<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 m = grid.size(), n = grid[0].size();
        if(m < 3 || n < 3) return 0;
        
        int ans = 0;

        int prevrow = 0;
        while(prevrow < m-2){

            int prevcol = 0;
            while(prevcol < n-2){
                vector<bool> present(10);
                bool flag = true;

                for(int i = prevrow; i <= prevrow+2; i++){
                    for(int j = prevcol; j <= prevcol+2; j++){
                        if(present[grid[i][j]] || grid[i][j] < 1 || grid[i][j] > 9) {
                            flag = false;
                            break;
                        }
                        present[grid[i][j]] = true;
                    }
                    if(flag == false) break;
                }

                int row1 = grid[prevrow+0][prevcol+0] + grid[prevrow+0][prevcol+1] + grid[prevrow+0][prevcol+2];
                int row2 = grid[prevrow+1][prevcol+0] + grid[prevrow+1][prevcol+1] + grid[prevrow+1][prevcol+2];
                int row3 = grid[prevrow+2][prevcol+0] + grid[prevrow+2][prevcol+1] + grid[prevrow+2][prevcol+2];

                int col1 = grid[prevrow+0][prevcol+0] + grid[prevrow+1][prevcol+0] + grid[prevrow+2][prevcol+0];
                int col2 = grid[prevrow+0][prevcol+1] + grid[prevrow+1][prevcol+1] + grid[prevrow+2][prevcol+1];
                int col3 = grid[prevrow+0][prevcol+2] + grid[prevrow+1][prevcol+2] + grid[prevrow+2][prevcol+2];

                int di1 = grid[prevrow+0][prevcol+0] + grid[prevrow+1][prevcol+1] + grid[prevrow+2][prevcol+2];
                int di2 = grid[prevrow+0][prevcol+2] + grid[prevrow+1][prevcol+1] + grid[prevrow+2][prevcol+0];

                if(flag && row1 != row2 || row1 != row3 || row2 != row3) flag = false;
                if(flag && (col1 != col2 || col1 != col3 || col2 != col3)) flag = false;
                if(flag && (row1 != col1)) flag = false;
                if(flag && (di1 != di2)) flag = false;
                if(flag && (row1 != di1)) flag = false;

                if(flag) ans++;

                prevcol++;
            }

            prevrow++;
        }

        return ans;
    }
};
11000