<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 isMagicSquare(const vector<vector<int>>& grid, int row, int col) {
        int sum = 0;
        set<int>st;

        for(int i = 0; i < 3; i++){
            for(int j = 0; j < 3; j++){
                int x = row + i, y = col + j;
                if(grid[x][y] > 9 || grid[x][y] < 1){
                    return 0;
                }
                st.insert(grid[x][y]);
            }
            sum += grid[row][col + i];
        }

        if(st.size() != 9){
            return 0;
        }

        for (int i = 0; i < 3; ++i) {
            if (grid[row + i][col] + grid[row + i][col + 1] + grid[row + i][col + 2] != sum) {
                return 0;
            }
        }

        for (int j = 0; j < 3; ++j) {
            if (grid[row][col + j] + grid[row + 1][col + j] + grid[row + 2][col + j] != sum) {
                return 0;
            }
        }

        if (grid[row][col] + grid[row + 1][col + 1] + grid[row + 2][col + 2] != sum) {
            return 0;
        }
        if (grid[row + 2][col] + grid[row + 1][col + 1] + grid[row][col + 2] != sum) {
            return 0;
        }

        return 1;
    }
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int n = grid.size(), m = grid[0].size(), cnt = 0;
        for (int i = 0; i <= n - 3; ++i) {
            for (int j = 0; j <= m - 3; ++j) {
                cnt += (isMagicSquare(grid, i, j));
            }
        }

        return cnt;
    }
};
12000