<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 output{0};

    for (int i = 0; i + 2 < grid.size(); i++) {
      for (int j = 0; j + 2 < grid[i].size(); j++) {
        if (0 < grid[i][j] && grid[i][j] < 9 && !(grid[i][j] % 2)) {
          bool isMagicSquare{true};
          int index{grid[i][j] / 2 - 1};

          for (int k = 0; k < 3 && isMagicSquare; k++) {
            for (int l = 0; l < 3 && isMagicSquare; l++)
              isMagicSquare = grid[i + k][j + l] == magicSquares[index][k][l];
          }

          if (!isMagicSquare) {
            isMagicSquare = true;

            for (int k = 0; k < 3 && isMagicSquare; k++) {
              for (int l = 0; l < 3 && isMagicSquare; l++) 
                isMagicSquare = grid[i + k][j + l] == magicSquares[index][l][k];
            }
          }

          if (isMagicSquare)
            output++;
        }
      }
    }

    return output;
  }

 private:
  static constexpr int magicSquares[4][3][3]{
    {
      {2, 9, 4},
      {7, 5, 3},
      {6, 1, 8}
    },
    {
      {4, 3, 8},
      {9, 5, 1},
      {2, 7, 6}
    },
    {
      {6, 7, 2},
      {1, 5, 9},
      {8, 3, 4}
    },
    {
      {8, 1, 6},
      {3, 5, 7},
      {4, 9, 2}
    }
  };
};

/*
8 7 4 1 7 2
5 8 4 2 6 9
4 2 1 4 2 8
6 5 9 2 7 4
8 2 3 9 5 3
3 9 5 6 8 1
*/
10400