<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>

from typing import List

class Solution:
    def firstCompleteIndex(self, arr: List[int], mat: List[List[int]]) -> int:
        m, n = len(mat), len(mat[0])
        
        # Dictionary to store the position of each number in the matrix
        position = {}
        for i in range(m):
            for j in range(n):
                position[mat[i][j]] = (i, j)
        
        # Dictionaries to keep track of painted cells in each row and column
        row_paint = [0] * m
        col_paint = [0] * n
        
        for i, num in enumerate(arr):
            x, y = position[num]
            
            # Paint the cell and update the count of painted cells in the row and column
            row_paint[x] += 1
            col_paint[y] += 1
            
            # Check if the current row or column is fully painted
            if row_paint[x] == n or col_paint[y] == m:
                return i
        
        return -1

# Example usage:
solution = Solution()
arr = [1,3,4,2]
mat = [[1,4],[2,3]]
print(solution.firstCompleteIndex(arr, mat))  # Output: 2

arr = [2,8,7,4,1,3,5,6,9]
mat = [[3,2,5],[1,4,6],[8,7,9]]
print(solution.firstCompleteIndex(arr, mat))  # Output: 3
926