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

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

<ol>
	<li>Cover all the <strong>empty</strong> cells.</li>
	<li>Do not cover any of the <strong>occupied</strong> cells.</li>
	<li>We can put as <strong>many</strong> stamps as we want.</li>
	<li>Stamps can <strong>overlap</strong> with each other.</li>
	<li>Stamps are not allowed to be <strong>rotated</strong>.</li>
	<li>Stamps must stay completely <strong>inside</strong> the grid.</li>
</ol>

<p>Return <code>true</code> <em>if it is possible to fit the stamps while following the given restrictions and requirements. Otherwise, return</em> <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/03/ex1.png" style="width: 180px; height: 237px;" />
<pre>
<strong>Input:</strong> 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
<strong>Output:</strong> true
<strong>Explanation:</strong> We have two overlapping stamps (labeled 1 and 2 in the image) that are able to cover all the empty cells.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/03/ex2.png" style="width: 170px; height: 179px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], stampHeight = 2, stampWidth = 2 
<strong>Output:</strong> false 
<strong>Explanation:</strong> There is no way to fit the stamps onto all the empty cells without the stamps going outside the grid.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[r].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>grid[r][c]</code> is either <code>0</code> or <code>1</code>.</li>
	<li><code>1 &lt;= stampHeight, stampWidth &lt;= 10<sup>5</sup></code></li>
</ul>


class Solution:
    def possibleToStamp(
        self, grid: List[List[int]], stampHeight: int, stampWidth: int
    ) -> bool:
        grid_height = len(grid)
        grid_width = len(grid[0])
        if sum([sum(row) for row in grid]) >= grid_height * grid_width:
            return True
        if (stampHeight > grid_height) or (stampWidth > grid_width):
            return False
        for ii in range(grid_height):
            for jj in range(grid_width):
                if grid[ii][jj] == 1:
                    continue
                if grid[ii][jj] == -1:
                    continue
                # try to cover with stamp
                cover_success = False
                for move_up in range(stampHeight):
                    if cover_success:
                        continue
                    if (ii - move_up < 0) or (
                        ii - move_up + stampHeight > grid_height
                    ):
                        continue
                    for move_left in range(stampWidth):
                        if cover_success:
                            continue
                        if (jj - move_left < 0) or (
                            jj - move_left + stampWidth > grid_width
                        ):
                            continue
                        row = ii - move_up
                        col = jj - move_left
                        stamp_is_legal = True
                        for iii in range(row, row + stampHeight):
                            for jjj in range(col, col + stampWidth):
                                if grid[iii][jjj] == 1:
                                    stamp_is_legal = False
                        if stamp_is_legal:
                            cover_success = True
                            for iii in range(row, row + stampHeight):
                                for jjj in range(col, col + stampWidth):
                                    grid[iii][jjj] = -1
                if not cover_success:
                    return False
        return True


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