题目描述
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:
<dl> <dt>w_{1, 1} \ w_{1, 2} \ w_{1, 3} \ ... \ w_{1, N}</dt> <dt>w_{2, 1} \ w_{2, 2} \ w_{2, 3} \ ... \ w_{2, N}</dt> <dd>: :w_{N, 1} \ w_{N, 2} \ w_{N, 3} \ ... \ w_{N, N}</dd> </dl>
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
输入格式
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输出格式
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