CF2118B Make It Permutation

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: