Enzo, a caveman, recently developed an interest in collecting stones as a hobby. He has a collection called $$$A$$$ with $$$N$$$ stones lined up in various colors and identified each color with an integer (for example, he defined color number $$$1$$$ as the color green).

The special aspect of his collection is that, for a given number $$$x$$$, he is very particular about what he calls the "kuga-buga-$$$x$$$ value"; this value is the number of colors that appear with a frequency that is a multiple of $$$x$$$. For example, if he has $$$3$$$ yellow stones and $$$6$$$ blue stones, the kuga-buga-$$$3$$$ value is $$$2$$$, since he has two colors that appear a number of times that is a multiple of $$$3$$$.

Since he always wants to maintain the same number of stones but wants to keep the collection up to date, he frequently replaces stones he no longer likes with a new one of another color. He calls this update a type $$$1$$$ query.

From time to time, he wonders about the kuga-buga value for a given number $$$x$$$. He calls this question a type $$$2$$$ query.

With that, Enzo wants your help to answer these kuga-buga queries given the stone collection $$$A$$$ and the updates that occur over time.