Tauren has an integer sequence A of length n (1-based). He wants you to invert an interval [l, r] (1 ≤ l ≤ r ≤ n) of A (that is, replace Al, Al + 1, ..., Ar with Ar, Ar - 1, ..., Al) 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 Ax1, Ax2, ..., Axm with 1 ≤ x1 < x2 < ... < xm ≤ n and Ax1 ≤ Ax2 ≤ ... ≤ Axm.
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 A1, A2, ..., An without any space.
1 ≤ T ≤ 100, 1 ≤ n ≤ 105, 0 ≤ Ai ≤ 9 (i = 1, 2, ..., n).
It is guaranteed that the sum of n in all test cases does not exceed 2·105.
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.
In the first example, 864852302 after inverting [1, 8] is 032584682, one of the longest non-decreasing subsequences of which is 03588.
In the second example, 203258468 after inverting [1, 2] is 023258468, one of the longest non-decreasing subsequences of which is 023588.
## Input
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 A1, A2, ..., An without any space.1 ≤ T ≤ 100, 1 ≤ n ≤ 105, 0 ≤ Ai ≤ 9 (i = 1, 2, ..., n).It is guaranteed that the sum of n in all test cases does not exceed 2·105.
## Output
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.
[samples]
## Note
In the first example, 864852302 after inverting [1, 8] is 032584682, one of the longest non-decreasing subsequences of which is 03588.In the second example, 203258468 after inverting [1, 2] is 023258468, one of the longest non-decreasing subsequences of which is 023588.
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case, let $ n \in \mathbb{Z} $ be the length of sequence $ A = (A_1, A_2, \dots, A_n) $, where $ A_i \in \{0, 1, \dots, 9\} $.
**Constraints**
1. $ 1 \leq T \leq 100 $
2. $ 1 \leq n \leq 10^5 $
3. $ 0 \leq A_i \leq 9 $ for all $ i \in \{1, \dots, n\} $
4. $ \sum_{\text{all test cases}} n \leq 2 \cdot 10^5 $
**Objective**
Find an interval $ [l, r] $ with $ 1 \leq l \leq r \leq n $, such that after reversing the subsequence $ A[l:r] $, the length of the longest non-decreasing subsequence (LNDS) of the resulting sequence is maximized.
Let $ m^* $ denote the maximum possible LNDS length over all such reversals.
Output $ m^* $ and any pair $ (l, r) $ achieving it.