<p>Given a <code>m x n</code> matrix <code>mat</code> and an integer <code>threshold</code>, return <em>the maximum side-length of a square with a sum less than or equal to </em><code>threshold</code><em> or return </em><code>0</code><em> if there is no such square</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/12/05/e1.png" style="width: 335px; height: 186px;" />
<pre>
<strong>Input:</strong> mat = [[1,1,3,2,4,3,2],[1,1,3,2,4,3,2],[1,1,3,2,4,3,2]], threshold = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> The maximum side length of square with sum less than 4 is 2 as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> mat = [[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2]], threshold = 1
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</code></li>
	<li><code>0 &lt;= mat[i][j] &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= threshold &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def maxSideLength(self, mat: List[List[int]], threshold: int) -> int:
        m, n = len(mat), len(mat[0])
        prefix_sums = [[0 for i in range(n)] for j in range(m)]
        prefix_sums[0][0] = mat[0][0]
        for i in range(1, m):
            prefix_sums[i][0] = mat[i][0] + prefix_sums[i - 1][0]
        for j in range(1, n):
            prefix_sums[0][j] = mat[0][j] + prefix_sums[0][j - 1]
        for i in range(1, m):
            for j in range(1, n):
                prefix_sums[i][j] = prefix_sums[i - 1][j] + prefix_sums[i][j - 1] - prefix_sums[i - 1][j - 1] + mat[i][j]
        print(prefix_sums)

        def square(i, j, k):
            if i + k - 1 >= m or j + k - 1 >= n:
                return float('inf')
            res = prefix_sums[i+k-1][j+k-1]
            if i > 0 and j > 0:
                res = res + prefix_sums[i - 1][j - 1] 
            if i > 0:
                res = res - prefix_sums[i - 1][j + k - 1]
            if j > 0:
                res = res - prefix_sums[i + k - 1][j - 1]
            return res

        res = 0

        for i in range(m):
            for j in range(n):
                while square(i, j, res + 1) <= threshold:
                    print(i, j, res + 1)
                    print(square(i, j, res + 1))
                    res += 1
                
        return res
        
24000