C. Nastya Is Transposing Matricestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputNastya 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 operation As 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).InputThe 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}).OutputPrint "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).ExamplesInput
2 2
1 1
6 1
1 6
1 1
Output
YESInput
2 2
4 4
4 5
5 4
4 4
Output
NOInput
3 3
1 2 3
4 5 6
7 8 9
1 4 7
2 5 6
3 8 9
Output
YESNoteConsider the third example. The matrix A initially looks as follows. \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix} Then we choose the whole matrix as transposed submatrix and it becomes \begin{bmatrix} 1 & 4 & 7\\ 2 & 5 & 8\\ 3 & 6 & 9 \end{bmatrix} Then we transpose the submatrix with corners in cells (2, 2) and (3, 3).  \begin{bmatrix} 1 & 4 & 7\\ 2 & \textbf{5} & \textbf{8}\\ 3 & \textbf{6} & \textbf{9} \end{bmatrix} So matrix becomes \begin{bmatrix} 1 & 4 & 7\\ 2 & 5 & 6\\ 3 & 8 & 9 \end{bmatrix} and it is B.
2 2
1 1
6 1
1 6
1 1

YES
['constructive algorithms', 'sortings', '*1500']