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For a given list of numbers, erase as few of these numbers as possible such that the remaining numbers appear in increasing order

Consider the following list of numbers.

Your job is to erase as few of these numbers as possible such that the remaining numbers appear in increasing order.

For example,

Erasing everything except the first two numbers leaves an increasing sequence;

Erasing everiting except for first,third,sixth and eighth numbers does the same:

9,44,32,12,7,42,34,92,35,37,41,8,20,27,83,64,61,28,39,93,29,17,13,14,55,21,66,72,23,73,99,1,2,88,77,5,65,83,84,62,5,11,74,68,76,78,67,75,69,70,22,71,24,25,26.

And solve the above exercise 1,such that the remainig number are in decreasing order

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