I hate Matrix Construction

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.

Examples

Input

2 0 1 1 0 1 1 1 0

Output

1 1 1 0

Input

2 1 1 1 0 15 15 15 11

Output

15 11 15 11

inputFormat

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}

outputFormat

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.

Examples

Input

2 0 1 1 0 1 1 1 0

Output

1 1 1 0

Input

2 1 1 1 0 15 15 15 11

Output

15 11 15 11

样例

2
1 1
1 0
15 15
15 11

15 11
15 11

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