yujun777 commented on code in PR #68646:
URL: https://github.com/apache/doris/pull/68646#discussion_r4214819224


##########
fe/fe-core/src/main/java/org/apache/doris/mtmv/MTMVRelationManager.java:
##########
@@ -349,34 +360,221 @@ public void dropTable(Table table) {
         // because a dropped table is the one change whose query is gone 
beyond doubt. What the two record
         // is the same state either way. Unlike a rename it stays an 
invalidation: the table is gone for
         // good, so the state is not something a later alter can make obsolete.
-        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", false);
+        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", null);
     }
 
     /**
      * update mtmv status to `SCHEMA_CHANGE`.
      *
      * @param isReplace
+     * @param queryJudgedColumns the names the alter gives the table or takes 
away from it, which leave the
+     *                           judgement about each MV's state to that MV's 
own query, or null when the
+     *                           alter is not one a query decides. The names 
are carried rather than judged
+     *                           before the call because the judgement is 
about them; see
+     *                           {@code AlterOp#queryJudgedColumnNames} for 
which operations name one, and
+     *                           {@link #invalidateMvUnlessQueryHolds} for 
what is asked about it. A rename
+     *                           of the base table names no column: it is left 
to the record below, which
+     *                           says what the MV that keeps spelling the old 
name needs to hear
      */
     @Override
-    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace) {
+    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace,
+            QueryJudgedChange queryJudgedChange) {
         // when replace, need deal two table
         if (isReplace) {
             // REPLACE TABLE already invalidates the IVM baseline explicitly, 
see Alter#processReplaceTable
-            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", false);
+            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", null);
         }
-        boolean renamed = !isReplace && newTableInfo.isPresent()
-                && !Objects.equals(oldTableInfo.getTableName(), 
newTableInfo.get().getTableName());
-        // A rename is the one change whose query check is skipped: the MV 
query keeps spelling the old
-        // name, so it is unanalyzable by construction, and the reason it 
would be invalidated with --
-        // "the query is no longer analyzable" -- says less than the message 
this call records anyway.
-        boolean checkQueryUsable = !renamed;
-        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", checkQueryUsable);
+        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", queryJudgedChange);
     }
 
 
     /**
-     * An MV's query is only as good as the base table schema it was analyzed 
against. Re-analyzing the
-     * MV query here (right after the alter was applied) is what detects a 
changed column identity:
+     * Whether the query, as it is analysed now, reads a column of any of 
these names, and reads it where
+     * the change can reach it.
+     *
+     * <p>There are two places a name is the change's to answer for. One is a 
column of the table the change
+     * is about: that is the column this view's rows were computed from, and 
the names are matched
+     * case-insensitively because a name is what moves. The other is a column 
the query reaches across a
+     * scope boundary -- the plan records those on the Apply that stands for 
the subquery, whose correlation
+     * slots are the outer columns its right side reads -- because such a name 
is the scopes' to answer for
+     * rather than the query's: the nearest column to the reference answers 
for it, so a column the change
+     * takes away from a scope inside leaves the name to one outside, and a 
column it gives to a scope inside
+     * takes the name over. A name reached with the qualifier of another table 
inside the query's own scope
+     * is neither: no later change can move it, so one to a column it does not 
name is one this view's rows
+     * do not depend on.
+     */
+    private static boolean reachesAnyColumnOf(Plan plan, BaseTableInfo 
baseTableInfo, Set<String> columnNames) {
+        if (plan == null) {
+            // A query whose plan was not kept is one this cannot be answered 
about, and "it does" is the
+            // answer that keeps the view safe.
+            return true;
+        }
+        Set<String> names = Sets.newTreeSet(String.CASE_INSENSITIVE_ORDER);
+        names.addAll(columnNames);
+        LineageInfo lineage = LineageInfoExtractor.extractLineageInfo(plan);
+        for (SetMultimap<?, Expression> byType : 
lineage.getDirectLineageMap().values()) {
+            if (reachesAnyColumn(byType.values(), names, baseTableInfo)) {
+                return true;
+            }
+        }
+        // The dataset predicates once, not once per output column: the 
per-output copy of them the lineage
+        // also offers holds the same expressions for every column the query 
produces, and scanning it would
+        // visit each of them once per column.
+        if (reachesAnyColumn(lineage.getDatasetIndirectLineageMap().values(), 
names, baseTableInfo)) {
+            return true;
+        }
+        if (reachesAnyColumnOfASubquery(plan, names, baseTableInfo)) {
+            return true;
+        }
+        return reachesAnyColumnAcrossScopes(plan, lineage, names, 
baseTableInfo);
+    }
+
+    /** Whether this slot is a column of this table, through whatever views 
stand between the two. */
+    private static boolean isColumnOf(Slot slot, BaseTableInfo baseTableInfo) {
+        if (!(slot instanceof SlotReference)) {
+            return false;
+        }
+        return ((SlotReference) slot).getOriginalTable()
+                .map(table -> new BaseTableInfo(table).equals(baseTableInfo))
+                .orElse(false);
+    }
+
+    /**
+     * Whether a name the change is about is answered for inside a subquery, 
out of that subquery's own
+     * scope.
+     *
+     * <p>This is the one place a name can move without any column the view 
produces depending on it: the
+     * scope of a subquery is internal, so which column answers for a name 
there changes what the query
+     * returns -- a row, or none -- while every column of the view stays the 
one it was. The lineage of the
+     * view's columns does not reach it, so the scope the subquery became is 
read here, expression by
+     * expression, the way the lineage is read for the view's own.
+     *
+     * <p>Two things are read. One is a value the subquery itself names -- an 
expression of its own under one
+     * of these names, rather than a column of a table -- because that is what 
a name the change takes away
+     * falls back to, and it decides the rows whether the subquery is a 
predicate or a value. It is read only
+     * where the table the change is about is one that subquery reads: what a 
name falls back to is what the
+     * scope that answered for it holds, so a scope that does not read the 
table holds nothing for the name
+     * and one of its own is one the change never reached. The other is a 
column of the table the change is
+     * about, which decides the rows only when the subquery's output is one 
the query reads: an EXISTS tests
+     * the rows of its subquery and not what it projects, so a name it 
projects and never compares is one
+     * this view's rows do not depend on.
+     *
+     * <p>Each scope is read on its own. A subquery inside one of these is a 
scope of its own, and it is
+     * judged where it is read and not as a part of its enclosing one: its 
projection is held only where
+     * that scope's own output is read, so an EXISTS inside an IN is still not 
compared by the IN.
+     */
+    private static boolean reachesAnyColumnOfASubquery(Plan plan, Set<String> 
names,
+            BaseTableInfo baseTableInfo) {
+        for (LogicalApply<?, ?> apply : 
plan.<LogicalApply>collectToList(LogicalApply.class::isInstance)) {
+            List<Plan> itsOwnScope = ownScopeOf(apply);
+            boolean outputDecidesRows = !apply.isExist();
+            boolean isOneOfItsTables = readsAnyTableOf(itsOwnScope, 
baseTableInfo);
+            for (Plan node : itsOwnScope) {
+                for (Expression expression : node.getExpressions()) {
+                    if ((isOneOfItsTables && 
readsAnyNameTheSubqueryAnswersFor(expression, names))

Review Comment:
   Confirmed as over-invalidation, and not fixed in 5dcbddd3e14. Measured on 
the shape in the comment: after the light `ADD COLUMN c.flag` the MV is put 
into `SCHEMA_CHANGE` with its rewrite snapshot dropped, while the subquery's 
output is still `1` and the MV holds the same row the query returns.
   
   You are right about the reading. The check holds a name against the change 
wherever that name is read as a value the scope answers for itself, and it does 
not ask which clause the read is in; `ORDER BY` resolves the output alias 
before the table's column, so `c.flag` was never a column that name could have 
been bound to. Telling those clauses apart -- where a column can capture a 
reference and where the alias is resolved first -- is the binding question the 
other threads here are about rather than a name this reads, and getting it 
wrong in the other direction costs a view its correctness instead of a rebuild, 
so I would rather leave the coarser answer than approximate further inside this 
change.
   



