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        ItemID();
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        ItemID();
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        bool operator ==(const ItemID& other) const;
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        bool operator ==(const ItemID& other) const;
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        bool operator !=(const ItemID& other) const;
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        bool operator !=(const ItemID& other) const;
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        bool operator <(const ItemID& other) const;
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        bool operator <(const ItemID& other) const;
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		template<typename X>
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		friend std::ostream& operator<<(std::ostream& os, const ItemID<FaceTag>&);
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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 unsigned int IndexType;
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        static const IndexType INVALID_INDEX =  0xffffffff;
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        static const IndexType INVALID_INDEX =  0xffffffff;
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    template<typename T>
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    template<typename T>
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    inline bool ItemID<T>::operator <(const ItemID& other) const
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    inline bool ItemID<T>::operator <(const ItemID& other) const
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    { return index < other.index; }
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    { return index < other.index; }
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	template<typename T>
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	inline std::ostream& operator<<(std::ostream& os, const FaceID& iid)
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	inline std::ostream& operator<<(std::ostream& os, const ItemID<T>& iid)
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	{
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	{
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		return (os << iid.index);
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		return (os << iid.index);
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	}
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	}
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}
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}