G2. Into Blocks (hard version)
time limit per test
5 seconds
memory limit per test
256 megabytes
standard input
standard output

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.


The first line contains integers $$$n$$$ and $$$q$$$ ($$$1 \le n \le 200\,000$$$, $$$0 \le q \le 200\,000$$$), the length of the sequence and the number of the updates.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 200\,000$$$), the initial sequence.

Each of the following $$$q$$$ lines contains integers $$$i_t$$$ and $$$x_t$$$ ($$$1 \le i_t \le n$$$, $$$1 \le x_t \le 200\,000$$$), the position and the new value for this position.


Print $$$q+1$$$ integers, the answer for the initial sequence and the answer after every update.

5 6
1 2 1 2 1
2 1
4 1
5 3
2 3
4 2
2 1