<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 distinct(int x, int y, vector<vector<int>>& grid) {
        map<int, int> ma;
        for(int i=x; i<x+3; i++) {
            for(int j=y; j<y+3; j++) {
                if(grid[i][j]<1 || grid[i][j] > 9) return false;
                if(!ma[grid[i][j]]) ma[grid[i][j]]++;
                else
                    return false;
            }
        }
        return true;
    }
    // [4,7,8]
    // [9,5,1]
    // [2,3,6]
    bool diagonals(int x, int y, vector<vector<int>>& grid) {
        int a = grid[x][y]   + grid[x+1][y+1] + grid[x+2][y+2];
        int b = grid[x+2][y] + grid[x+1][y+1] + grid[x][y+2];
        if(a == b)
        {
            for(int i=x; i<x+3; i++) {
                int val = 0;
                for(int j=y; j<y+3; j++) {
                    val += grid[i][j];
                }
                // cout << val << " ";
                if(val != a) return false;
            }
            for(int i=y; i<y+3; i++) {
                int val = 0;
                for(int j=x; j<x+3; j++) {
                    val += grid[j][i];
                }
                // cout << val << " ";
                if(val != a) return false;
            }
            return true;
        }
        return false;
    }
    int numMagicSquaresInside(vector<vector<int>>& grid) {
        int row = grid.size();
        int col = grid[0].size();
        int ans = 0;
        for(int i=0; i<=row-3; i++) {
            for(int j=0; j<=col-3; j++) {
                if(distinct(i, j, grid) && diagonals(i, j, grid)) {
                    cout << "\n" << i << "," << j << " " << distinct(i, j, grid)  << " " << diagonals(i, j, grid) << " check ";
                    ans++;
                }
            }
        }
        return ans;
    }
    // [4,1,2]
    // [7,9,3]
    // [8,6,5]
};
12300