### Monge array of m*n

An m-by-n matrix is said to be a Monge array if, for all $\scriptstyle i,\, j,\, k,\, \ell$ such that
$1\le i < k\le m\text{ and }1\le j < \ell\le n$
one obtains
$A[i,j] + A[k,\ell] \le A[i,\ell] + A[k,j].\,$
So whenever we pick two rows and two columns of a Monge array (a 2 × 2 sub-matrix) and consider the four elements at the intersection points, the sum of the upper-left and lower right elements (across the main diagonal) is less than or equal to the sum of the lower-left and upper-right elements (across the antidiagonal).
This matrix is a Monge array:
$\begin{bmatrix} 10 & 17 & 13 & 28 & 23 \\ 17 & 22 & 16 & 29 & 23 \\ 24 & 28 & 22 & 34 & 24 \\ 11 & 13 & 6 & 17 & 7 \\ 45 & 44 & 32 & 37 & 23 \\ 36 & 33 & 19 & 21 & 6 \\ 75 & 66 & 51 & 53 & 34 \end{bmatrix}$
For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:
$\begin{bmatrix} 17 & 23\\ 11 & 7 \end{bmatrix}$
17 + 7 = 24
23 + 11 = 34
The sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.

Suggest an algorithm such that given an array of (m*n) ,it can give output whether it is Monge or not.