Cossack Vus and the Matrix

Kozak Vus has a matrix $a$ of size $n\times m$, consisting only of zeros and ones.

The Manhattan distance between two elements in the matrix is defined as follows: if one element is at row $i$ and column $j$, and another is at row $p$ and column $k$, then their Manhattan distance is $\mid i-p\mid +\mid j-k\mid$ (the sum of the absolute differences of their row and column indices).

The "beauty" of an element in the matrix is the Manhattan distance from that element to the nearest element that is a one. Note that the "beauty" of any element that is a one is zero. Additionally, it is guaranteed that the matrix contains at least one one.

Your task is to determine the "beauty" of the least "beautiful" element in the matrix.

Input

The first line contains two integers $n$ and $m$ $(1\le n,m\le 20)$, representing the number of rows and columns in the matrix.

Each of the next $n$ lines contains $m$ digits $a_{i,1},a_{i,2},\dots ,a_{i,m}$ $(0\le a_{i,j}\le 1)$, representing the elements of the matrix.

It is guaranteed that there is at least one one in the matrix.

Output

Output a single number — the maximum "beauty" of any element in the matrix.

Examples

Note

Consider the matrix from the first example, where the "beauty" of each element is:

Here, the elements at (second row, first column) and (second row, third column) have the highest "beauty" of 2.

For the second example, the "beauty" matrix is:

Scoring

Solutions that correctly handle the case where $n=1$ will score at least 30 points.

Solutions that correctly handle the case where $n=2$ will score at least 30 points.