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G2. Into Blocks (hard version)

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThis 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.

Input

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.

Output

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

Example

Input

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

Output

2 1 0 0 2 3 0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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