Zombie Virus

There is a village in the shape of an $N$ x $M$ grid. One day a zombie virus breaks out and spreads quickly through the village. An investigation of the virus revealed three types, numbered $1$, $2$, and $3$.

The viruses behave as follows.

• Viruses $1$ and $2$ have a low mortality rate but are highly contagious. They spread simultaneously to the villages adjacent up, down, left, and right, and take 1 hour to fully infect a village.
• A virus can spread to another village only after the current village is fully infected, and it does not invade a village that another virus has fully infected.
• If a virus of a different type arrives at a village before one virus has fully infected it, virus $3$ is created.
• Virus $3$ has a high mortality rate and, being weakly contagious, no longer spreads from the village it infects.
• A village holding a cure cannot be infected.

Villages infected with virus $1$ and virus $2$ have appeared. Given that the viruses spread as far as they can, find how many villages are infected with virus $1$, virus $2$, and virus $3$, respectively.

The first line gives $N$ ($2≤N≤1\,000$) and $M$ ($2≤M≤1\,000$).

Starting from the second line, $N$ lines each give the state of $M$ villages. A village state is one of the following.

• $-1$: a village holding a cure
• $0$: a village not yet infected
• $1$: a village infected with virus $1$
• $2$: a village infected with virus $2$

Exactly one village infected with virus $1$ and exactly one village infected with virus $2$ are given.

Print the numbers of villages infected with virus $1$, virus $2$, and virus $3$, separated by spaces, on one line.