A14036. LaIS

Let's call a sequence $b_1, b_2, b_3 \dots, b_{k - 1}, b_k$ almost increasing if $$$$\min(b_1, b_2) \le \min(b_2, b_3) \le \dots \le \min(b_{k - 1}, b_k). $$ In particular, any sequence with no more than two elements is almost increasing.</p><p>You are given a sequence of integers $a\_1, a\_2, \\dots, a\_n$ . Calculate the length of its longest almost increasing subsequence.</p><p>You'll be given $t$$$ test cases. Solve each test case independently.

Reminder: a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

The first line contains a single integer $t$ ( $1 \le t \le 1000$ ) — the number of independent test cases.

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

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le n$ ) — the sequence itself.

It's guaranteed that the total sum of $n$ over all test cases doesn't exceed $5 \cdot 10^5$ .

For each test case, print one integer — the length of the longest almost increasing subsequence.

In the first test case, one of the optimal answers is subsequence $1, 2, 7, 2, 2, 3$ .

In the second and third test cases, the whole sequence $a$ is already almost increasing.