<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 ans = 0;
        int m = grid.size();
        int n = grid[0].size();
        for (int row = 0; row + 2 < m; row++) {
            for (int col = 0; col + 2 < n; col++) {
                if (isMagicSquare(grid, row, col)) {
                    ans++;
                }
            }
        }
        return ans;
    }

private:
    bool isMagicSquare(vector<vector<int>>& grid, int row, int col) {
        // The sequences are each repeated twice to account for
        // the different possible starting points of the sequence
        // in the magic square
        string sequence = "2943816729438167";
        string sequenceReversed = "7618349276183492";

        string border = "";
        // Flattened indices for bordering elements of 3x3 grid
        vector<int> borderIndices = {0, 1, 2, 5, 8, 7, 6, 3};
        for (int i : borderIndices) {
            int num = grid[row + i / 3][col + (i % 3)];
            border += to_string(num);
        }

        // Make sure the sequence starts at one of the corners
        return (grid[row][col] % 2 == 0 && grid[row + 1][col + 1] == 5 &&
                (sequence.find(border) != string::npos ||
                 sequenceReversed.find(border) != string::npos));
    }
};
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