CF1468A.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.

You are given a sequence of integers $a_1, a_2, \dots, a_n$. Calculate the length of its longest almost increasing subsequence.

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.

我们称一个序列 $b_1, b_2, b_3 \dots, b_{k - 1}, b_k$ 是近似递增的（almost increasing），如果满足

$$\min(b\_1, b\_2) \le \min(b\_2, b\_3) \le \dots \le \min(b\_{k - 1}, b\_k).$$

特别地，任何长度不超过两个元素的序列都是近似递增的。

给定一个整数序列 $a_1, a_2, \dots, a_n$。请计算其最长近似递增子序列的长度。

你将收到 $t$ 组测试用例。请独立求解每组测试用例。

提示：子序列是指从原序列中删除若干元素（可为零个）后，保持剩余元素相对顺序所得到的序列。

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 $5 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 1000$）—— 表示独立测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 5 \cdot 10^5$）—— 表示序列 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le n$）—— 即该序列本身。

保证所有测试用例的 $n$ 值之和不超过 $5 \cdot 10^5$。

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

对于每个测试用例，输出一个整数——最长近似递增子序列的长度。

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.

在第一个测试用例中，一个最优答案是子序列 $1, 2, 7, 2, 2, 3$。

在第二个和第三个测试用例中，整个序列 $a$ 已经几乎是递增的。