Problem Statement

kamipeipaa likes sliding puzzles (reference), and he also likes magic squares (reference).
You are given the board of an $N × N$ sliding puzzle, so let's try to make a magic square.

On a board of $N × N$ cells, pieces with pairwise distinct integers from $1$ to $N^{2}-1$ written on them are arranged.
You may repeatedly slide a piece adjacent to the empty cell (above, below, left, or right of it) into the empty cell.
The puzzle is considered complete by putting the piece $N^{2}$ into the empty cell. The piece $N^2$ can be placed anywhere as long as the cell is empty.

Input

$N$
$A_{1,1}$ $A_{1,2}$ $…$ $A_{1,N}$
$A_{2,1}$ $A_{2,2}$ $…$ $A_{2,N}$
$⋮$
$A_{N,1}$ $A_{N,2}$ $…$ $A_{N,N}$

The first line contains an integer $1 \le N \le 50$ representing the size of the sliding puzzle.
$A_{i,j}$ are pairwise distinct integers from $0$ to $N^{2}-1$, where $0$ represents the empty cell.

Output

If a magic square can be made from the current board, print "possible" on the first line, and print the target magic square on the following $N$ lines.
The format of the magic square is the same as the input: print $N$ space-separated elements on each line.
If a magic square cannot be made, print "impossible".

This problem uses a special judge. You may print any magic square board that can be made from the current board.

Sample

3
8 1 6
3 5 7
4 0 2

possible
8 1 6
3 5 7
4 9 2

3
8 1 6
3 0 7
4 5 2

possible
8 1 6
3 5 7
4 9 2

2
0 1
2 3

impossible