CF1747B BAN BAN

You are given an integer $ n $ . Let's define $ s(n) $ as the string "BAN" concatenated $ n $ times. For example, $ s(1) $ = "BAN", $ s(3) $ = "BANBANBAN". Note that the length of the string $ s(n) $ is equal to $ 3n $ . Consider $ s(n) $ . You can perform the following operation on $ s(n) $ any number of times (possibly zero): - Select any two distinct indices $ i $ and $ j $ $ (1 \leq i, j \leq 3n, i \ne j) $ . - Then, swap $ s(n)_i $ and $ s(n)_j $ . You want the string "BAN" to not appear in $ s(n) $ as a subsequence. What's the smallest number of operations you have to do to achieve this? Also, find one such shortest sequence of operations. A string $ a $ is a subsequence of a string $ b $ if $ a $ can be obtained from $ b $ by deletion of several (possibly, zero or all) characters.

The input consists of multiple test cases. The first line contains a single integer $ t $ $ (1 \leq t \leq 100) $ — the number of test cases. The description of the test cases follows. The only line of each test case contains a single integer $ n $ $ (1 \leq n \leq 100) $ .

For each test case, in the first line output $ m $ ( $ 0 \le m \le 10^5 $ ) — the minimum number of operations required. It's guaranteed that the objective is always achievable in at most $ 10^5 $ operations under the constraints of the problem. Then, output $ m $ lines. The $ k $ -th of these lines should contain two integers $ i_k $ , $ j_k $ $ (1\leq i_k, j_k \leq 3n, i_k \ne j_k) $ denoting that you want to swap characters at indices $ i_k $ and $ j_k $ at the $ k $ -th operation. After all $ m $ operations, "BAN" must not appear in $ s(n) $ as a subsequence. If there are multiple possible answers, output any.

In the first testcase, $ s(1) = $ "BAN", we can swap $ s(1)_1 $ and $ s(1)_2 $ , converting $ s(1) $ to "ABN", which does not contain "BAN" as a subsequence. In the second testcase, $ s(2) = $ "BANBAN", we can swap $ s(2)_2 $ and $ s(2)_6 $ , converting $ s(2) $ to "BNNBAA", which does not contain "BAN" as a subsequence.