##########
fe/fe-core/src/main/java/org/apache/doris/mtmv/MTMVRelationManager.java:
##########
@@ -349,34 +360,221 @@ public void dropTable(Table table) {
         // because a dropped table is the one change whose query is gone 
beyond doubt. What the two record
         // is the same state either way. Unlike a rename it stays an 
invalidation: the table is gone for
         // good, so the state is not something a later alter can make obsolete.
-        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", false);
+        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", null);
     }
 
     /**
      * update mtmv status to `SCHEMA_CHANGE`.
      *
      * @param isReplace
+     * @param queryJudgedColumns the names the alter gives the table or takes 
away from it, which leave the
+     *                           judgement about each MV's state to that MV's 
own query, or null when the
+     *                           alter is not one a query decides. The names 
are carried rather than judged
+     *                           before the call because the judgement is 
about them; see
+     *                           {@code AlterOp#queryJudgedColumnNames} for 
which operations name one, and
+     *                           {@link #invalidateMvUnlessQueryHolds} for 
what is asked about it. A rename
+     *                           of the base table names no column: it is left 
to the record below, which
+     *                           says what the MV that keeps spelling the old 
name needs to hear
      */
     @Override
-    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace) {
+    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace,
+            QueryJudgedChange queryJudgedChange) {
         // when replace, need deal two table
         if (isReplace) {
             // REPLACE TABLE already invalidates the IVM baseline explicitly, 
see Alter#processReplaceTable
-            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", false);
+            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", null);
         }
-        boolean renamed = !isReplace && newTableInfo.isPresent()
-                && !Objects.equals(oldTableInfo.getTableName(), 
newTableInfo.get().getTableName());
-        // A rename is the one change whose query check is skipped: the MV 
query keeps spelling the old
-        // name, so it is unanalyzable by construction, and the reason it 
would be invalidated with --
-        // "the query is no longer analyzable" -- says less than the message 
this call records anyway.
-        boolean checkQueryUsable = !renamed;
-        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", checkQueryUsable);
+        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", queryJudgedChange);
     }
 
