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Lord of Extinction's power and toughness are each equal to the number of cards in all graveyards.
If an instant or sorcery spell deals damage to Lord of Extinction or lowers its toughness, that spell is put into its owner’s graveyard before state-based actions are performed. That card will raise Lord of Extinction’s toughness before the game checks to see if it dies.
The ability that defines Lord of Extinction’s power and toughness works in all zones, not just the battlefield. If Lord of Extinction is in your graveyard, it will count itself.
