<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(vector<vector<int>> &g, vector<vector<int>> &cg, int cr, int cc, int color) {
        if(cr == -1 || cc >= g[0].size() || cr == -1 || cr >= g.size() || !g[cr][cc] || cg[cr][cc]) {
            return 0;
        }
        cg[cr][cc] = color;
        return (1 +
            paint(g, cg, cr+1, cc, color) +
            paint(g, cg, cr-1, cc, color) +
            paint(g, cg, cr, cc+1, color) +
            paint(g, cg, cr, cc-1, color)
        );
    }
    int largestIsland(vector<vector<int>>& grid) {
        vector<vector<int>> cg(grid.size(), vector<int>(grid[0].size()));
        vector<int> paintToSize(1);
        int paintCode = 1;
        int mxSize = 0;
        for(int i=0; i<grid.size(); i++) {
            for(int j=0; j<grid[i].size(); j++) {
                if(!cg[i][j]) {
                    int areaSize = paint(grid, cg, i, j, paintCode);
                    paintToSize.push_back(areaSize);
                    mxSize = max(mxSize, areaSize);
                    paintCode++;
                }
            }
        }
        int mx = 0;
        for(int i=0; i<grid.size(); i++) {
            for(int j=0; j<grid[i].size(); j++) {
                if(cg[i][j]) {
                    continue;
                }
                set<int> colors;
                colors.insert(cg[i][j]);
                if(i+1<grid.size() && cg[i][j] != cg[i+1][j]) {
                    colors.insert(cg[i+1][j]);
                }
                if(j+1<grid[0].size() && cg[i][j] != cg[i][j+1]) {
                    colors.insert(cg[i][j+1]);
                }
                if(j-1>=0 && cg[i][j] != cg[i][j-1]) {
                    colors.insert(cg[i][j-1]);
                }
                if(i-1>=0 && cg[i][j] != cg[i-1][j]) {
                    colors.insert(cg[i-1][j]);
                }

                int tmx = 0;
                for(auto it=colors.begin(); it != colors.end(); it++) {
                    tmx += paintToSize[*it];
                }
                mx = max(tmx+1, mx);
            }
        }
        return max(mx, mxSize);
    }
};
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