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Stamping the Grid

You are given an m x n binary matrix grid where each cell is either 0 (empty) or 1 (occupied).

You are given an m x n binary matrix grid where each cell is either 0 (empty) or 1 (occupied).

You are then given stamps of size stampHeight x stampWidth. We want to fit the stamps such that they follow the given restrictions and requirements:

Return true if it is possible to fit the stamps while following the given restrictions and requirements. Otherwise, return false.

Stamping the Grid diagram

Example 1

Input: grid = [[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0],[1,0,0,0]], stampHeight = 4, stampWidth = 3

Output: true

Explanation: We have two overlapping stamps (labeled 1 and 2 in the image) that are able to cover all the empty cells.

Example 2

Input: grid = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], stampHeight = 2, stampWidth = 2

Output: false

Explanation: There is no way to fit the stamps onto all the empty cells without the stamps going outside the grid.

Constraints

  • m == grid.length
  • n == grid[r].length
  • 1 <= m, n <= 10^5
  • 1 <= m * n <= 2 * 10^5
  • grid[r][c] is either 0 or 1.
  • 1 <= stampHeight, stampWidth <= 10^5

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