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 Fortran (GNU Fortran 9.2.1) (judge verdict: Runtime Error)

program i_hate_matrix_construction
  implicit none
  integer :: n, i, j, k
  integer(8) :: x
  integer, dimension(500) :: s = 0, t = 0
  integer(8), dimension(500) :: u = 0, v = 0
  integer(8), dimension(500, 500) :: a = 0
  read(*,*) n
  read(*,*) s(1:n)
  read(*,*) t(1:n)
  read(*,*) u(1:n)
  read(*,*) v(1:n)
  do k = 0, 62
    do i = 1, n
      if (s(i) == merge(1, 0, btest(u(i), k))) cycle
      do j = 1, n
        a(i, j) = set(a(i, j), k, s(i) == 0)
      end do
    end do
    do j = 1, n
      if (t(j) == merge(1, 0, btest(v(j), k))) cycle
      do i = 1, n
        a(i, j) = set(a(i, j), k, t(j) == 0)
      end do
    end do
    do i = 1, n
      if (s(i) == 0) cycle
      if (.not.btest(u(i), k)) cycle
      do j = 1, n
        !if (t(j) == 1) cycle
        if (btest(a(i, j), k)) cycle
        a(i, j) = ibset(a(i, j), k)
        if (all(btest(a(i, 1:n), k))) then
          a(i, j) = ibclr(a(i, j), k)
        else
          exit
        end if
      end do
    end do
    do j = 1, n
      if (t(j) == 0) cycle
      if (.not.btest(v(j), k)) cycle
      do i = 1, n
        !if (s(i) == 1) cycle
        if (btest(a(i, j), k)) cycle
        a(i, j) = ibset(a(i, j), k)
        if (all(btest(a(1:n, j), k))) then
          a(i, j) = ibclr(a(i, j), k)
        else
          exit
        end if
      end do
    end do
  end do
  do i = 1, n
    x = a(i, 1)
    do j = 2, n
      x = operate(x, a(i, j), s(i) == 0)
    end do
    if (x /= u(i)) then
      write(*,'(i0)') -1
      stop
    end if
  end do
  do j = 1, n
    x = a(1, j)
    do i = 2, n
      x = operate(x, a(i, j), t(j) == 0)
    end do
    if (x /= v(j)) then
      write(*,'(i0)') -1
      stop
    end if
  end do
  do i = 1, n
    write(*,'(i0)',advance='no') a(i, 1)
    do j = 2, n
      write(*,'(x,i0)',advance='no') a(i, j)
    end do
    write(*,*)
  end do
contains
  integer(8) function set(a, k, b) result(res)
    integer(8), intent(in) :: a
    integer, intent(in) :: k
    logical, intent(in) :: b
    res = merge(ibset(a, k), ibclr(a, k), b)
  end
  integer(8) function operate(a1, a2, b) result(res)
    integer(8), intent(in) :: a1, a2
    logical, intent(in) :: b
    res = merge(and(a1, a2), or(a1, a2), b)
  end
end program i_hate_matrix_construction