<p>You are given a <strong>0-indexed</strong> integer array <code>arr</code>, and an <code>m x n</code> integer <strong>matrix</strong> <code>mat</code>. <code>arr</code> and <code>mat</code> both contain <strong>all</strong> the integers in the range <code>[1, m * n]</code>.</p>

<p>Go through each index <code>i</code> in <code>arr</code> starting from index <code>0</code> and paint the cell in <code>mat</code> containing the integer <code>arr[i]</code>.</p>

<p>Return <em>the smallest index</em> <code>i</code> <em>at which either a row or a column will be completely painted in</em> <code>mat</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="image explanation for example 1" /><img alt="image explanation for example 1" src="https://assets.leetcode.com/uploads/2023/01/18/grid1.jpg" style="width: 321px; height: 81px;" />
<pre>
<strong>Input:</strong> arr = [1,3,4,2], mat = [[1,4],[2,3]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The moves are shown in order, and both the first row and second column of the matrix become fully painted at arr[2].
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="image explanation for example 2" src="https://assets.leetcode.com/uploads/2023/01/18/grid2.jpg" style="width: 601px; height: 121px;" />
<pre>
<strong>Input:</strong> arr = [2,8,7,4,1,3,5,6,9], mat = [[3,2,5],[1,4,6],[8,7,9]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The second column becomes fully painted at arr[3].
</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>arr.length == m * n</code></li>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i], mat[r][c] &lt;= m * n</code></li>
	<li>All the integers of <code>arr</code> are <strong>unique</strong>.</li>
	<li>All the integers of <code>mat</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def firstCompleteIndex(self, arr: List[int], mat: List[List[int]]) -> int:
        m, n = len(mat), len(mat[0])
        mapping = {mat[i][j]: (i,j) for i in range(m) for j in range(n)}
        rowRemaining, colRemaining = [n]*m, [m]*n
        for i, num in enumerate(arr):
            row, col = mapping[num]
            rowRemaining[row] -= 1
            colRemaining[col] -= 1
            if rowRemaining[row]==0 or colRemaining[col]==0:
                return i
885