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 Ruby (2.7.1) (judge verdict: Wrong Answer)

N = gets.to_i
Ss, Ts, Us, Vs = readlines.map{_1.split.map(&:to_i)}

def go(a, b, c, d)
  (0 ... N).select{b[_1] == 1}.each do |i|
    lsum = a[i].inject(:|)
    up = c[i] - lsum
    next if up == 0
    (0 ... N).select{d[_1] == 0}.each do |j|
      lpro = (a.transpose)[j].inject(:&)
      up1 = (~lpro) & up
      a[i][j] += up1
      up -= up1
      break if up == 0
    end
  end
  a
end

ans = Array.new(N){Array.new(N, 0)}
N.times do |i|
  N.times do |j|
    ans[i][j] |= Us[i] if Ss[i] == 0
    ans[i][j] |= Vs[j] if Vs[j] == 0
    ans[i][j] |= (Us[i] & Vs[j])
  end
end
ans = go(ans, Ss, Us, Ts)
ans = go(ans.transpose, Ts, Vs, Ss).transpose
ans.each{puts _1.join(' ')}