# Expedition

King Chandragupta is waging wars to expand his kingdom. His army is powerful enough to win every battle.

On a single day, Chandragupta can simultaneously wage wars on his neighboring kingdoms (i.e., the kingdoms which are in the North, South, East, and West directions).

Given a map of `M x N` regions, where **1** indicates Chandragupta's kingdom, **0** indicates other kingdoms and **x** indicates barren lands (where no one lives). Find out how many days king Chandragupta require to occupy all the kingdoms on the given map.

Write a program that reads a matrix `M x N` which represents the map and prints the number of days king Chandragupta require to occupy all the kingdoms.

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#### Input

The first line of input contains two space-separated integers representing `M` and `N` respectively.
The next `M` lines of input contain space-separated characters. (Characters will be either **1**, **0**, or **x**)

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#### Output

The output should be a single line containing an integer that is the number of days king Chandragupta require to occupy all the kingdoms.

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#### Explanation

For example, if the given `M = 3`, `N = 3` and the next `M` lines are,

0 1 0
0 0 x
0 0 x

- On **Day 1**, the war is waged on the neighboring kingdoms (i.e., the kingdoms which are in the North, South, East, and West directions to Chandragupta's kingdom).

- In this case, war is waged on three kingdoms and by the end of the first-day king Chandragupta will have **4** kingdoms.

  1 1 1
  0 1 x
  0 0 x

- On **Day 2**, the war is waged on the neighboring kingdoms (i.e., the kingdoms which are in the North, South, East, and West directions to Chandragupta's kingdoms).

- In this case, war is waged on two kingdoms and by the end of the second-day king Chandragupta will have **6** kingdoms.

  1 1 1
  1 1 x
  0 1 x

- By the end of **Day 3**, the remaining one kingdom is occupied and king Chandragupta will have **7** kingdoms

  1 1 1
  1 1 x
  1 1 x

- So, king Chandragupta needs **3** days to occupy all the kingdoms.

The output should be **3**.

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`M = 4`, `N = 4`

1 0 0 0
0 1 0 0
0 0 x 0
0 0 0 x