Problem Statement

You are given an integer $N$ and arrays $S,T,U$ of length $N$. Construct any 1 $N \times N$ matrix $a$ that satisfies the following conditions.

• $a_{i,j}$ is $0$ or $1$
• For all pairs $(i,j)$ such that $1 \le i,j \le N$, $a_{S_i,j}+a_{j,T_i} \times 2 \neq U_i$

Input

$N$
$S_1\ S_2\ \cdots\ S_N$
$T_1\ T_2\ \cdots\ T_N$
$U_1\ U_2\ \cdots\ U_N$

All inputs are integers
$1 \le N \le 500$
$1 \le S_i,T_i \le N$
$0 \le U_i \le 3$

Output

If a matrix satisfying the conditions exists, output $1$ such matrix in the following format.

$a_{1,1} \cdots\ a_{1,N}$
$\vdots$
$a_{N,1} \cdots\ a_{N,N}$

Sample

3
2 1 2
3 3 1
3 1 0

0 0 0
1 0 1
0 0 0

4
4 4 3 3
2 1 1 2
1 0 0 3

-1