Diverta City

Diverta City is a new city consisting of N towns numbered 1, 2, ..., N.

The mayor Ringo is planning to connect every pair of two different towns with a bidirectional road. The length of each road is undecided.

A Hamiltonian path is a path that starts at one of the towns and visits each of the other towns exactly once. The reversal of a Hamiltonian path is considered the same as the original Hamiltonian path.

There are N! / 2 Hamiltonian paths. Ringo wants all these paths to have distinct total lengths (the sum of the lengths of the roads on a path), to make the city diverse.

Find one such set of the lengths of the roads, under the following conditions:

• The length of each road must be a positive integer.
• The maximum total length of a Hamiltonian path must be at most 10^{11}.

Constraints

• N is a integer between 2 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print a set of the lengths of the roads that meets the objective, in the following format:

w_{1, 1} \ w_{1, 2} \ w_{1, 3} \ ... \ w_{1, N} w_{2, 1} \ w_{2, 2} \ w_{2, 3} \ ... \ w_{2, N} : : : w_{N, 1} \ w_{N, 2} \ w_{N, 3} \ ... \ w_{N, N}

where w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:

• w_{i, i} = 0
• w_{i, j} = w_{j, i} \ (i \neq j)
• 1 \leq w_{i, j} \leq 10^{11} \ (i \neq j)

If there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.

Examples

Input

3

Output

0 6 15 6 0 21 15 21 0

Input

4

Output

0 111 157 193 111 0 224 239 157 224 0 258 193 239 258 0

inputFormat

Input

Input is given from Standard Input in the following format:

N

outputFormat

Output

Print a set of the lengths of the roads that meets the objective, in the following format:

w_{1, 1} \ w_{1, 2} \ w_{1, 3} \ ... \ w_{1, N} w_{2, 1} \ w_{2, 2} \ w_{2, 3} \ ... \ w_{2, N} : : : w_{N, 1} \ w_{N, 2} \ w_{N, 3} \ ... \ w_{N, N}

where w_{i, j} is the length of the road connecting Town i and Town j, which must satisfy the following conditions:

• w_{i, i} = 0
• w_{i, j} = w_{j, i} \ (i \neq j)
• 1 \leq w_{i, j} \leq 10^{11} \ (i \neq j)

If there are multiple sets of lengths of the roads that meet the objective, any of them will be accepted.

Examples

Input

3

Output

0 6 15 6 0 21 15 21 0

Input

4

Output

0 111 157 193 111 0 224 239 157 224 0 258 193 239 258 0

样例

4

0 111 157 193
111 0 224 239
157 224 0 258
193 239 258 0

</p>