306037: CF1136C. Nastya Is Transposing Matrices
Memory Limit:256 MB
Time Limit:1 S
Judge Style:Text Compare
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Description
Nastya Is Transposing Matrices
题意翻译
给出两个大小皆为n*m的矩阵A和B. 每次操作可以从矩阵A中,选一个子方阵,对这个方阵进行转制。 矩阵C的转置C’满足C’[i][j]=C[j][i] 且 C‘和C大小相同。 问能否经过有限次操作将A变成B. 可以输出yes,不行输出no.题目描述
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 $ . ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1136C/7711a999558fa948bea147de25b2bda2e2007e83.png)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).输入输出格式
输入格式
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} $ ).
输出格式
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).
输入输出样例
输入样例 #1
2 2
1 1
6 1
1 6
1 1
输出样例 #1
YES
输入样例 #2
2 2
4 4
4 5
5 4
4 4
输出样例 #2
NO
输入样例 #3
3 3
1 2 3
4 5 6
7 8 9
1 4 7
2 5 6
3 8 9
输出样例 #3
YES