Josip is a strange painter. He wants to paint a picture consisting of $N \times N$ pixels, where $N$ is a power of two ($1, 2, 4, 8, 16$ etc.). Each pixel will be either black or white. Josip already has an idea of how each pixel will be coloured.

This would be no problem if Josip’s painting process wasn’t strange. He uses the following recursive process:
 - If the picture is a single pixel, he colours it the way he intended.
 - Otherwise, split the square into four smaller squares and then:
 - Select one of the four squares and colour it white.
 - Select one of the three remaining squares and colour it black.
 - Consider the two remaining squares as new paintings and use the same three-step process on them.

Soon he noticed that it was not possible to convert all his visions to paintings with this process. Your task is to write a program that will paint a picture that differs as little as possible from the desired picture. The difference between two pictures is the number of pairs of pixels in corresponding positions that differ in colour.

-----Input-----
The first line contains an integer $N$ ($1 \leq N \leq 512$), the size of the picture Josip would like to paint. $N$ will be a power of $2$. Each of the following $N$ lines contains $N$ digits $0$ or $1$, white and black squares in the target picture.

-----Output-----
On the first line, output the smallest possible difference that can be achieved. On the next $N$ lines, output a picture that can be painted with Josip’s process and achieves the smallest difference. The picture should be in the same format as in the input.

Note: The second part of the output (the picture) may not be unique. Any correct output will be accepted.

-----Examples-----
Sample Input 1:
4
0001
0001
0011
1110
Sample Output 1:
1
0001
0001
0011
1111

Sample Input 2:
4
1111
1111
1111
1111
Sample Output 2:
6
0011
0011
0111
1101

Source: kattis | Difficulty: HARD


Solutions: