Sequence Sorting

2000ms

262144K

Description:

You are given a sequence $$$a_1, a_2, \dots, a_n$$$, consisting of integers.

You can apply the following operation to this sequence: choose some integer $$$x$$$ and move all elements equal to $$$x$$$ either to the beginning, or to the end of $$$a$$$. Note that you have to move all these elements in one direction in one operation.

For example, if $$$a = [2, 1, 3, 1, 1, 3, 2]$$$, you can get the following sequences in one operation (for convenience, denote elements equal to $$$x$$$ as $$$x$$$-elements):

$$$[1, 1, 1, 2, 3, 3, 2]$$$ if you move all $$$1$$$-elements to the beginning;
$$$[2, 3, 3, 2, 1, 1, 1]$$$ if you move all $$$1$$$-elements to the end;
$$$[2, 2, 1, 3, 1, 1, 3]$$$ if you move all $$$2$$$-elements to the beginning;
$$$[1, 3, 1, 1, 3, 2, 2]$$$ if you move all $$$2$$$-elements to the end;
$$$[3, 3, 2, 1, 1, 1, 2]$$$ if you move all $$$3$$$-elements to the beginning;
$$$[2, 1, 1, 1, 2, 3, 3]$$$ if you move all $$$3$$$-elements to the end;

You have to determine the minimum number of such operations so that the sequence $$$a$$$ becomes sorted in non-descending order. Non-descending order means that for all $$$i$$$ from $$$2$$$ to $$$n$$$, the condition $$$a_{i-1} \le a_i$$$ is satisfied.

Note that you have to answer $$$q$$$ independent queries.

Input:

The first line contains one integer $$$q$$$ ($$$1 \le q \le 3 \cdot 10^5$$$) — the number of the queries. Each query is represented by two consecutive lines.

The first line of each query contains one integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — the number of elements.

The second line of each query contains $$$n$$$ integers $$$a_1, a_2, \dots , a_n$$$ ($$$1 \le a_i \le n$$$) — the elements.

It is guaranteed that the sum of all $$$n$$$ does not exceed $$$3 \cdot 10^5$$$.

Output:

For each query print one integer — the minimum number of operation for sorting sequence $$$a$$$ in non-descending order.

Sample Input:

3
7
3 1 6 6 3 1 1
8
1 1 4 4 4 7 8 8
7
4 2 5 2 6 2 7

Sample Output:

2
0
1

Note:

In the first query, you can move all $$$1$$$-elements to the beginning (after that sequence turn into $$$[1, 1, 1, 3, 6, 6, 3]$$$) and then move all $$$6$$$-elements to the end.

In the second query, the sequence is sorted initially, so the answer is zero.

In the third query, you have to move all $$$2$$$-elements to the beginning.

Informação

Provedor Codeforces

Código CF1223D