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		template<typename X>
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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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		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 unsigned int IndexType;
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        typedef size_t IndexType;
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        static const IndexType INVALID_INDEX =  0xffffffff;
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        static const IndexType INVALID_INDEX =  -1;
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        ItemID(IndexType index);
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        ItemID(IndexType index);
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        friend class ConnectivityKernel;
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        friend class ConnectivityKernel;
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        template<typename ITEM, typename ITEMID>
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        template<typename ITEM, typename ITEMID>