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Chef has to cook many dishes today. In between cooking two of them, he decided to relax and play a card game with his friend. The game is played with cards that have integer *ranks* written on them. There may be multiple cards with the same rank. At the beginning of the game, Chef gets $N$ cards with ranks $a_1, a_2, \ldots, a_N$ and his friend gets $N$ cards with ranks $b_1, b_2, \ldots, b_N$.