Problem Statement

Given are an integer $N$ and arrays $S$, $T$, $U$, and $V$, each of length $N$. Construct an $N×N$ matrix $a$ that satisfy the following conditions:

• $a_{i,j}$ is an integer.
• $0 \leq a_{i,j} \lt 2^{64}$.
• If $S_{i} = 0$, the bitwise AND of the elements in the $i$-th row is $U_{i}$.
• If $S_{i} = 1$, the bitwise OR of the elements in the $i$-th row is $U_{i}$.
• If $T_{i} = 0$, the bitwise AND of the elements in the $i$-th column is $V_{i}$.
• If $T_{i} = 1$, the bitwise OR of the elements in the $i$-th column is $V_{i}$.

However, there may be cases where no matrix satisfies the conditions.

Constraints

• All values in input are integers.
• $1 \leq N \leq 500$
• $0 \leq S_{i} \leq 1$
• $0 \leq T_{i} \leq 1$
• $0 \leq U_{i} \lt 2^{64}$
• $0 \leq V_{i} \lt 2^{64}$

Input

Input is given from Standard Input in the following format:

N
S_{1} S_{2} ...  S_{N}
T_{1} T_{2} ...  T_{N}
U_{1} U_{2} ...  U_{N}
V_{1} V_{2} ...  V_{N}

Output

If there exists a matrix that satisfies the conditions, print one such matrix in the following format:

a_{1,1} ...  a_{1,N}
:
a_{N,1} ...  a_{N,N}

Note that any matrix satisfying the conditions is accepted.

If no matrix satisfies the conditions, print $-1$.