CF2121D 1709

You are given two arrays of integers $ a_1, a_2, \ldots, a_n $ and $ b_1, b_2, \ldots, b_n $ . It is guaranteed that each integer from $ 1 $ to $ 2 \cdot n $ appears in exactly one of the arrays. You need to perform a certain number of operations (possibly zero) so that both of the following conditions are satisfied: - For each $ 1 \leq i < n $ , it holds that $ a_i < a_{i + 1} $ and $ b_i < b_{i + 1} $ . - For each $ 1 \leq i \leq n $ , it holds that $ a_i < b_i $ . During each operation, you can perform exactly one of the following three actions: 1. Choose an index $ 1 \leq i < n $ and swap the values $ a_i $ and $ a_{i + 1} $ . 2. Choose an index $ 1 \leq i < n $ and swap the values $ b_i $ and $ b_{i + 1} $ . 3. Choose an index $ 1 \leq i \leq n $ and swap the values $ a_i $ and $ b_i $ . You do not need to minimize the number of operations, but the total number must not exceed $ 1709 $ . Find any sequence of operations that satisfies both conditions.

Each test 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 first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 40 $ ) — the length of the arrays $ a $ and $ b $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 2 \cdot n $ ). The third line of each test case contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1 \leq b_i \leq 2 \cdot n $ ). It is guaranteed that each integer from $ 1 $ to $ 2 \cdot n $ appears either in array $ a $ or in array $ b $ .

For each test case, output the sequence of operations. In the first line for each test case, output the number of operations $ k $ . Note that $ 0 \leq k \leq 1709 $ . In the following $ k $ lines for each test case, output the operations themselves: - If you want to swap the values $ a_i $ and $ a_{i + 1} $ , output two integers $ 1 $ and $ i $ . Note that $ 1 \leq i < n $ . - If you want to swap the values $ b_i $ and $ b_{i + 1} $ , output two integers $ 2 $ and $ i $ . Note that $ 1 \leq i < n $ . - If you want to swap the values $ a_i $ and $ b_i $ , output two integers $ 3 $ and $ i $ . Note that $ 1 \leq i \leq n $ . It can be shown that under the given constraints, a solution always exists.

In the first test case, $ a_1 < b_1 $ , so no operations need to be applied. In the second test case, $ a_1 > b_1 $ . After applying the operation, these values will be swapped. In the third test case, after applying the operation, $ a = [1, 3] $ and $ b = [2, 4] $ . In the fourth test case, after applying the operation, $ a = [1, 2] $ and $ b = [3, 4] $ .