Given a 2D array, , an hourglass is a subset of values with indices falling in the following pattern:

There are hourglasses in a array. The is the sum of the values in an hourglass. Calculate the hourglass sum for every hourglass in , then print the hourglass sum.

Example

-9 -9 -9  1 1 1 
 0 -9  0  4 3 2
-9 -9 -9  1 2 3
 0  0  8  6 6 0
 0  0  0 -2 0 0
 0  0  1  2 4 0

The hourglass sums are:

-63, -34, -9, 12, 
-10,   0, 28, 23, 
-27, -11, -2, 10, 
  9,  17, 25, 18

The highest hourglass sum is from the hourglass beginning at row , column :

0 4 3
  1
8 6 6

Note: If you have already solved the Java domain's Java 2D Array challenge, you may wish to skip this challenge.

Function Description

Complete the function with the following parameter(s):

• : a 2-D array of integers

Returns

• : the maximum hourglass sum