 
     /**
-     * An MV's query is only as good as the base table schema it was analyzed 
against. Re-analyzing the
-     * MV query here (right after the alter was applied) is what detects a 
changed column identity:
+     * Whether the query, as it is analysed now, reads a column of any of 
these names, and reads it where
+     * the change can reach it.
+     *
+     * <p>There are two places a name is the change's to answer for. One is a 
column of the table the change
+     * is about: that is the column this view's rows were computed from, and 
the names are matched
+     * case-insensitively because a name is what moves. The other is a column 
the query reaches across a
+     * scope boundary -- the plan records those on the Apply that stands for 
the subquery, whose correlation
+     * slots are the outer columns its right side reads -- because such a name 
is the scopes' to answer for
+     * rather than the query's: the nearest column to the reference answers 
for it, so a column the change
+     * takes away from a scope inside leaves the name to one outside, and a 
column it gives to a scope inside
+     * takes the name over. A name reached with the qualifier of another table 
inside the query's own scope
+     * is neither: no later change can move it, so one to a column it does not 
name is one this view's rows
+     * do not depend on.
+     */
+    private static boolean reachesAnyColumnOf(Plan plan, BaseTableInfo 
baseTableInfo, Set<String> columnNames) {
+        if (plan == null) {
+            // A query whose plan was not kept is one this cannot be answered 
about, and "it does" is the
+            // answer that keeps the view safe.
+            return true;
+        }
+        Set<String> names = Sets.newTreeSet(String.CASE_INSENSITIVE_ORDER);
+        names.addAll(columnNames);
+        LineageInfo lineage = LineageInfoExtractor.extractLineageInfo(plan);
+        for (SetMultimap<?, Expression> byType : 
lineage.getDirectLineageMap().values()) {
+            if (reachesAnyColumn(byType.values(), names, baseTableInfo)) {
+                return true;
+            }
+        }
+        // The dataset predicates once, not once per output column: the 
per-output copy of them the lineage
+        // also offers holds the same expressions for every column the query 
produces, and scanning it would
+        // visit each of them once per column.
+        if (reachesAnyColumn(lineage.getDatasetIndirectLineageMap().values(), 
names, baseTableInfo)) {
+            return true;
+        }
+        if (reachesAnyColumnOfASubquery(plan, names, baseTableInfo)) {
+            return true;
+        }
+        return reachesAnyColumnAcrossScopes(plan, lineage, names, 
baseTableInfo);
+    }
+
+    /** Whether this slot is a column of this table, through whatever views 
stand between the two. */
+    private static boolean isColumnOf(Slot slot, BaseTableInfo baseTableInfo) {
+        if (!(slot instanceof SlotReference)) {
+            return false;
+        }
+        return ((SlotReference) slot).getOriginalTable()
+                .map(table -> new BaseTableInfo(table).equals(baseTableInfo))
+                .orElse(false);
+    }
+
+    /**
+     * Whether a name the change is about is answered for inside a subquery, 
out of that subquery's own
+     * scope.
+     *
+     * <p>This is the one place a name can move without any column the view 
produces depending on it: the
+     * scope of a subquery is internal, so which column answers for a name 
there changes what the query
+     * returns -- a row, or none -- while every column of the view stays the 
one it was. The lineage of the
+     * view's columns does not reach it, so the scope the subquery became is 
read here, expression by
+     * expression, the way the lineage is read for the view's own.
+     *
+     * <p>Two things are read. One is a value the subquery itself names -- an 
expression of its own under one
+     * of these names, rather than a column of a table -- because that is what 
a name the change takes away
+     * falls back to, and it decides the rows whether the subquery is a 
predicate or a value. It is read only
+     * where the table the change is about is one that subquery reads: what a 
name falls back to is what the
+     * scope that answered for it holds, so a scope that does not read the 
table holds nothing for the name
+     * and one of its own is one the change never reached. The other is a 
column of the table the change is
+     * about, which decides the rows only when the subquery's output is one 
the query reads: an EXISTS tests
+     * the rows of its subquery and not what it projects, so a name it 
projects and never compares is one
+     * this view's rows do not depend on.
+     *
+     * <p>Each scope is read on its own. A subquery inside one of these is a 
scope of its own, and it is
+     * judged where it is read and not as a part of its enclosing one: its 
projection is held only where
+     * that scope's own output is read, so an EXISTS inside an IN is still not 
compared by the IN.
+     */
+    private static boolean reachesAnyColumnOfASubquery(Plan plan, Set<String> 
names,
+            BaseTableInfo baseTableInfo) {
+        for (LogicalApply<?, ?> apply : 
plan.<LogicalApply>collectToList(LogicalApply.class::isInstance)) {
+            List<Plan> itsOwnScope = ownScopeOf(apply);
+            boolean outputDecidesRows = !apply.isExist();
+            boolean isOneOfItsTables = readsAnyTableOf(itsOwnScope, 
baseTableInfo);
+            for (Plan node : itsOwnScope) {
+                for (Expression expression : node.getExpressions()) {
+                    if ((isOneOfItsTables && 
readsAnyNameTheSubqueryAnswersFor(expression, names))
+                            || (outputDecidesRows && 
reachesAnyColumn(expression, names, baseTableInfo))) {
+                        return true;
+                    }
+                }
+            }
+        }
+        return false;
+    }
+
+    /**
+     * The nodes of a subquery that belong to the scope this Apply stands for: 
its right side, with the
+     * right side of every subquery nested in it left out.
+     *
+     * <p>A nested Apply is a scope of its own and is read as one, so its 
right side belongs to that read
+     * rather than to this one; the relation it is asked about is the 
enclosing scope's own and stays.
+     */
+    private static List<Plan> ownScopeOf(LogicalApply<?, ?> apply) {
+        List<Plan> itsOwnScope = Lists.newArrayList();
+        collectItsOwnScope((Plan) apply.right(), itsOwnScope);
+        return itsOwnScope;
+    }
+
+    private static void collectItsOwnScope(Plan node, List<Plan> itsOwnScope) {
+        itsOwnScope.add(node);
+        if (node instanceof LogicalApply) {
+            collectItsOwnScope(((LogicalApply<?, ?>) node).left(), 
itsOwnScope);
+            return;
+        }
+        for (Plan child : node.children()) {
+            collectItsOwnScope(child, itsOwnScope);
+        }
+    }
+
+    /** Whether one of these nodes reads this table, through whatever views 
stand between the two. */
+    private static boolean readsAnyTableOf(List<Plan> itsOwnScope, 
BaseTableInfo baseTableInfo) {
+        return itsOwnScope.stream().anyMatch(node -> node instanceof 
LogicalCatalogRelation
+                && new BaseTableInfo(((LogicalCatalogRelation) 
node).getTable()).equals(baseTableInfo));
+    }
+
+    /**
+     * Whether this expression reads a value the subquery answers for itself, 
under one of these names: a
+     * slot of the subquery's own -- an alias or a value it computed -- rather 
than a column of a table.
+     *
+     * <p>Read rather than merely named, because an expression of the subquery 
carrying one of these names
+     * says nothing on its own: a subquery that names a `flag` of its own 
while no reference in it resolves
+     * to that name is one whose rows the change cannot reach, and one that 
reads the name it names is where
+     * a reference that answered for the changed column falls back to.
+     */
+    private static boolean readsAnyNameTheSubqueryAnswersFor(Expression 
expression, Set<String> names) {
+        for (Slot slot : expression.getInputSlots()) {
+            if (names.contains(slot.getName()) && !isColumnOfATable(slot)) {

