B. Make It Permutation
constructive algorithms
There is a matrix \(A\) of size \(n\times n\) where \(A_{i,j}=j\) for all \(1 \le i,j \le n\). In one operation, you can select a row and reverse any subarray\(^{\text{∗}}\) in it. Find a sequence of at most \(2n\) operations such that every column will contain a permutation\(^{\text{†}}\) of length \(n\).It can be proven that the construction is always possible. If there are multiple solutions, output any of them.\(^{\text{∗}}\)An array \(a\) is a subarray of an array \(b\) if \(a\) can be obtained from \(b\) by deleting zero or more elements from the beginning and zero or more elements from the end.\(^{\text{†}}\)A permutation of length \(n\) is an array consisting of \(n\) distinct integers from \(1\) to \(n\) in arbitrary order. For example, \([2,3,1,5,4]\) is a permutation, but \([1,2,2]\) is not a permutation (\(2\) appears twice in the array), and \([1,3,4]\) is also not a permutation (\(n=3\) but there is \(4\) in the array).
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 100\)). The description of the test cases follows. The first line of each test case contains one integer \(n\) (\(3 \le n \le 5000\)) — denoting the number of rows and columns in the matrix.It is guaranteed that the sum of \(n\) over all test cases does not exceed \(5000\).
For each test case, on the first line, print an integer \(k\) \((0 \le k \le 2n)\), the number of operations you wish to perform. On the next lines, you should print the operations.To print an operation, use the format ""\(i\;l\;r\)"" (\(1 \leq l \leq r \leq n\) and \(1 \leq i \leq n\)) which reverses the subarray \(A_{i, l}\), \(A_{i, l+1}\), \(\ldots\), \(A_{i, r}\).
In the first test case, the following operations are a valid solution: