Gahee and Sajik Stadium

Gahee wants to place $N$ idols on the stage of Sajik Stadium, the home ground of the Lotte Giants, which she supports. The stage has $R$ rows and $C$ columns. Each idol has a number from 1 to $N$. Three of the idols are called the Three Musketeers. When the three are adjacent to each other horizontally, vertically, or diagonally, they produce a special effect. Gahee wants to place the $N$ idols on the stage to maximize their total charm. Tell her how to do it.

The first line has $R$, $C$, and $N$ separated by spaces. The second line has the numbers of the Three Musketeers, $a_1$, $a_2$, and $a_3$, separated by spaces. The third line has the extra charm gained when idol $a_1$ and idol $a_2$ are adjacent, when idol $a_2$ and idol $a_3$ are adjacent, and when idol $a_1$ and idol $a_3$ are adjacent, separated by spaces. The next $R$ lines each have $C$ numbers separated by spaces. The $c$-th number on the $r$-th line is the charm gained when an idol stands at row $r$, column $c$.

Print the maximum total charm that Gahee can obtain when she places all $N$ idols on the stage.

$1 \le R \le 200$. $1 \le C \le 200$. $3 \le R \times C \le 200$. $3 \le N \le R \times C$. Each charm value at a point on the stage is between 1 and $10^4$. $a_1$, $a_2$, and $a_3$ are all different integers between 1 and $N$. The extra charm for each adjacent pair among the Three Musketeers is an integer between 1 and $10^4$.