Objective
Today, we're 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.

Input Format

There are  lines of input, where each line contains  space-separated integers describing 2D Array ; every value in  will be in the inclusive range of  to .

Constraints

Output Format

Print the largest (maximum) hourglass sum found 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

Solution:
arr = Array.new(6)
max = -10000000

6.times do |i|
	arr[i] = gets.rstrip.split(' ').map(&:to_i)
end

6.times  do |i|
	6.times  do |j|
		if (j + 2) < 6 and (i + 2) < 6
			sum = (arr[i][j] + arr[i][j + 1] + arr[i][j + 2]) +
			(arr[i + 1][j + 1]) + (arr[i + 2][j] + arr[i + 2][j + 1] + arr[i + 2][j + 2])

			if sum  > max
				max = sum
			end
		end
	end
end

puts max