PROGRAMMING:Cycle schedule
There are n players in the round robin competition, in which n = $$2 ^ m $$, each player is required to compete with other n − 1 players once a day, and each player is required to compete once a day. The round robin competition lasts for n − 1 days, and no players are required to take turns every day.
###Input format:
Input: m (m < = 7).
###Output format:
Output: table form of competition schedule. The data in a row is separated by a space.
###Input example:
```in
three
```
###Output example:
The corresponding output is given here. For example:
```out
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
```
Note: the first behavior: 1, 2, 3, 4, 5, 6, 7, 8, 1 means that the competition between No.1 player and other players in this line, for example, the second number 2 (its subscript can be regarded as 1) means the competition between No.1 and No.2 on the first day, and the fifth number 5 (its subscript can be regarded as 4) means the competition between No.1 and No.5 on the fourth day< br>
answer：If there is no answer, please comment
###Input format:
Input: m (m < = 7).
###Output format:
Output: table form of competition schedule. The data in a row is separated by a space.
###Input example:
```in
three
```
###Output example:
The corresponding output is given here. For example:
```out
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
```
Note: the first behavior: 1, 2, 3, 4, 5, 6, 7, 8, 1 means that the competition between No.1 player and other players in this line, for example, the second number 2 (its subscript can be regarded as 1) means the competition between No.1 and No.2 on the first day, and the fifth number 5 (its subscript can be regarded as 4) means the competition between No.1 and No.5 on the fourth day< br>
answer：If there is no answer, please comment