Dr. Alice, a myrmecologist, was studying the traveling pattern of ants in ant colonies. She represented an ant colony in the form of a rectangular array of size $N*M$. Each cell of this rectangular array is either 0 or 1.  0 represents that an ant is present in the cell and 1 represents that sugar is present in the cell. A cell in $i^{th}$ row and $j$^th column is represented by $(i,j)$. In the study, Dr. Alice made an interesting observation: each ant tries to go the sugar cell that is nearest to it. She wants to determine the nearest distance to a sugar cell for each cell.

Here the distance between two cells $a(a_i,a_j)$ and $b(b_i,b_j)$ is defined as:

$Dist(a,b) = |a_i-b_i| + |a_j-b_j|$

It is given that at least one cell contains sugar.

Input

The first line contains 2 space-separated Integers $N$ and $M$ denoting the number of rows and columns respectively.

Then $N$ lines follows. Each contains $M$ space-separated values (either 1 or 0).

Output

The output should be a 2-D matrix of $N$ rows and $M$ columns.In the $i^{th}$ line , $1 \leq i \leq N$, there should be written $M$ integers $d(i,j)$ separated by single spaces, where $d(i,j)$ is the distance from the cell $(i,j)$ to the nearest sugar cell.

Constraints

• $1 \leq N \leq 150$
• $1 \leq M \leq 150$
• Each entry of the input matrix is either 1 or 0.