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 ≤ a_i,j < 2⁶⁴.
• 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 ≤ N ≤ 500
• 0 ≤ S_i ≤ 10
• 0 ≤ T_i ≤ 10
• 0 ≤ U_i < 2⁶⁴
• 0 ≤ V_i < 2⁶⁴

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.