E. Impressionismtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputBurenka 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.InputThe 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.OutputIn 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.ExamplesInput
3 3
1 0 2
0 0 0
2 0 1
2 0 1
0 0 0
1 0 2
Output
1
1 1 3
Input
4 4
0 0 1 2
3 0 0 0
0 1 0 0
1 0 0 0
2 0 0 1
0 3 0 0
0 1 0 0
0 0 1 0
Output
4
1 3 4
2 3 4
2 2 3
2 1 2
Input
3 3
1 2 0
0 0 0
0 0 0
1 0 0
2 0 0
0 0 0
Output
-1

3 3
1 0 2
0 0 0
2 0 1
2 0 1
0 0 0
1 0 2

1 1 1 3 
['constructive algorithms', 'graphs', 'implementation', 'math', '*3500']