<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>

import itertools as it
class Solution:
    def possibleToStamp(self, grid: List[List[int]], stampHeight: int, stampWidth: int) -> bool:
        
        def hasAny(accumGrid: List[List[int]], start: Tuple[int, int], stop: Tuple[int, int]) -> bool:
            res = accumGrid[stop[0]][stop[1]]
            if start[0] > 0:
                res -= accumGrid[start[0] - 1][stop[1]]
                if start[1] > 0:
                    res -= accumGrid[stop[0]][start[1] - 1] - accumGrid[start[0] - 1][start[1] - 1]
            elif start[1] > 0:
                res -= accumGrid[stop[0]][start[1] - 1]
            return res
        
        def buildAccumGrid(mygrid: List[List[int]]) -> None:
            accumGrid = []
            for r in mygrid:
                r = list(it.accumulate(r))
                if accumGrid:
                    for j in range(len(r)):
                        r[j] += accumGrid[-1][j]
                accumGrid.append(r)
            return accumGrid
        
        blockAccumGrid = buildAccumGrid(grid)
        availGrid = [[0] * len(r) for r in grid]

        for i in range(len(grid) - stampHeight + 1):
            for j in range(len(grid[i]) - stampWidth + 1):
                availGrid[i][j] = int(not hasAny(blockAccumGrid, (i, j), (i + stampHeight - 1, j + stampWidth - 1)))
        
        availGrid = buildAccumGrid(availGrid)
        for i in range(len(grid)):
            for j in range(len(grid[i])):
                if grid[i][j]:
                    continue
                start = (max(i - stampHeight + 1, 0), max(j - stampWidth + 1, 0))
                stop = (i, j)
                if not hasAny(availGrid, start, stop):
                    return False
        
        return True


                


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