diff --git a/src/Interpreters/ActionsDAG.cpp b/src/Interpreters/ActionsDAG.cpp
index 9fa48f6ceab..8b1c5afa014 100644
--- a/src/Interpreters/ActionsDAG.cpp
+++ b/src/Interpreters/ActionsDAG.cpp
@@ -161,6 +161,9 @@ const ActionsDAG::Node & ActionsDAG::addArrayJoin(const Node & child, std::strin
     if (!array_type)
         throw Exception("ARRAY JOIN requires array argument", ErrorCodes::TYPE_MISMATCH);
 
+    if (result_name.empty())
+        result_name = "arrayJoin(" + child.result_name + ")";
+
     Node node;
     node.type = ActionType::ARRAY_JOIN;
     node.result_type = array_type->getNestedType();
diff --git a/src/Interpreters/ActionsDAG.h b/src/Interpreters/ActionsDAG.h
index 9bea1d1c040..e06662af725 100644
--- a/src/Interpreters/ActionsDAG.h
+++ b/src/Interpreters/ActionsDAG.h
@@ -279,4 +279,10 @@ private:
     static ActionsDAGPtr cloneActionsForConjunction(NodeRawConstPtrs conjunction, const ColumnsWithTypeAndName & all_inputs);
 };
 
+/// This is an ugly way to bypass impossibility to forward declare ActionDAG::Node.
+struct ActionDAGNodes
+{
+    ActionsDAG::NodeRawConstPtrs nodes;
+};
+
 }
diff --git a/src/Storages/MergeTree/KeyCondition.cpp b/src/Storages/MergeTree/KeyCondition.cpp
index 05b5399a84f..fd9e846cf16 100644
--- a/src/Storages/MergeTree/KeyCondition.cpp
+++ b/src/Storages/MergeTree/KeyCondition.cpp
@@ -644,11 +644,14 @@ static const ActionsDAG::Node & cloneASTWithInversionPushDown(
     switch (node.type)
     {
         case (ActionsDAG::ActionType::INPUT):
-            /// Should be already added
-            throw Exception(ErrorCodes::LOGICAL_ERROR, "Cannot clone input in cloneASTWithInversionPushDown");
+        {
+            /// Note: inputs order is not important here. Will match columns by names.
+            res = &inverted_dag.addInput({node.column, node.result_type, node.result_name});
+            break;
+        }
         case (ActionsDAG::ActionType::COLUMN):
         {
-            res = &inverted_dag.addInput({node.column, node.result_type, node.result_name});
+            res = &inverted_dag.addColumn({node.column, node.result_type, node.result_name});
             break;
         }
         case (ActionsDAG::ActionType::ALIAS):
@@ -661,7 +664,7 @@ static const ActionsDAG::Node & cloneASTWithInversionPushDown(
         case (ActionsDAG::ActionType::ARRAY_JOIN):
         {
             const auto & arg = cloneASTWithInversionPushDown(*node.children.front(), inverted_dag, to_inverted, context, false);
-            res = &inverted_dag.addArrayJoin(arg, node.result_name);
+            res = &inverted_dag.addArrayJoin(arg, "");
             break;
         }
         case (ActionsDAG::ActionType::FUNCTION):
@@ -691,6 +694,8 @@ static const ActionsDAG::Node & cloneASTWithInversionPushDown(
 
                 assert(function_builder);
 
+                /// We match columns by name, so it is important to fill name correctly.
+                /// So, use empty string to make it automatically.
                 const auto & func = inverted_dag.addFunction(function_builder, children, "");
                 to_inverted[&node] = &func;
                 return func;
@@ -722,23 +727,22 @@ static const ActionsDAG::Node & cloneASTWithInversionPushDown(
     return *res;
 }
 
-static ActionsDAGPtr cloneASTWithInversionPushDown(const ActionsDAG & dag, const ContextPtr & context)
+static ActionsDAGPtr cloneASTWithInversionPushDown(ActionsDAG::NodeRawConstPtrs nodes, const ContextPtr & context)
 {
-    auto res = std::make_shared<ActionsDAG>(dag.getRequiredColumns());
+    auto res = std::make_shared<ActionsDAG>();
 
     std::unordered_map<const ActionsDAG::Node *, const ActionsDAG::Node *> to_inverted;
-    const auto & res_inputs = res->getInputs();
-    auto it = res_inputs.begin();
-    for (const auto * input : dag.getInputs())
+
+    for (auto & node : nodes)
+        node = &cloneASTWithInversionPushDown(*node, *res, to_inverted, context, false);
+
+    if (nodes.size() > 1)
     {
-        to_inverted[input] = *it;
-        ++it;
+        auto function_builder = FunctionFactory::instance().get("and", context);
+        nodes = {&res->addFunction(function_builder, std::move(nodes), "")};
     }
 
-    ActionsDAG::NodeRawConstPtrs index;
-    index.reserve(dag.getIndex().size());
-    for (const auto * node : dag.getIndex())
-        index.push_back(&cloneASTWithInversionPushDown(*node, *res, to_inverted, context, false));
+    res->getIndex().swap(nodes);
 
     return res;
 }
@@ -828,7 +832,7 @@ KeyCondition::KeyCondition(
 }
 
 KeyCondition::KeyCondition(
-    const ActionsDAG & dag,
+    ActionDAGNodes dag_nodes,
     PreparedSets prepared_sets_,
     ContextPtr context,
     const Names & key_column_names,
@@ -848,10 +852,10 @@ KeyCondition::KeyCondition(
             key_columns[name] = i;
     }
 
-    auto inverted_dag = cloneASTWithInversionPushDown(dag, context);
-
-    if (!inverted_dag->getIndex().empty())
+    if (!dag_nodes.nodes.empty())
     {
+        auto inverted_dag = cloneASTWithInversionPushDown(std::move(dag_nodes.nodes), context);
+
         Block empty;
         for (const auto * node : inverted_dag->getIndex())
             traverseAST(Tree(node), context, empty);
diff --git a/src/Storages/MergeTree/KeyCondition.h b/src/Storages/MergeTree/KeyCondition.h
index f0ffbf9e6bf..8c54d9bb751 100644
--- a/src/Storages/MergeTree/KeyCondition.h
+++ b/src/Storages/MergeTree/KeyCondition.h
@@ -18,6 +18,7 @@ class IFunction;
 using FunctionBasePtr = std::shared_ptr<IFunctionBase>;
 class ExpressionActions;
 using ExpressionActionsPtr = std::shared_ptr<ExpressionActions>;
+struct ActionDAGNodes;
 
 /** A field, that can be stored in two representations:
   * - A standalone field.
@@ -238,7 +239,7 @@ public:
         bool strict_ = false);
 
     KeyCondition(
-        const ActionsDAG & dag,
+        ActionDAGNodes dag_nodes,
         PreparedSets prepared_sets_,
         ContextPtr context,
         const Names & key_column_names,