Snake

A snake fills a $3 \times n$ board with no empty squares. The snake's squares are numbered from $1$ to $3n$ in order. Squares with consecutive numbers ($1$ and $2$, $2$ and $3$, $3$ and $4$, $\ldots$) share an edge.

A snake can fill a $3 \times 9$ board as follows, for example.

Some of the numbers have been erased. Reconstruct the snake.

The first line contains a single integer $n$ ($1 \le n \le 1000$), the length of the board.

The next three lines describe the board. The $i$-th of these lines contains $n$ integers $a_{ij}$ ($0 \le a_{ij} \le 3n$ for $1 \le j \le n$).

If $a_{ij} > 0$, then $a_{ij}$ is the number of the snake segment on the $j$-th square of the $i$-th row. If $a_{ij} = 0$, the number on that square is unknown.

Print three lines. The $i$-th line should contain $n$ positive integers $b_{ij}$ (for $1 \le j \le n$), separated by spaces. Together, the numbers $b_{ij}$ must be a permutation of $1, 2, \ldots, 3n$.

The output must agree with every positive number in the input, and squares that hold consecutive numbers must share an edge.

A valid reconstruction always exists, and it is unique.