<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 DisU{
    public:
    vector<int> rank;
    vector<int> parent;
    vector<int> size;

    DisU(int n){

        for(int i=0;i<n;i++){
            rank.push_back(1);
            size.push_back(1);
            parent.push_back(i);
        }

    }

    int find(int i){
        if(parent[i]==i){return i;}
        return parent[i]=find(parent[i]);
    }

    void union_rank(int i,int j){
        int par_i=find(i);
        int par_j=find(j);
        if(par_i==par_j){return;}
        if(rank[par_i]>rank[par_j]){
            parent[par_j]=par_i;
            return;
        }else if(rank[par_j]>rank[par_i]){
            parent[par_i]=par_j;
            return;           
        }else{
            parent[par_j]=par_i;
            rank[par_i]++;
            return;            
        }
    }

    void union_size(int i, int j){
        int par_i=find(i);
        int par_j=find(j);
        if(par_i==par_j){return;}
        if(size[par_i]>size[par_j]){
            parent[par_j]=par_i;
            size[par_i]+=size[par_j];
            return;
                 
        }else{
            parent[par_i]=par_j;
            size[par_j]+=size[par_i];
            return;            
        }        
    }
};

class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        DisU d(n*n);

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){continue;}
                vector<int> d1={-1,0,1,0};
                vector<int> d2={0,-1,0,1};

                for(int k=0;k<4;k++){
                    if(i+d1[k]>=0 && j+d2[k]>=0 && i+d1[k]<n && j+d2[k]<n){
                        if(grid[i+d1[k]][j+d2[k]]==1){
                            d.union_size(n*i+j,n*(i+d1[k])+(j+d2[k]));
                        }
                    }
                }
            }
        }

        int ans=0; 

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1){continue;}
                int temp=1;
                
                vector<int> d1={-1,0,1,0};
                vector<int> d2={0,-1,0,1};
                set<int> par;
                for(int k=0;k<4;k++){
                    int i1=i+d1[k];
                    int j1=j+d2[k];

                    if(i1>=0 && j1>=0 && i1<n && j1<n){
                        
                        if(grid[i1][j1]==1){
                            par.insert(d.find(n*i1+j1));
                            
                        }


                    }
                }
                for(auto it:par){
                    cout<<it<<endl;
                    temp+=d.size[it];
                }
                cout<<endl;
                ans=max(ans,temp);
            }
        }

        for(int i=0;i<n*n;i++){
            ans=max(ans,d.size[d.find(i)]);
        }

        return ans;
    }
};
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