<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:
    class DSU{
    public:
    vector<int> parent;
    vector<int> rank;
    public:
    DSU(int N){
        parent.resize(N, -1);
        rank.resize(N, 0);
    }
    int find(int i){
        if(parent[i]==-1) return i;
        return parent[i]=find(parent[i]);
    }

    void Union(int i, int j){
        int p1= find(i);
        int p2= find(j);
        if(p1!=p2){

        if(rank[p1]<rank[p2]){
            parent[p1]=p2;

        }else if(rank[p1]>rank[p2]){
            parent[p2]=p1;
        }else{
            rank[p1]++;
            parent[p2]=p1;
        }

        }
    }
};
    bool check(int nx, int ny, int n){
        return nx>=0 && ny>=0 && max(nx, ny)<n;
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        DSU* d=new DSU(n*n);
        vector<int> siz(n*n, 0);
        unordered_map<int, int> mpp;
        int dx[4]={1, 0, -1, 0};
        int dy[4]={0, -1, 0, 1};
        for(int i=0; i<grid.size(); i++){
          for(int j=0; j<grid.size(); j++){
            if(grid[i][j]==0) continue;
            for(auto k:{0,1,2,3}){
                int nx=i+dx[k];
                int ny=j+dy[k];
                if(check(nx, ny, n) && grid[nx][ny]){
                    d->Union(nx*n+ny, i*n+j);
                }
            }

          }
        }
        for(int i=0; i<n*n; i++){
            int p=d->find(i);
            mpp[p]++;
            if(mpp[p]==n*n) return n*n;
        }
        for(auto p: mpp){
            // cout<< p.first<<" "<<p.second<<endl;
        }
        
        int ans=0;
        for(int i=0; i<n; i++){

            for(int j=0; j<n; j++){
               
                if(grid[i][j]==0){
                     unordered_set<int> st;
                     for(auto k:{0,1,2,3}){
                        int nx=i+dx[k];
                        int ny=j+dy[k];
                       
                         if(check(nx, ny, n) && grid[nx][ny]){
                            st.insert(d->find(nx*n+ny));
                         }
                         
                     }
                    int res=0;
                    for(auto s: st){
                    res+= mpp[s];
                    }
                    // cout<<st.size()<<endl;
                    ans=max(res+1, ans);

                }
            }
        }

        return ans;
        
    }
};
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