<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:
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size(), ans = 0;
        vector<int> req = {1,2,3,4,5,6,7,8,9};
        for(int i = 0; i<=n-3; i++){
            for(int j = 0; j<=m-3; j++){

                    vector<int> v;
                    for(int k = i; k<i+3; k++){
                        for(int l = j; l<j+3; l++){
                            v.push_back(grid[k][l]);
                        }
                    }
                    auto sorted = v; sort(sorted.begin(), sorted.end());
                    if(req!=sorted)continue;
                    int d1 = v[0] + v[4] + v[8];
                    int d2 = v[2] + v[4] + v[6];
                    if(d1!=d2)continue;
                    bool ok = 1;
                    for(int i = 0; i<9; i+=3){
                        int cur = 0;
                        for(int j = i; j<i+3; j++){
                            cur += v[j];
                        }
                        if(d1!=cur)ok = 0;
                    }
                    for(int i = 0; i<3; i++){
                        int cur = 0;
                        for(int j = i; j<9; j+=3){
                            cur += v[j];
                        }
                        if(d1!=cur)ok = 0;
                    }
                    if(ok)ans++;
                // }
            }
        }
        return ans;
    }
};
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