With plenty of free time on their hands (or rather, hooves), the cows on Farmer
John's farm often pass the time by playing video games. One of their favorites
is based on a popular human video game called Puyo Puyo; the cow version is of
course called Mooyo Mooyo.

The game of Mooyo Mooyo is played on a tall narrow grid \(N\) cells tall
(\(1 \leq N \leq 100\)) and 10 cells wide. Here is an example with \(N = 6\):

0000000000
0000000300
0054000300
1054502230
2211122220
1111111223

Each cell is either empty (indicated by a 0), or a haybale in one of nine
different colors (indicated by characters 1..9). Gravity causes haybales to
fall downward, so there is never a 0 cell below a haybale.

Two cells belong to the same connected region if they are directly adjacent
either horizontally or vertically, and they have the same nonzero color. Any
time a connected region exists with at least \(K\) cells, its haybales all
disappear, turning into zeros. If multiple such connected regions exist at the
same time, they all disappear simultaneously. Afterwards, gravity might cause
haybales to fall downward to fill some of the resulting cells that became zeros.
In the resulting configuration, there may again be connected regions of size at
least \(K\) cells. If so, they also disappear (simultaneously, if there are
multiple such regions), then gravity pulls the remaining cells downward, and the
process repeats until no connected regions of size at least \(K\) exist.

Given the state of a Mooyo Mooyo board, please output a final picture of the
board after these operations have occurred.

Problem credits: Brian Dean

Problem credits: Brian Dean

The first line of input contains \(N\) and \(K\) (\(1 \leq K \leq 10N\)). The
remaining \(N\) lines specify the initial state of the board.

Please output \(N\) lines, describing a picture of the final board state.

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출처 올림피아드 > USACO > 2018-2019 > December > Silver