You maintain a square grid of computers where each one is only connected to the neighboring computers that are directly adjacent to it, i.e. vertically or horizontally. You have discovered, to your chagrin, that several of your computers have been infected with an alien virus. Your healthy computers become infected if two or more of their adjacent neighbors are infected. Which of your computers end up as infected after the infection has spread as far as it can?

Input definition

An input file will contain an n by n square grid of numbers consisting of 0s and 1s. Each of the n rows will contain exactly n binary digits and no whitespace between 0s and 1s. In the grid, 1s represent infected computers and 0s represent healthy ones. The grid is always square and n can range from 7 to 9, inclusive.

Output definition

Your output should contain an n by n square grid of numbers consisting of 0s and 1s, representing the final state of the infection. As before, 1s shall represent infected computers and 0s shall represent healthy ones.

Example input

```
00000000
01010000
00010000
01001000
00010010
00001000
00001001
01000000
```

Example output

```
00000000
01111111
01111111
01111111
01111111
01111111
01111111
01111111
```