CF1475F Unusual Matrix

You are given two binary square matrices $ a $ and $ b $ of size $ n \times n $ . A matrix is called binary if each of its elements is equal to $ 0 $ or $ 1 $ . You can do the following operations on the matrix $ a $ arbitrary number of times (0 or more): - vertical xor. You choose the number $ j $ ( $ 1 \le j \le n $ ) and for all $ i $ ( $ 1 \le i \le n $ ) do the following: $ a_{i, j} := a_{i, j} \oplus 1 $ ( $ \oplus $ — is the operation [xor](https://en.wikipedia.org/wiki/Exclusive_or) (exclusive or)). - horizontal xor. You choose the number $ i $ ( $ 1 \le i \le n $ ) and for all $ j $ ( $ 1 \le j \le n $ ) do the following: $ a_{i, j} := a_{i, j} \oplus 1 $ . Note that the elements of the $ a $ matrix change after each operation. For example, if $ n=3 $ and the matrix $ a $ is: $ $$$ \begin{pmatrix} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} $ $ Then the following sequence of operations shows an example of transformations:

• vertical xor, $ j=1 $ . $ $ a= \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} $ $
• horizontal xor, $ i=2 $ . $ $ a= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{pmatrix} $ $
• vertical xor, $ j=2 $ . $ $ a= \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} $ $

Check if there is a sequence of operations such that the matrix $ a $ becomes equal to the matrix $ b$$$.

N/A

N/A

The first test case is explained in the statements. In the second test case, the following sequence of operations is suitable: - horizontal xor, $ i=1 $ ; - horizontal xor, $ i=2 $ ; - horizontal xor, $ i=3 $ ; It can be proved that there is no sequence of operations in the third test case so that the matrix $ a $ becomes equal to the matrix $ b $ .