# Binomial Filter

Time Limit: 1 Second    Memory Limit: 32768 KB

## Sunny Cup 2003 - Preliminary Round

April 20th, 12:00 - 17:00

### Problem B: Binomial Filter

A common approach to reduce video image noise (so as to increase the image quality) is casting binomial filter on the bitmap image. The binomial filter works as this:

Assume that the image is represented as an N * N matrix of integers between 0 and 255 (we only concern about the Y component of YUV image, the brightness). We define the original image to be I, and the filtered image to be I'. So a pixel on the original image is represented as I[x,y], a pixel on the filtered image is I'[x,y].

We define the filter matrix B as:

to do the binomial filter, we calculate the filtered image pixel as:

If the pixel is on the image border(top,bottom,left,right):

else:

The division is integer division, we ignore the fraction part.

Now your job is to implement the binomial filter algorithm.

## Input

There are multiple tests. Each test begins with an integer N (1 <= N <= 500), the image size. The following are N * N integers, each within [0,255], the pixels of the original image.

The input terminates with N = 0. Do not process this case.

## Output

For each test case, first print one line with "Case c:", c is the case number, starting from 1.

N lines follow, each containing N integers, seperated by one space (no space after the last integer!), which are the pixels of the filtered image.

```3
1 2 3
4 5 6
7 8 9
4
1 1 1 1
1 100 100 1
1 100 100 1
1 1 1 1
0
```

## Sample Output

```Case 1:
1 2 3
4 5 6
7 8 9
Case 2:
1 1 1 1
1 56 56 1
1 56 56 1
1 1 1 1```
Submit

Source: Zhejiang University Local Contest 2003, Preliminary