 | eight | 1 | -1 |   |   
+     | 8 | 8 | eight | 2 |  2 |   |   
+     | 8 | 8 | eight | 3 | -3 |   |   
+     | 8 | 8 | eight | 2 |  4 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 8 | 8 | eight | 5 | -5 |   |   
+     | 8 | 8 | eight | 0 |    |   |   
+     | 8 | 8 | eight |   |    |   |   
      | 8 | 8 | eight |   |  0 |   |   
+     | 0 |   | zero  | 1 | -1 |   |   
+     | 0 |   | zero  | 2 |  2 |   |   
+     | 0 |   | zero  | 3 | -3 |   |   
+     | 0 |   | zero  | 2 |  4 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     | 0 |   | zero  | 5 | -5 |   |   
+     | 0 |   | zero  | 0 |    |   |   
+     | 0 |   | zero  |   |    |   |   
      | 0 |   | zero  |   |  0 |   |   
+     |   |   | null  | 1 | -1 |   |   
+     |   |   | null  | 2 |  2 |   |   
+     |   |   | null  | 3 | -3 |   |   
+     |   |   | null  | 2 |  4 |   |   
+     |   |   | null  | 5 | -5 |   |   
+     |   |   | null  | 5 | -5 |   |   
+     |   |   | null  | 0 |    |   |   
+     |   |   | null  |   |    |   |   
      |   |   | null  |   |  0 |   |   
+     |   | 0 | zero  | 1 | -1 |   |   
+     |   | 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 |   |   
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     | 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
+     |   |   | 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
+     |   | 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
 (891 rows)