Round-robin Tournament Matches

You are given an integer N representing the number of teams in a tournament. Your task is to generate all possible matches for a round-robin tournament. A match is represented as a pair \((i, j)\) (written as two space-separated integers on one line) where \(1 \leq i < j \leq N\). The matches should be listed in lexicographical order.

Example:

Input: 4
Output:
1 2
1 3
1 4
2 3
2 4
3 4

</p>

If there is only one team, then there are no matches and the output should be empty.

inputFormat

The input consists of a single integer N on standard input.

Constraints:

• \(1 \leq N \leq 10^4\)

outputFormat

Output all matches, each on a separate line. Each line should contain two space-separated integers \(i\) and \(j\) representing a match. If no match exists, output nothing.

## sample

1