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ProblemSubmissionsLeaderboardDiscussionsYou are given two grids of numbers a𝑎 and b𝑏, with n𝑛 rows and m𝑚 columns. All the values in the grid are 0, 1 or 2 You can perform the following operation on a𝑎 any number of times: • Pick any subrectangle in the grid with length and width ≥2. You are allowed to choose the entire grid as a subrectangle. • The subrectangle has four corners. Take any pair of diagonally opposite corners of the chosen subrectangle and add 1 to their values modulo 3. • For the pair of corners not picked, add 2 to their values modulo 3. Note that the operation only changes the values of the corners of the picked subrectangle. Is it possible to convert the grid a𝑎 into grid b𝑏 by applying the above operation any number of times (possibly zero)?Input FormatThe first line contains two integers n𝑛 and m𝑚, the number of rows and columns in the grid (2≤n,m≤500). Each of the next n lines contain m characters — the j-th character of the i-th line represents ai,j. Each of the next n lines contain m characters — the j-th character of the i-th line represents bi,j(0≤ai,j,bi,j≤2). It is guaranteed that the sum of n𝑛 over all test cases and the sum of m𝑚 over all test cases do not exceed 500.Constraints(2≤n,m≤500).Output FormatFor each test case print "YES" (without quotes) if it is possible to convert grid a into grid b and "NO" (without quotes) otherwise.

Question

ProblemSubmissionsLeaderboardDiscussionsYou are given two grids of numbers a𝑎 and b𝑏, with n𝑛 rows and m𝑚 columns. All the values in the grid are 0, 1 or 2 You can perform the following operation on a𝑎 any number of times: • Pick any subrectangle in the grid with length and width ≥2. You are allowed to choose the entire grid as a subrectangle. • The subrectangle has four corners. Take any pair of diagonally opposite corners of the chosen subrectangle and add 1 to their values modulo 3. • For the pair of corners not picked, add 2 to their values modulo 3. Note that the operation only changes the values of the corners of the picked subrectangle. Is it possible to convert the grid a𝑎 into grid b𝑏 by applying the above operation any number of times (possibly zero)?Input FormatThe first line contains two integers n𝑛 and m𝑚, the number of rows and columns in the grid (2≤n,m≤500). Each of the next n lines contain m characters — the j-th character of the i-th line represents ai,j. Each of the next n lines contain m characters — the j-th character of the i-th line represents bi,j(0≤ai,j,bi,j≤2). It is guaranteed that the sum of n𝑛 over all test cases and the sum of m𝑚 over all test cases do not exceed 500.Constraints(2≤n,m≤500).Output FormatFor each test case print "YES" (without quotes) if it is possible to convert grid a into grid b and "NO" (without quotes) otherwise.

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Solution

This problem is asking whether it is possible to transform one grid of numbers into another grid of numbers by performing a specific operation any number of times. The operation involves selecting a subrectangle within the grid and adding 1 or 2 (modulo 3) to the values at the corners of the subrectangle.

Here's a step-by-step guide on how to approach this problem:

  1. Understand the problem: The problem is asking whether it is possible to transform grid a into grid b by performing a specific operation. The operation involves selecting a subrectangle within the grid and adding 1 or 2 (modulo 3) to the values at the corners of the subrectangle.

  2. Read the input: The first line of the input contains two integers n and m, which represent the number of rows and columns in the grid. The next n lines contain m characters each, representing the values in grid a. The following n lines contain m characters each, representing the values in grid b.

  3. Process the input: For each cell in grid a, calculate the difference with the corresponding cell in grid b. This difference represents the number of operations needed to transform the cell in grid a into the cell in grid b.

  4. Perform the operations: For each cell in grid a, perform the necessary number of operations to transform the cell into the corresponding cell in grid b. Remember that each operation involves selecting a subrectangle and adding 1 or 2 (modulo 3) to the values at the corners of the subrectangle.

  5. Check the result: After performing all the necessary operations, check whether grid a has been transformed into grid b. If it has

This problem has been solved

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