The board game Dominion is a card-drafting game where the player with the most victory points wins. You are playing Dominion with a group of friends, and are on the last turn. The only two remaining cards that you can purchase are Duchies and Dukes. Each Duchy is worth 3 victory points and costs 5 gold. Each Duke gives you 1 victory point per Duchy in your possession, and also costs 5 gold. Assuming you have N gold and can purchase as many cards as you like, how many Dukes and Duchies should you buy to maximize your victory points?

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