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        ItemID(): index(INVALID_INDEX){}
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        ItemID(): index(INVALID_INDEX){}
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        bool operator ==(const ItemID& other) const { return index == other.index; }
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        bool operator ==(const ItemID& other) const { return index == other.index; }
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        bool operator !=(const ItemID& other) const { return index != other.index; }
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        bool operator !=(const ItemID& other) const { return index != other.index; }
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        bool operator <(const ItemID& other) const { return index < other.index; }
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        bool operator <(const ItemID& other) const { return index < other.index; }
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		template<typename X>
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		friend std::ostream& operator<<(std::ostream& os, const ItemID<X>&);
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    private:
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    private:
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        typedef size_t IndexType;
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        typedef size_t IndexType;
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        static const IndexType INVALID_INDEX =  -1;
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        static const IndexType INVALID_INDEX =  -1;
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        IndexType index;
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        explicit ItemID(IndexType _index): index(_index){}
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        explicit ItemID(IndexType _index): index(_index){}
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        friend class ConnectivityKernel;
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        friend class ConnectivityKernel;
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        template<typename ITEM> friend class ItemVector;
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        template<typename ITEM> friend class ItemVector;
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        template<typename ITEM, typename ITEMID> friend class AttributeVector;
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        template<typename ITEM, typename ITEMID> friend class AttributeVector;
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        template<typename X>
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        friend std::ostream& operator<<(std::ostream& os, const ItemID<X>&);
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        IndexType index;
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    };
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    };
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	template<typename T>
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	template<typename T>
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	inline std::ostream& operator<<(std::ostream& os, const ItemID<T>& iid)
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	inline std::ostream& operator<<(std::ostream& os, const ItemID<T>& iid)
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	{
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	{