Problem #7

This month's problem was created by Philippe Fondanaiche.

In order to manage my overdrafts, I have found an agreement with my banker who is as fond of mathematical puzzles as I am. My bank account is updated every month. The agreement is the following:

For each month of the year, determine the maximum number of bank transactions that I can make subject to these conditions.

Note: This is a generalization of an International Mathematical Olympiad problem.

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