Boardroom Meeting

Recently, you have been hired by an investment fund. You quickly developed a feeling, though, that something here was amiss, especially when a client's money has been invested in two companies carefully selected by their best astrologist.

Unfortunately, for the last $n$ days the stock prices were (mostly) falling. The boss called an urgent meeting.

• "Ladies and gentlemen, you all know the situation. Any ideas?" - the boss had a nice habit of gettingstraight to the point (even when this point apparently lied in another dimension of reality).

• "We can choose a good subset of days, so that the prices are only increasing, then show the client onlythat company's prices for these days!" - volunteered Billy, the last Employee of the Month.

• "We can do better! Select the days such that both companies' prices form an increasing sequence!" -Anna, the senior manager, wouldn't allow herself to stay behind.

• "How about ditching the astrologist and doing some serious research?" - the words came from youalmost involuntarily, as if your brain and vocal cords had acted without your consent.

The boss looked at you. It wasn't exactly a look of earnest approval...

Now you have some bruises, a lot of stairs to climb, and much work to do. Given the stock prices of the two companies for $n$ consecutive days, find the maximum subset of days so that both price subsequences are (strictly) increasing. It is enough to output the maximum number of days.