Problem I
Fishing Contest
At point $(x, y)$, fish first appear at second $t_{x, y}$ and disappear just before time $t_{x, y} + k$ seconds. Outside of this time, no fish can be caught at this position. It takes no time to catch all the fish at a point, and all points contain the same amount of fish. Furthermore, moving to the point immediately north, west, south or east from the point you are currently at takes exactly $1$ second (though you are not required to move).
Assume that you start at some position $(x_0, y_0)$ at second $1$, and can catch fish until (and including) second $l$. From how many points in the lake can you catch fish, if you travel optimally on the lake?
Input
The input consists of:
-
one line with the integers $r$, $c$, $k$ and $l$ ($1 \le r, c \le 100$, $1 \le k \le 5$, $1 \le l \le 10^5$), the dimensions of the lake, the number of seconds fish stays at a point, and the number of seconds you can catch fish.
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one line with the integers $x_0$ and $y_0$ ($0 \le x_0 < r$, $0 \le y_0 < c$), your original position.
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$r$ lines, the $x$’th of which contains $c$ integers $t_{x, 0}, \dots , t_{x, c - 1}$ (each between $1$ and $l$, inclusive), the times at which fish appears on points in the $x$’th row.
Output
Output the maximum number of points you could catch fish from.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 2 1 10 0 0 1 4 3 2 |
2 |
| Sample Input 2 | Sample Output 2 |
|---|---|
2 3 5 6 1 1 1 1 6 1 2 2 |
5 |
| Sample Input 3 | Sample Output 3 |
|---|---|
2 3 5 7 1 1 1 1 6 1 2 2 |
6 |
