A15318. Xor-Subsequence (easy version)

It is the easy version of the problem. The only difference is that in this version $a_i \le 200$ .

You are given an array of $n$ integers $a_0, a_1, a_2, \ldots a_{n - 1}$ . Bryap wants to find the longest beautiful subsequence in the array.

An array $b = [b_0, b_1, \ldots, b_{m-1}]$ , where $0 \le b_0 < b_1 < \ldots < b_{m - 1} < n$ , is a subsequence of length $m$ of the array $a$ .

Subsequence $b = [b_0, b_1, \ldots, b_{m-1}]$ of length $m$ is called beautiful, if the following condition holds:

- For any $p$ ( $0 \le p < m - 1$ ) holds: $a_{b_p} \oplus b_{p+1} < a_{b_{p+1}} \oplus b_p$ .

Here $a \oplus b$ denotes the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of $a$ and $b$ . For example, $2 \oplus 4 = 6$ and $3 \oplus 1=2$ .

Bryap is a simple person so he only wants to know the length of the longest such subsequence. Help Bryap and find the answer to his question.

The first line contains a single integer $t$ ( $1 \leq t \leq 10^5$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $2 \leq n \leq 3 \cdot 10^5$ ) — the length of the array.

The second line of each test case contains $n$ integers $a_0,a_1,...,a_{n-1}$ ( $0 \leq a_i \leq 200$ ) — the elements of the array.

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

For each test case print a single integer — the length of the longest beautiful subsequence.

In the first test case, we can pick the whole array as a beautiful subsequence because $1 \oplus 1 < 2 \oplus 0$ .

In the second test case, we can pick elements with indexes $1$ , $2$ and $4$ (in $0$ -indexation). For this elements holds: $2 \oplus 2 < 4 \oplus 1$ and $4 \oplus 4 < 1 \oplus 2$ .