Practice Image processing and Lists with the exercise "Simple Blur"

Learning Opportunities

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

Statement

Goal

Take a data representation of an image and blur it by averaging each pixel's color with its neighbors above, below, and to the left and right of it.

Rules:

The average value should be the arithmetic mean, that is, all the values you are combining, divided by the number of values.

If the outcome of an average operation is not an integer, round it down.

Each pixel should be blurred using five pixels: itself, and its four neighbors (above, below, left, and right). The exception is edge and corner pixels, which will use themselves and their three/two neighbors respectively. In the diagram below, X represents a target pixel, and the N's represent the other pixels that it should be blended with. The O's represent pixels that should not be included.

Standard example:

ONO
NXN
ONO

Corner example:

XN
NO

Edge example:

NO
XN
NO

Input

A 2-dimensional grid of pixels, with each pixel defined by its red, green, and blue values.

The first line of input gives the size of the grid, in rows and columns respectively.
Each subsequent line contains a pixel's RGB values in a space-separated list. The pixels are given in left-to-right, top-to-bottom order.

Output

Output the transformed image, one pixel per line. Each pixel will be expressed as a space-separated list of the pixel's RGB values.

Constraints

Each color value will be an integer in the range 0 ≤ r,g,b ≤ 255.

Each dimension of the image grid will be an integer in the range 1 ≤ rows,cols ≤ 15.

Example

Input

Output

Solve it

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