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Sharky wants to unlock his friend Krishna's combination lock. The lock consists of 4 4 reels, each reel displays the numbers from 01 to 99. Krishna tells Sharky that the first number from left to right is a multiple of 3, the second is a prime, the third is a multiple of 2 and the last number is divisible by 4. For example,

57 97 88 08 |57|97|88|08|

By following Krishna's clue, let n n be the digit sum of the maximum number of possible choices for unlocking Krishna's lock. Find n n .

Source from PMWC.

\infty 18 17 19 970200

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