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.

布尔恩卡有两幅画 $a$ 和 $b$，它们均为大小为 $n \times m$ 的表格。每幅画的每个格子均有一种颜色——一个从 $0$ 到 $2 \cdot 10^5$ 的整数；且在每幅画的任意一行或一列中，除颜色 $0$ 外，其余颜色均不重复。

布尔恩卡希望将画 $a$ 变为画 $b$。为实现该目标，她可执行以下两种操作之一：交换 $a$ 的任意两行，或交换 $a$ 的任意两列。请告诉布尔恩卡她能否达成目标；若可以，请给出所需的操作序列。

行编号从上到下依次为 $1$ 至 $n$，列编号从左到右依次为 $1$ 至 $m$。

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 $0$.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n \cdot m \leq 2 \cdot 10^5$）—— 表格的尺寸。

接下来的 $n$ 行中，第 $i$ 行包含 $m$ 个整数 $a_{i, 1}, a_{i, 2}, \ldots, a_{i, m}$（$0 \leq a_{i,j} \leq 2 \cdot 10^5$）—— 图片 $a$ 第 $i$ 行的颜色。保证在同一行或同一列中，除颜色 $0$ 外不存在相同的颜色。

再接下来的 $n$ 行中，第 $i$ 行包含 $m$ 个整数 $b_{i, 1}, b_{i, 2}, \ldots, b_{i, m}$（$0 \leq b_{i,j} \leq 2 \cdot 10^5$）—— 图片 $b$ 第 $i$ 行的颜色。保证在同一行或同一列中，除颜色 $0$ 外不存在相同的颜色。

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.

第一行输出数字 $-1$，表示无法实现布尔恩卡的目标；否则输出你所构造的解中操作次数 $k$（$0 \le k \le 2 \cdot 10^5$）。可以证明：若解存在，则必存在一个满足 $k \le 2 \cdot 10^5$ 的解。

接下来 $k$ 行，每行描述一次操作：首先输出操作类型（$1$ 表示交换两行，$2$ 表示交换两列），然后输出被操作的两行或两列的下标。

注意：你无需最小化操作次数。