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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