# Should the number of Markowitz Optimization steps be counted as backtest trials?

I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in them. Each month, the portfolio is equally-weighted in the stocks. The number of trials required for this backtest is $36$ and the backtest period is $84$ months.

Now suppose that instead of an equally-weighted portfolio, each month I construct a Markowitz-optimized portfolio instead. So given any month, optimal weightages to be assigned to the shortlisted stocks are determined and the investment is made in a portfolio constructed on the basis of these optimal weightages. Also the number of steps in each Markowitz optimization is $1000$.

My question: should the number of trials be updated to $36 \times 84 \times 1000$? I'm not clear on this because I tried Googling "markowitz optimization number of trials" and didn't come across any page that discusses treatment of a Markowitz optimization procedure step as a "trial". Would this be too many trials, and how do I know what's a good upper bound on the number of trials?