<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):
        n, lands = len(grid), []
        stats = tuple([False]*n for _ in range(n))
        for y, (row, stat) in enumerate(zip(grid, stats)):
            for x, val in enumerate(row):
                if val:
                    lands.append((x, y))
                    stat[x] = True

        if len(lands) == 0 or len(lands) == n*n:return -1

        dis, suc = 1, True
        while suc:
            suc = False
            for lx, ly in lands:
                for dx, dy in zip(range(dis, -1, -1), range(dis+1)):
                    if (y := ly+dy) < n:
                        if (x := lx+dx) < n and not stats[y][x]:stats[y][x] = suc = True
                        if (x := lx-dx) > -1 and not stats[y][x]:stats[y][x] = suc = True
                    if (y := ly-dy) > -1:
                        if (x := lx+dx) < n and not stats[y][x]:stats[y][x] = suc = True
                        if (x := lx-dx) > -1 and not stats[y][x]:stats[y][x] = suc = True
            if not suc:return dis-1
            dis += 1
609