**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
```