Practice Image processing and Arrays with the exercise "Fractal Image Recognition"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

These fractals are more similar to those of Bill Williams, which are used in price chart analysis, rather than fractals of Benoit Mandelbrot.

Place fractals around extremums of the image.
An extremum is a pixel P that is filled ("1") and has at least 5 consecutive empty ("0") spaces around it.
East fractal is represented by "2"
North = "3"
North-east = "4"
North-west = "5"
South = "6"
South-east = "7"
South-west = "8"
West = "9"
To place a fractal to the north ("3") of pixel P, pixels "9", "5", "3", "4", "2" around pixel P must be empty.
To place a fractal to the northeast ("4") of pixel P, pixels "5", "3", "4", "2", "7" around pixel P must be empty.

Input

An integer imageSize for the width and height of the square image.
Next imageSize lines: strings of 1 and 0 pixels, space separated.

Output

imageSize lines: strings containing pixels and fractals, space separated.

Constraints

imageSize = 10
Each pixel color is "0" or "1"

Example

Input

10
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 1 0 0 0
0 0 0 0 1 0 1 0 0 0
0 0 0 1 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0

Output

0 0 0 0 0 0 3 4 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 1 0 0 0
0 0 0 0 1 0 1 0 0 0
0 0 9 1 0 0 1 0 0 0
0 0 8 6 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 8 6 7 0 0

Solve it

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