Review Comment:
   Confirmed as over-invalidation, and not fixed in 5dcbddd3e14. Measured: `ADD 
COLUMN changed_t.flag` invalidates the MV and drops its snapshot, while 
`a.flag` stays bound to the derived table's constant and every row of the query 
is the same.
   
   It is read at all because the check only has the analysed plan: the name 
reaches it as a value the scope answers for itself, which is the shape a 
reference that moved into an alias takes, and an explicitly qualified reference 
to a derived table looks the same to it. Separating "the scope produced this 
value and this reference named it" from "the scope produced this value and this 
reference could have taken it over" needs the reference's own qualification, 
which the analysed plan has resolved away -- the same missing half as the 
creation-time question in the earlier thread.
   
   Not approximated here for the reason in the threads above: the direction a 
wrong answer would take is the one that serves stale rows.
   



##########
fe/fe-core/src/main/java/org/apache/doris/mtmv/MTMVRelationManager.java:
##########
@@ -349,34 +360,221 @@ public void dropTable(Table table) {
         // because a dropped table is the one change whose query is gone 
beyond doubt. What the two record
         // is the same state either way. Unlike a rename it stays an 
invalidation: the table is gone for
         // good, so the state is not something a later alter can make obsolete.
-        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", false);
+        processBaseTableChange(new BaseTableInfo(table), "The base table has 
been deleted:", null);
     }
 
