<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 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 &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    int paint(int i, int j, int c, vector<vector<int>>& g, bool flip = false) {
        if (!flip && (min(i, j) < 0 || i >= g.size() || j >= g[0].size() ||
                      g[i][j] == 0 || g[i][j] == c))
            return 0;
        g[i][j] = g[i][j] == 0 ? 0 : c;
        return 1 + paint(i + 1, j, c, g) + paint(i - 1, j, c, g) +
               paint(i, j + 1, c, g) + paint(i, j - 1, c, g);
    }
    int largestIsland(vector<vector<int>>& g, int res = 0) {
        for (int i = 0; i < g.size(); ++i)
            for (int j = 0; j < g[i].size(); ++j)
                if (g[i][j] == 0) {
                    res = max(res, paint(i, j, 2, g, true));
                    paint(i, j, 1, g, true);
                }
        return res == 0 ? g.size() * g[0].size() : res;
    }
};
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