JOI emblem

The Japan committee for the Olympiad in Informatics is preparing a new JOI flag. The flag is an $M$ by $N$ grid of squares, and each square shows J, O, or I.

The committee also fixed a JOI emblem: a $2$ by $2$ grid of squares with J, O, or I in each cell.

An emblem occurrence in the flag is a $2$ by $2$ region whose four letters match the emblem exactly without rotation or reflection. Overlapping regions are counted separately.

The committee has the old flag and one blank sticker that can cover a single square. The sticker can show any of J, O, or I. Exactly one of these actions is allowed:

Keep the old flag unchanged and do not use the sticker.

Write one letter on the sticker, place it on one square of the old flag, and use the resulting grid as the new flag.

Find the maximum possible number of emblem occurrences in the new flag.

The first line contains $M$ and $N$. The next $M$ lines are strings of length $N$ over J, O, and I describing the old flag. Row $i$, column $j$ is the $j$-th character on the $i$-th of these lines.

The following two lines are strings of length $2$ over J, O, and I describing the emblem.

Print one integer: the maximum number of emblem occurrences in the new flag.

$2 \le M \le 1000$

$2 \le N \le 1000$