CF1136C.Nastya Is Transposing Matrices

Nastya came to her informatics lesson, and her teacher who is, by the way, a little bit famous here gave her the following task.

Two matrices $A$ and $B$ are given, each of them has size $n \times m$ . Nastya can perform the following operation to matrix $A$ unlimited number of times:

• take any square square submatrix of $A$ and transpose it (i.e. the element of the submatrix which was in the $i$ -th row and $j$ -th column of the submatrix will be in the $j$ -th row and $i$ -th column after transposing, and the transposed submatrix itself will keep its place in the matrix $A$ ).

Nastya's task is to check whether it is possible to transform the matrix $A$ to the matrix $B$ .

Example of the operationAs it may require a lot of operations, you are asked to answer this question for Nastya.

A square submatrix of matrix $M$ is a matrix which consist of all elements which comes from one of the rows with indeces $x, x+1, \dots, x+k-1$ of matrix $M$ and comes from one of the columns with indeces $y, y+1, \dots, y+k-1$ of matrix $M$ . $k$ is the size of square submatrix. In other words, square submatrix is the set of elements of source matrix which form a solid square (i.e. without holes).

The first line contains two integers $n$ and $m$ separated by space ( $1 \leq n, m \leq 500$ ) — the numbers of rows and columns in $A$ and $B$ respectively.

Each of the next $n$ lines contains $m$ integers, the $j$ -th number in the $i$ -th of these lines denotes the $j$ -th element of the $i$ -th row of the matrix $A$ ( $1 \leq A_{ij} \leq 10^{9}$ ).

Each of the next $n$ lines contains $m$ integers, the $j$ -th number in the $i$ -th of these lines denotes the $j$ -th element of the $i$ -th row of the matrix $B$ ( $1 \leq B_{ij} \leq 10^{9}$ ).

Print "YES" (without quotes) if it is possible to transform $A$ to $B$ and "NO" (without quotes) otherwise.

You can print each letter in any case (upper or lower).

Consider the third example. The matrix $A$ initially looks as follows.

$$ \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix} $$ </p><p>Then we choose the whole matrix as transposed submatrix and it becomes</p><p> $$ \begin{bmatrix} 1 & 4 & 7\\ 2 & 5 & 8\\ 3 & 6 & 9 \end{bmatrix} $$ </p><p>Then we transpose the submatrix with corners in cells $(2, 2)$ and $(3, 3)$ . </p><p> $$ \begin{bmatrix} 1 & 4 & 7\\ 2 & \textbf{5} & \textbf{8}\\ 3 & \textbf{6} & \textbf{9} \end{bmatrix} $$ </p><p>So matrix becomes</p><p> $$ \begin{bmatrix} 1 & 4 & 7\\ 2 & 5 & 6\\ 3 & 8 & 9 \end{bmatrix} $$ </p><p>and it is $B$$$.