<p>Given an <code>n x n</code> <code>grid</code>&nbsp;containing only values <code>0</code> and <code>1</code>, where&nbsp;<code>0</code> represents water&nbsp;and <code>1</code> represents land, find a water cell such that its distance to the nearest land cell is maximized, and return the distance.&nbsp;If no land or water exists in the grid, return <code>-1</code>.</p>

<p>The distance used in this problem is the Manhattan distance:&nbsp;the distance between two cells <code>(x0, y0)</code> and <code>(x1, y1)</code> is <code>|x0 - x1| + |y0 - y1|</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/05/03/1336_ex1.JPG" style="width: 185px; height: 87px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,1],[0,0,0],[1,0,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The cell (1, 1) is as far as possible from all the land with distance 2.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/05/03/1336_ex2.JPG" style="width: 184px; height: 87px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0],[0,0,0],[0,0,0]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The cell (2, 2) is as far as possible from all the land with distance 4.
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n&nbsp;&lt;= 100</code></li>
	<li><code>grid[i][j]</code>&nbsp;is <code>0</code> or <code>1</code></li>
</ul>

class Solution:
    def maxDistance(self, grid: List[List[int]]) -> int:
        n = len(grid)
        distances = [[0 for _ in range(n)] for _ in range(n)]
        
        for i in range(n):
            for j in range(n):
                if grid[i][j] == 0:
                    a = b = 1000
                    if i > 0:
                        a = distances[i-1][j]
                    if j > 0:
                        b = distances[i][j-1]
                    distances[i][j] = min(a, b) + 1
        
        max_distance = 0
        for i in range(-1, -n-1, -1):
            for j in range(-1, -n-1, -1):
                if grid[i][j] == 0:
                    a = b = 1000
                    if i < -1:
                        a = distances[i+1][j] + 1
                    if j < -1:
                        b = distances[i][j+1] + 1
                    distances[i][j] = min(distances[i][j], a, b)
                    max_distance = max(max_distance, distances[i][j])
        
        return max_distance if max_distance > 0 and max_distance < 1000 else -1
332