<p>Given an <code>m x n</code> binary matrix <code>mat</code>, return <em>the distance of the nearest </em><code>0</code><em> for each cell</em>.</p>

<p>The distance between two adjacent cells is <code>1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/01-1-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> mat = [[0,0,0],[0,1,0],[0,0,0]]
<strong>Output:</strong> [[0,0,0],[0,1,0],[0,0,0]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/01-2-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> mat = [[0,0,0],[0,1,0],[1,1,1]]
<strong>Output:</strong> [[0,0,0],[0,1,0],[1,2,1]]
</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;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>4</sup></code></li>
	<li><code>mat[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
	<li>There is at least one <code>0</code> in <code>mat</code>.</li>
</ul>

class Solution:
    from collections import deque
    def updateMatrix(self, mat: List[List[int]]) -> List[List[int]]:
        m, n = len(mat), len(mat[0])
        dist = [[-1]*n for _ in range(m)]
        Q = deque()
        for i in range(m):
            for j in range(n):
                if not mat[i][j]:
                    Q.append((i,j))

        directions = [(0,1), (0,-1), (1,0), (-1,0)]

        level = 0
        while Q:
            N = len(Q)

            for _ in range(N):
                i, j = Q.popleft()
                if dist[i][j] != -1:
                    continue
                
                dist[i][j] = level
                
                for ai, aj in directions:
                    ni, nj = i + ai, j + aj
                    if ni < 0 or nj < 0 or ni >= m or nj >= n:
                        continue
                    if dist[ni][nj] != -1 or not mat[ni][nj]:
                        continue
                    Q.append((ni,nj))

            level += 1

        return dist
19600