Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is $16$ ($=8+7+1$).

$-2$	$5$	$3$	$2$
$9$	$-6$	$5$	$1$
$3$	$2$	$7$	$3$
$-1$	$8$	$-4$	$8$

Now, let us repeat the search, but on a much larger scale:

First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator":

For $1\le k\le 55$, $s_k=[100003-200003k+300007k^3](\mathrm{mod}1000000)-500000$.
For $56\le k\le 4000000$, $s_k=[s_{k-24}+s_{k-55}+1000000](\mathrm{mod}1000000)-500000$.

Thus, $s_{10}=-393027$ and $s_{100}=86613$.

The terms of $s$ are then arranged in a $2000\times 2000$ table, using the first $2000$ numbers to fill the first row (sequentially), the next $2000$ numbers to fill the second row, and so on.

Finally, find the greatest sum of (any number of) adjacent entries in any direction (horizontal, vertical, diagonal or anti-diagonal).