Into Blocks (hard version)

This is a harder version of the problem. In this version $$$q \le 200\,000$$$.

A sequence of integers is called nice if its elements are arranged in blocks like in $$$[3, 3, 3, 4, 1, 1]$$$. Formally, if two elements are equal, everything in between must also be equal.

Let's define difficulty of a sequence as a minimum possible number of elements to change to get a nice sequence. However, if you change at least one element of value $$$x$$$ to value $$$y$$$, you must also change all other elements of value $$$x$$$ into $$$y$$$ as well. For example, for $$$[3, 3, 1, 3, 2, 1, 2]$$$ it isn't allowed to change first $$$1$$$ to $$$3$$$ and second $$$1$$$ to $$$2$$$. You need to leave $$$1$$$'s untouched or change them to the same value.

You are given a sequence of integers $$$a_1, a_2, \ldots, a_n$$$ and $$$q$$$ updates.

Each update is of form "$$$i$$$ $$$x$$$" — change $$$a_i$$$ to $$$x$$$. Updates are not independent (the change stays for the future).

Print the difficulty of the initial sequence and of the sequence after every update.