Maximum Hourglass Sum

Given an MxN matrix of integers, an hourglass shape is defined as follows:

[ a\quad b\quad c ]
[\quad d]
[ e\quad f\quad g ]

Your task is to compute the maximum hourglass sum in the matrix. An hourglass sum is defined as the sum of the 7 values in an hourglass shape. It is guaranteed that the matrix dimensions are such that at least one hourglass exists.

inputFormat

The first line contains two integers M and N, separated by a space, representing the number of rows and columns of the matrix respectively. The next M lines each contain N space-separated integers representing the matrix elements.

outputFormat

Output a single integer – the maximum hourglass sum found in the matrix.## sample

3 3
1 1 1
0 1 0
1 1 1

7