<p>A <code>3 x 3</code> <strong>magic square</strong> is a <code>3 x 3</code> grid filled with distinct numbers <strong>from </strong>1<strong> to </strong>9 such that each row, column, and both diagonals all have the same sum.</p>

<p>Given a <code>row x col</code> <code>grid</code> of integers, how many <code>3 x 3</code> magic square subgrids are there?</p>

<p>Note: while a magic square can only contain numbers from 1 to 9, <code>grid</code> may contain numbers up to 15.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_main.jpg" style="width: 322px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[4,3,8,4],[9,5,1,9],[2,7,6,2]]
<strong>Output:</strong> 1
<strong>Explanation: </strong>
The following subgrid is a 3 x 3 magic square:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_valid.jpg" style="width: 242px; height: 242px;" />
while this one is not:
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/11/magic_invalid.jpg" style="width: 242px; height: 242px;" />
In total, there is only one magic square inside the given grid.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[8]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>row == grid.length</code></li>
	<li><code>col == grid[i].length</code></li>
	<li><code>1 &lt;= row, col &lt;= 10</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 15</code></li>
</ul>

class Solution {
public:

    bool check(int r, int c, vector<vector<int>>& v){
        set<int> st;
        set<int> s2;
        for(int i = 0;i<3;i++){
            for(int j = 0;j<3;j++){
                s2.insert(v[r+i][c+j]);
            }
        }
        if(s2.size()!=9 || *s2.rbegin()>9 || *s2.begin()==0) return false;
        int t1 = v[r][c]+v[r][c+1]+v[r][c+2];
        int t2 = v[r+1][c]+v[r+1][c+1]+v[r+1][c+2];
        int t3 = v[r+2][c]+v[r+2][c+1]+v[r+2][c+2];
        int t4 = v[r][c]+v[r+1][c]+v[r+2][c];
        int t5 = v[r][c+1]+v[r+1][c+1]+v[r+2][c+1];
        int t6 = v[r][c+2]+v[r+1][c+2]+v[r+2][c+2];
        int t7 = v[r][c]+v[r+1][c+1]+v[r+2][c+2];
        int t8 = v[r+2][c]+v[r+1][c+1]+v[r][c+2];
        // cout<<t1<<" "<<t2<<" "<<t3<<" "<<t4<<" "<<t5<<" "<<t6<<" "<<t7<<" "<<t8<<endl;
        st.insert(t1);
        st.insert(t2);
        st.insert(t3);
        st.insert(t4);
        st.insert(t5);
        st.insert(t6);
        st.insert(t7);
        st.insert(t8);
        if(st.size()>1) return false;
        return true;
    }

    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        int ans = 0;
        for(int i = 0;i<n-2;i++){
            for(int j = 0;j<m-2;j++){
                if(check(i, j, grid)==true) ans++;
            }
        }
        return ans;
    }
};
13000