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

a b c d e f g 

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