Your platoon of wandering lizards has entered a strange room in the labyrinth you are exploring. As you are looking around for hidden treasures, one of the rookies steps on an innocent-looking stone and the room's floor suddenly disappears! Each lizard in your platoon is left standing on a fragile-looking pillar, and a fire begins to rage below...

Leave no lizard behind! Get as many lizards as possible out of the room, and report the number of casualties.

The pillars in the room are aligned as a grid, with each pillar one
unit away from the pillars to its east, west, north and south. Pillars
at the edge of the grid are one unit away from the edge of the room
(safety). Not all pillars necessarily have a lizard. A lizard is able
to leap onto any unoccupied pillar that is within *d* units of
his current one. A lizard standing on a pillar within leaping distance
of the edge of the room may always leap to safety... but there's
a catch: each pillar becomes weakened after each jump, and will soon
collapse and no longer be usable by other lizards. Leaping onto
a pillar does not cause it to weaken or collapse; only leaping off of
it causes it to weaken and eventually collapse. Only one lizard may be
on a pillar at any given time.

**Input:** The input file will begin with a line containing
a single integer representing the number of test cases, which is at
most 25. Each test case will begin with a line containing a single
positive integer *n* representing the number of rows in the map,
followed by a single non-negative integer *d* representing the
maximum leaping distance for the lizards. Two maps will follow, each
as a map of characters with one row per line. The first map will
contain a digit (0-3) in each position representing the number of
jumps the pillar in that position will sustain before collapsing (0
means there is no pillar there). The second map will follow, with an
`'L'` for every position where a lizard is on the pillar and
a `'.'` for every empty pillar. There will never be a lizard on
a position where there is no pillar.

Each input map is guaranteed to be a rectangle of size n x m, where 1 ≤ n ≤ 20 and 1 ≤ m ≤ 20. The leaping distance is always 1 ≤ d ≤ 3.

**Output:** For each input case, print a single line containing
the number of lizards that could not escape. The format should follow
the samples provided below.

**Warning:** Brute force methods examining every path will
likely exceed the allotted time limit.

Example input: |
Example output: |

4 3 1 1111 1111 1111 LLLL LLLL LLLL 3 2 00000 01110 00000 ..... .LLL. ..... 3 1 00000 01110 00000 ..... .LLL. ..... 5 2 00000000 02000000 00321100 02000000 00000000 ........ ........ ..LLLL.. ........ ........ |
Case #1: 2
lizards were left behind. Case #2: no lizard was left behind. Case #3: 3 lizards were left behind. Case #4: 1 lizard was left behind. |

*Last modified on October 30, 2005 at 1:15 PM.*