6357：Hills And Valleys

Tauren has an integer sequence $A$ of length $n$ (1-based). He wants you to invert an interval $[l, r]$ $(1 \leq l \leq r \leq n)$ of $A$ (i.e. replace $A_l, A_{l + 1}, \cdots, A_r$ with $A_r, A_{r - 1}, \cdots, A_l$) to maximize the length of the longest non-decreasing subsequence of $A$. Find that maximal length and any inverting way to accomplish that mission.
A non-decreasing subsequence of $A$ with length $m$ could be represented as $A_{x_1}, A_{x_2}, \cdots, A_{x_m}$ with $1 \leq x_1 < x_2 < \cdots < x_m \leq n$ and $A_{x_1} \leq A_{x_2} \leq \cdots \leq A_{x_m}$.

The first line contains one integer $T$, indicating the number of test cases.
The following lines describe all the test cases. For each test case:
The first line contains one integer $n$.
The second line contains $n$ integers $A_1, A_2, \cdots, A_n$ without any space.
$1 \leq T \leq 100$, $1 \leq n \leq 10^5$, $0 \leq A_i \leq 9$ $(i = 1, 2, \cdots, n)$.
It is guaranteed that the sum of $n$ in all test cases does not exceed $2 \cdot 10^5$.

For each test case, print three space-separated integers $m, l$ and $r$ in one line, where $m$ indicates the maximal length and $[l, r]$ indicates the relevant interval to invert.