<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>

typedef long long ll;
const int MOD= 1000000007;
int dx[4]={-1,1,0,0};
int dy[4]= {0,0,-1,1};
class Solution {

    void bfs(int i, int j ,vector<vector<int>> &grid, vector<vector<int>> &vis, int n , int type, vector<int> &cnt)
    {
        queue<pair<int,int>> q;
        q.push({i,j});
        vis[i][j]=type;
        int ans=0;
        while(!q.empty())
        {
            pair<int,int> p= q.front();
            ans++;
            q.pop();
            int x= p.first;
            int y= p.second;
            vis[x][y]=type;
            for(int i=0;i<4;i++)
            {
                int nx= x+dx[i];
                int ny= y+dy[i];

                if(nx>=0 && nx<n && ny>=0 && ny<n && grid[nx][ny]==1 && vis[nx][ny]==0)
                {
                    q.push({nx,ny});
                    vis[nx][ny]=type;
                }
            }
        }
        cnt[type]=ans;
    }
    
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n= grid.size();

        vector<vector<int>> vis(n+1, vector<int> (n+1,0));
        vector<int> cnt(n*n+1,0);
        int type=1;
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(vis[i][j]==0 && grid[i][j]==1)
                {
                    bfs(i,j,grid,vis,n,type,cnt);
                    type++;
                }
            }
        }
        int maxno= INT_MIN;
        for(int i=0;i<=(n*n);i++)
        {
            maxno= max(maxno, cnt[i]);
        }
        // cout<<maxno<<" ";

        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(grid[i][j]==0)
                {
                    int l1=0,l2=0,l3=0,l4=0;
                    set<int> s;
                    if(j-1>=0 && grid[i][j-1]==1)
                    {
                        s.insert(vis[i][j-1]);
                    }
                    if(j+1<n && grid[i][j+1]==1)
                    {
                        s.insert(vis[i][j+1]);
                    }
                    if(i+1<n && grid[i+1][j]==1)
                    {
                        s.insert(vis[i+1][j]);
                    }
                    if(i-1>=0 && grid[i-1][j]==1)
                    {
                        s.insert(vis[i-1][j]);
                    }
                    int sum=0;
                    for(auto it= s.begin();it!=s.end();it++)
                    {
                        sum+=cnt[*it];
                    }
                    cout<<sum<<" ";
                    maxno= max(maxno, sum+1);
                }
            }
        }
        return maxno;
        
    }
};
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