ABC164——Task F：I hate Matrix Construction - Problem

Problem5330--ABC164——Task F：I hate Matrix Construction

5330: ABC164——Task F：I hate Matrix Construction

_{[Creator : ]}

Time Limit : 1.000 sec Memory Limit : 256 MiB

Submit Solved: 0 Submit Num: 2 Statistics ShowOff!

Description

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

$_{i, j}$ is an integer.
$0 \leq_{i, j} <^{64}$ .
If $_{i} = 0$ , the bitwise AND of the elements in the $i$ -th row is $_{i}$ .
If $_{i} = 1$ , the bitwise OR of the elements in the $i$ -th row is $_{i}$ .
If $_{i} = 0$ , the bitwise AND of the elements in the $i$ -th column is $_{i}$ .
If $_{i} = 1$ , the bitwise OR of the elements in the $i$ -th column is $_{i}$ .

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

Input

Input is given from Standard Input in the following format:

N
S1 S2 ... SN
T1 T2 ... TN
U1 U2 ... UN
V1 V2 ... VN

Output

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

a1,1 ... a1,N
.
.
.
aN,1 ... aN,N

Note that any matrix satisfying the conditions is accepted.

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

Constraints

All values in input are integers.
$1 \leq N \leq 500$
$0 \leq_{i} \leq 1$
$0 \leq_{i} \leq 1$
$0 \leq_{i} <^{64}$
$0 \leq_{i} <^{64}$

Sample 1 Input

Sample 1 Output

1 1
1 0

In Sample Input $1$ , we need to find a matrix such that:

the bitwise AND of the elements in the $1$ -st row is $1$ ;
the bitwise OR of the elements in the $2$ -nd row is $1$ ;
the bitwise OR of the elements in the $1$ -st column is $1$ ;
the bitwise AND of the elements in the $2$ -nd column is $0$ .

Sample 2 Input

Sample 2 Output

15 11
15 11

HINT

题目来源
AtCoder Beginner Contest 164，Task F。https://atcoder.jp/contests/abc164/tasks/abc164_f

Source/Category

AtCoder_ABC 100.164.ABC164

Submit