# LeetCode — Maximum sum of an hourglass (Weekly contest)

You are given an `m x n`

integer matrix `grid`

.

We define an hourglass as a part of the matrix with the following form:

Return *the maximum sum of the elements of an hourglass*.

Note that an hourglass cannot be rotated and must be entirely contained within the matrix.

Example 1:

`Input: grid = [[6,2,1,3],[4,2,1,5],[9,2,8,7],[4,1,2,9]]`

Output: 30

Explanation: The cells shown above represent the hourglass with the maximum sum: 6 + 2 + 1 + 2 + 9 + 2 + 8 = 30.

Example 2:

`Input: grid = [[1,2,3],[4,5,6],[7,8,9]]`

Output: 35

Explanation: There is only one hourglass in the matrix, with the sum: 1 + 2 + 3 + 5 + 7 + 8 + 9 = 35.

Constraints:

`m == grid.length`

`n == grid[i].length`

`3 <= m, n <= 150`

`0 <= grid[i][j] <= 106`

Solution:

Time complexity: **O(N²)**

Space complexity: **O(N²)**