<p>You are given an <code>m x n</code> binary matrix <code>grid</code>. An island is a group of <code>1</code>&#39;s (representing land) connected <strong>4-directionally</strong> (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.</p>

<p>The <strong>area</strong> of an island is the number of cells with a value <code>1</code> in the island.</p>

<p>Return <em>the maximum <strong>area</strong> of an island in </em><code>grid</code>. If there is no island, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/maxarea1-grid.jpg" style="width: 500px; height: 310px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0,0]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The answer is not 11, because the island must be connected 4-directionally.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,0,0,0]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution:
    def union(self, c1, c2, comps, ranks):
        if ranks[c1] < ranks[c2]:
            c1, c2 = c2, c1
        comps[c2] = c1
        ranks[c1] = max(ranks[c1], ranks[c2]+1)

    def find(self, t, comps, ranks):
        if t not in comps:
            comps[t] = t
            return t
        if comps[t] == t:
            return t
        comps[t] = self.find(comps[t], comps, ranks)
        ranks[comps[t]] = 1
        return comps[t]

    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        ranks = defaultdict(int)
        comps = {}

        for i in range(m):
            for j in range(n):
                if grid[i][j] == 1:
                    c1 = self.find((i, j), comps, ranks)
                    for x, y in [(i-1, j), (i, j-1), (i, j+1), (i+1, j)]:
                        if 0 <= x < m and 0 <= y < n and grid[x][y] == 1:
                            c1 = self.find((i, j), comps, ranks)
                            c2 = self.find((x, y), comps, ranks)
                            if c1 != c2:
                                self.union(c1, c2, comps, ranks)

        area = 0
        compAreas = defaultdict(int)
        for c in comps:
            self.find(c, comps, ranks)
            compAreas[comps[c]] += 1
            area = max(area, compAreas[comps[c]])

        return area
17000