# Greatest remaining number

Number Theory Level pending

The number $$N=123456789101112...9899100$$ is written on a big board.

Remove any 100 digits from $$N$$ such that the remaining digits form a new number $$($$call it $$M)$$ in that order. For the maximal value of $$M$$, what is the sum of its digits?


Clarification: $$N$$ is the concatenation of all positive integers from 1 to 100.

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