     /**
      * update mtmv status to `SCHEMA_CHANGE`.
      *
      * @param isReplace
+     * @param queryJudgedColumns the names the alter gives the table or takes 
away from it, which leave the
+     *                           judgement about each MV's state to that MV's 
own query, or null when the
+     *                           alter is not one a query decides. The names 
are carried rather than judged
+     *                           before the call because the judgement is 
about them; see
+     *                           {@code AlterOp#queryJudgedColumnNames} for 
which operations name one, and
+     *                           {@link #invalidateMvUnlessQueryHolds} for 
what is asked about it. A rename
+     *                           of the base table names no column: it is left 
to the record below, which
+     *                           says what the MV that keeps spelling the old 
name needs to hear
      */
     @Override
-    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace) {
+    public void alterTable(BaseTableInfo oldTableInfo, Optional<BaseTableInfo> 
newTableInfo, boolean isReplace,
+            QueryJudgedChange queryJudgedChange) {
         // when replace, need deal two table
         if (isReplace) {
             // REPLACE TABLE already invalidates the IVM baseline explicitly, 
see Alter#processReplaceTable
-            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", false);
+            processBaseTableChange(newTableInfo.get(), "The base table has 
been updated:", null);
         }
-        boolean renamed = !isReplace && newTableInfo.isPresent()
-                && !Objects.equals(oldTableInfo.getTableName(), 
newTableInfo.get().getTableName());
-        // A rename is the one change whose query check is skipped: the MV 
query keeps spelling the old
-        // name, so it is unanalyzable by construction, and the reason it 
would be invalidated with --
-        // "the query is no longer analyzable" -- says less than the message 
this call records anyway.
-        boolean checkQueryUsable = !renamed;
-        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", checkQueryUsable);
+        processBaseTableChange(oldTableInfo, "The base table has been 
updated:", queryJudgedChange);
     }
 
 
     /**
-     * An MV's query is only as good as the base table schema it was analyzed 
against. Re-analyzing the
-     * MV query here (right after the alter was applied) is what detects a 
changed column identity:
+     * Whether the query, as it is analysed now, reads a column of any of 
these names, and reads it where
+     * the change can reach it.
+     *
+     * <p>There are two places a name is the change's to answer for. One is a 
column of the table the change
+     * is about: that is the column this view's rows were computed from, and 
the names are matched
+     * case-insensitively because a name is what moves. The other is a column 
the query reaches across a
+     * scope boundary -- the plan records those on the Apply that stands for 
the subquery, whose correlation
+     * slots are the outer columns its right side reads -- because such a name 
is the scopes' to answer for
+     * rather than the query's: the nearest column to the reference answers 
for it, so a column the change
+     * takes away from a scope inside leaves the name to one outside, and a 
column it gives to a scope inside
+     * takes the name over. A name reached with the qualifier of another table 
inside the query's own scope
+     * is neither: no later change can move it, so one to a column it does not 
name is one this view's rows
+     * do not depend on.
+     */
+    private static boolean reachesAnyColumnOf(Plan plan, BaseTableInfo 
baseTableInfo, Set<String> columnNames) {
+        if (plan == null) {
+            // A query whose plan was not kept is one this cannot be answered 
about, and "it does" is the
+            // answer that keeps the view safe.
+            return true;
+        }
+        Set<String> names = Sets.newTreeSet(String.CASE_INSENSITIVE_ORDER);
+        names.addAll(columnNames);
+        LineageInfo lineage = LineageInfoExtractor.extractLineageInfo(plan);
+        for (SetMultimap<?, Expression> byType : 
lineage.getDirectLineageMap().values()) {
+            if (reachesAnyColumn(byType.values(), names, baseTableInfo)) {
+                return true;
+            }
+        }
+        // The dataset predicates once, not once per output column: the 
per-output copy of them the lineage
+        // also offers holds the same expressions for every column the query 
produces, and scanning it would
+        // visit each of them once per column.
+        if (reachesAnyColumn(lineage.getDatasetIndirectLineageMap().values(), 
names, baseTableInfo)) {

Review Comment:
   Confirmed as over-invalidation, and not fixed in 5dcbddd3e14 -- with the CTE 
thread above being the same fix rather than a second one. Measured: `ADD COLUMN 
inner2.spare` invalidates the MV, while the enclosing EXISTS answers the same 
way (it tests whether the `inner1` row exists, not what the scalar returns) and 
every row of the query is the same.
   
   The scan reads the analysed plan's predicates as a whole, so a predicate 
inside a scope whose value the enclosing context never compares is read as a 
dependency of the view's rows. Restricting it to the predicates that can decide 
those rows -- the walk from the result the CTE thread calls for -- is a change 
to how this check traverses the plan rather than to a name it matches, and it 
would close both shapes at once.
   



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