Educational Codeforces Round 5 |
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Finished |

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C. The Labyrinth

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a rectangular field of *n* × *m* cells. Each cell is either empty or impassable (contains an obstacle). Empty cells are marked with '.', impassable cells are marked with '*'. Let's call two empty cells adjacent if they share a side.

Let's call a connected component any non-extendible set of cells such that any two of them are connected by the path of adjacent cells. It is a typical well-known definition of a connected component.

For each impassable cell (*x*, *y*) imagine that it is an empty cell (all other cells remain unchanged) and find the size (the number of cells) of the connected component which contains (*x*, *y*). You should do it for each impassable cell independently.

The answer should be printed as a matrix with *n* rows and *m* columns. The *j*-th symbol of the *i*-th row should be "." if the cell is empty at the start. Otherwise the *j*-th symbol of the *i*-th row should contain the only digit —- the answer modulo 10. The matrix should be printed without any spaces.

To make your output faster it is recommended to build the output as an array of *n* strings having length *m* and print it as a sequence of lines. It will be much faster than writing character-by-character.

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.

Input

The first line contains two integers *n*, *m* (1 ≤ *n*, *m* ≤ 1000) — the number of rows and columns in the field.

Each of the next *n* lines contains *m* symbols: "." for empty cells, "*" for impassable cells.

Output

Print the answer as a matrix as described above. See the examples to precise the format of the output.

Examples

Input

3 3

*.*

.*.

*.*

Output

3.3

.5.

3.3

Input

4 5

**..*

..***

.*.*.

*.*.*

Output

46..3

..732

.6.4.

5.4.3

Note

In first example, if we imagine that the central cell is empty then it will be included to component of size 5 (cross). If any of the corner cell will be empty then it will be included to component of size 3 (corner).

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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