CF1718E Impressionism

Burenka has two pictures $ a $ and $ b $ , which are tables of the same size $ n \times m $ . Each cell of each painting has a color — a number from $ 0 $ to $ 2 \cdot 10^5 $ , and there are no repeating colors in any row or column of each of the two paintings, except color $ 0 $ . Burenka wants to get a picture $ b $ from the picture $ a $ . To achieve her goal, Burenka can perform one of $ 2 $ operations: swap any two rows of $ a $ or any two of its columns. Tell Burenka if she can fulfill what she wants, and if so, tell her the sequence of actions. The rows are numbered from $ 1 $ to $ n $ from top to bottom, the columns are numbered from $ 1 $ to $ m $ from left to right.

The first line contains two integers $ n $ and $ m $ ( $ 1 \leq n \cdot m \leq 2 \cdot 10^5 $ ) — the sizes of the table. The $ i $ -th of the next $ n $ lines contains $ m $ integers $ a_{i, 1}, a_{i, 2}, \ldots, a_{i, m} $ ( $ 0 \leq a_{i,j} \leq 2 \cdot 10^5 $ ) — the colors of the $ i $ -th row of picture $ a $ . It is guaranteed that there are no identical colors in the same row or column, except color $ 0 $ . The $ i $ -th of the following $ n $ lines contains $ m $ integers $ b_{i, 1}, b_{i, 2}, \ldots, b_{i, m} $ ( $ 0 \leq b_{i,j} \leq 2 \cdot 10^5 $ ) — the colors of the $ i $ -th row of picture $ b $ . It is guaranteed that there are no identical colors in the same row or column, except color $ 0 $ .

In the first line print the number $ -1 $ if it is impossible to achieve what Burenka wants, otherwise print the number of actions in your solution $ k $ ( $ 0 \le k \le 2 \cdot 10^5 $ ). It can be proved that if a solution exists, then there exists a solution where $ k \le 2 \cdot 10^5 $ . In the next $ k $ lines print the operations. First print the type of the operation ( $ 1 $ — swap rows, $ 2 $ — columns), and then print the two indices of rows or columns to which the operation is applied. Note that you don't have to minimize the number of operations.