Description

Suppose there are $N$ players in a round-robin tournament, where $N=2^M$. Each player must play against every other player exactly once. Each player plays one match per day, and the round-robin tournament lasts for $N-1$ days. No player has a bye on any day.

Input Format

Input: $M$

Output Format

Output: The match schedule in table form. Each row's data is separated by a space.

Sample

3

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