<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) {
        if(grid.size() < 3 || grid[0].size() < 3)
            return 0;
        const int row = grid.size();
        const int col = grid[0].size();
        int i = 0, j = 0;
        int count = 0;
        while( i + 3 <= row)
        {
            j = 0;
            while(j + 3 <= col)
            {
                int temp = evaluate_block(grid, i, j);
                count += temp;
                ++j;
            }
            ++i;
        }
        return count;
    }
    int evaluate_block(vector<vector<int>>& grid, int i,int j)
    {
        const int sum1 = 15;
        int sum2 = 0;

        for(int k=i,l=j; k < i+3 && l < j+3; ++k,++l )
            sum2 += grid[k][l];

        if(sum1 != sum2)
            return 0;

        sum2 = 0;
        for(int k=i,l=j+2; k < i+3 && l >=j ; ++k,--l )
            sum2 += grid[k][l];

        if(sum1 != sum2)
            return 0;

        int num_check = 0;
        for(int k = i; k < i+3; k++)
        {
            sum2 = 0;
            for(int l = j ; l < j+3; l++)
            {
                if(grid[k][l] <= 9 && grid[k][l] >= 1 && (num_check & (1<<grid[k][l])) == 0)
                {
                    num_check |= 1<<grid[k][l];
                    sum2 += grid[k][l];
                }
                else
                    return 0;
            }
            if(sum1 != sum2 )
                return 0;
        }
        for(int k = j; k < j+3; k++)
        {
            sum2 = 0;
            for(int l = i ; l < i+3; l++)
            {
                sum2 += grid[l][k];
            }
            if(sum1 != sum2)
                return 0;
        }
        return 1;
    }
};
10200