A12935 | Sequence Sorting

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.

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 $3 \cdot 10^5$ .

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