<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>

from typing import  List


class Solution:
    def possibleToStamp(self, grid: List[List[int]], stampHeight: int, stampWidth: int) -> bool:
        g= grid
        a = [[-1 for _ in g[0] ] for _ in g]

        for j in range(len(g[0])):
            last = -1
            for i in range(len(g)):
                if g[i][j]==1:
                    last = i
                a[i][j]=i-last

        b = [[0 for _ in g[0] ] for _ in g]
        import heapq

        for i in range(len(g)):
            heap = []

            for j in range(len(g[0])):
                if a[i][j]>=stampHeight:
                    heapq.heappush(heap, j)

                while len(heap)>0 and  heap[0]<=j-stampWidth:
                    heapq.heappop(heap)

                if len(heap)>=stampWidth:
                    b[i-stampHeight+1][j-stampWidth+1]=1



        for i in range(len(b)):
            last = 0
            for j in range(len(b[0])):
                if b[i][j]==1:
                    last = stampWidth
                if last>0:
                    b[i][j]=1
                last-=1


        for j in range(len(b[0])):
            lsat = 0
            for i in range(len(b)):
                if b[i][j]==1:
                    last = stampHeight
                if last>0:
                    b[i][j]=1
                last-=1

        for i in range(len(b)):
            for j in range(len(b[0])):
                if g[i][j]==0 and b[i][j]==0:
                    return False

        return True


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