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  1. Prepare
  2. Tutorials
  3. 30 Days of Code
  4. Day 11: 2D Arrays

Day 11: 2D Arrays

Objective
Today, we are building on our knowledge of arrays by adding another dimension. Check out the Tutorial tab for learning materials and an instructional video.

Context
Given a 2D Array, : 

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

We define an hourglass in to be a subset of values with indices falling in this pattern in 's graphical representation:

a b c
  d
e f g

There are hourglasses in , and an hourglass sum is the sum of an hourglass' values.

Task
Calculate the hourglass sum for every hourglass in , then print the maximum hourglass sum.

Example

In the array shown above, the maximum hourglass sum is for the hourglass in the top left corner.

Input Format

There are lines of input, where each line contains space-separated integers that describe the 2D Array .

Constraints

Output Format

Print the maximum hourglass sum in .

Sample Input

1 1 1 0 0 0
0 1 0 0 0 0
1 1 1 0 0 0
0 0 2 4 4 0
0 0 0 2 0 0
0 0 1 2 4 0

Sample Output

19

Explanation

contains the following hourglasses:

1 1 1   1 1 0   1 0 0   0 0 0
  1       0       0       0
1 1 1   1 1 0   1 0 0   0 0 0

0 1 0   1 0 0   0 0 0   0 0 0
  1       1       0       0
0 0 2   0 2 4   2 4 4   4 4 0

1 1 1   1 1 0   1 0 0   0 0 0
  0       2       4       4
0 0 0   0 0 2   0 2 0   2 0 0

0 0 2   0 2 4   2 4 4   4 4 0
  0       0       2       0
0 0 1   0 1 2   1 2 4   2 4 0

The hourglass with the maximum sum () is:

2 4 4
  2
1 2 4