Problem:
Score : 600 points

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.

Sample Input 1

2
0 1
1 0
1 1
1 0

Sample Output 1

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 Input 2

2
1 1
1 0
15 15
15 11

Sample Output 2

15 11
15 11

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string   { sc.Scan(); return sc.Text() }
func scanRunes() []rune    { return []rune(scanString()) }
func scanInt() int         { a, _ := strconv.Atoi(scanString()); return a }
func scanInt64() int64     { a, _ := strconv.ParseInt(scanString(), 10, 64); return a }
func scanFloat64() float64 { a, _ := strconv.ParseFloat(scanString(), 64); return a }

func scanInts(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}
	return a
}

func debug(a ...interface{}) {
	if os.Getenv("ONLINE_JUDGE") == "false" {
		fmt.Fprintln(os.Stderr, a...)
	}
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

//•*¨*•.¸¸♪main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)
func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n := scanInt()
	s := scanInts(n)
	t := scanInts(n)
	u := scanInts(n)
	v := scanInts(n)

	a := make([][][64]int, n)
	b := make([][][64]bool, n)
	for i := 0; i < n; i++ {
		a[i] = make([][64]int, n)
		b[i] = make([][64]bool, n)
	}

	for i := 0; i < n; i++ {
		d := u[i]
		for k := 0; k < 64; k++ {
			f := d & 1
			if s[i] != f {
				for j := 0; j < n; j++ {
					a[i][j][k] = f
					b[i][j][k] = true
				}
			}

			d >>= 1
		}
	}

	for i := 0; i < n; i++ {
		d := v[i]
		for k := 0; k < 64; k++ {
			f := d & 1
			if t[i] != f {
				for j := 0; j < n; j++ {
					if b[j][i][k] && a[j][i][k] != f {
						fmt.Fprintln(wr, -1)
						return
					}
					a[j][i][k] = f
					b[j][i][k] = true
				}
			}

			d >>= 1
		}
	}

	c0 := make([][64]int, n)
	c1 := make([][64]int, n)
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			for k := 0; k < 64; k++ {
				c0[i][k] += a[i][j][k]
				c1[j][k] += a[i][j][k]
			}
		}
	}

	for i := 0; i < n; i++ {
		d := u[i]
		for k := 0; k < 64; k++ {
			f := d & 1
			if s[i] == 1 && f == 1 {
				ff := 0
				for j := 0; j < n; j++ {
					ff |= a[i][j][k]
				}
				if ff == 0 {
					for j := 0; j < n; j++ {
						if !b[i][j][k] && (t[j] == 0 && c1[j][k] < n-1 || t[j] == 1) {
							a[i][j][k] = 1
							b[i][j][k] = true
							c0[i][k]++
							break
						}
						if j == n-1 {
							fmt.Fprintln(wr, -1)
							return
						}
					}
				}
			}
			d >>= 1
		}
	}

	for i := 0; i < n; i++ {
		d := v[i]
		for k := 0; k < 64; k++ {
			f := d & 1
			if t[i] == 1 && f == 1 {
				ff := 0
				for j := 0; j < n; j++ {
					ff |= a[j][i][k]
				}
				if ff == 0 {
					for j := 0; j < n; j++ {
						if !b[j][i][k] && (s[j] == 0 && c0[j][k] < n-1 || s[j] == 1) {
							a[j][i][k] = 1
							break
						}
						if j == n-1 {
							fmt.Fprintln(wr, -1)
							return
						}
					}
				}
			}
			d >>= 1
		}
	}

	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			s := 0
			for k := 0; k < 64; k++ {
				s += a[i][j][k] << k
			}
			fmt.Fprint(wr, s, " ")
		}
		fmt.Fprintln(wr)
	}
}