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 Julia (1.4.0) (judge verdict: Runtime Error)

parseInt(x) = parse(Int,x)
parseUInt(x) = parse(UInt64,x)
transpose(x::Array{T,3} where T) = permutedims(x,[2,1,3])
import LinearAlgebra

function exec()
    n = readline() |> parseInt
    s = readline() |> split .|> parseInt
    t = readline() |> split .|> parseInt
    u = readline() |> split .|> parseUInt
    v = readline() |> split .|> parseUInt

    tabl = fill(-1,n,n,64)
    for bits = 0:63
        for i = 1:n, j = 1:n
            if (u[i] >> bits) & 1 == (v[j] >> bits) & 1
                tabl[i,j,bits+1] = (u[i] >> bits) & 1
            end
        end
        for i = 1:n
            if t[i] == 0 && (v[i] >> bits) & 1 == 1
                tabl[:,i,bits+1] .= 1
            elseif t[i] == 1 && (v[i] >> bits) & 1 == 0
                tabl[:,i,bits+1] .= 0
            end
        end
        tabl = transpose(tabl)
        for i = 1:n
            if s[i] == 0 && (u[i] >> bits) & 1 == 1
                if count(e -> e == 0, view(tabl,:,i,bits+1)) > 0
                    println(-1)
                    return
                end
                tabl[:,i,bits+1] .= 1
            elseif s[i] == 1 && (u[i] >> bits) & 1 == 0
                if count(e -> e == 1, view(tabl,:,i,bits+1)) > 0
                    println(-1)
                    return
                end
                tabl[:,i,bits+1] .= 0
            end
        end
        for i = 1:n
            if s[i] == 1 && (u[i] >> bits) & 1 == 1 && 
                count(e -> e == 1, view(tabl,:,i,bits+1)) == 0
                suc = false
                for j = 1:n
                    if tabl[j][i][bits+1] != -1 continue end
                    if count(e -> e != 1, view(tabl,j,:,bits+1)) > 1
                        suc = true
                        tabl[j][i][bits+1] = 1
                    end
                end
                if !suc
                    println(-1)
                    return
                end
            end
        end

        tabl = transpose(tabl)
        for i = 1:n
            if t[i] == 1 && (v[i] >> bits) & 1 == 1 && 
                count(e -> e == 1, view(tabl,:,i,bits+1)) == 0
                suc = false
                for j = 1:n
                    if tabl[j][i][bits+1] != -1 continue end
                    if count(e -> e != 1, view(tabl,j,:,bits+1)) > 1
                        suc = true
                        tabl[j][i][bits+1] = 1
                    end
                end
                if !suc
                    println(-1)
                    return
                end
            end
        end
    end
    tabl = transpose(tabl)
    for i=1:n
        for j=1:n
            r = UInt64(0)
            for bits = 64:-1:1
                r = r * 2 + (tabl[j,i,bits] == 1 ? 1 : 0)
            end
            print(r, " ")
        end
        println()
    end
end

exec()