### COCI 2008/2009, Contest #4

Josip is a strange painter. He wants to paint a picture consisting of NxN 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:
1. Select one of the four squares and colour it white.
2. Select one of the three remaining squares and colour it black.
3. 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 ≤ N ≤ 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.

### Scoring

In test cases worth 50% points, N will be at most 8.

### Input

`40001000100111110`

### Output

`10001000100111111`

### Input

`41111111111111111`

### Output

`60011001101111101`

### Input

`80101000110100011010101111010111101010111101000110101000110100000`

### Output

`160000000100000011000001110000111111110111111100111111000111110000`

Point Value: 20 (partial)
Time Limit: 2.00s
Memory Limit: 16M

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

• (1/1)
nice array name, Jacob =P

• (1/2)
You know it =D

int supersmashbrosbrawl[515][515];

• (1/2)
xD
a while ago I tried to make a struct with the name Mod_2147483647_Integer_I_Have_To_Do_This_Because_Of_the_Evil_Hanson_XD
but later I was annoyed at the mess it created when debugging, so I changed it back to EvilInteger haha

• (2/0)
BLASPHEMY