Tournament Schedule

You are given an integer N representing the number of players in a tournament. Each player must play against every other player exactly once. Your task is to compute the total number of matches and output a unique schedule of matches.

The total number of matches is given by the formula:

\(\frac{N \times (N-1)}{2}\)

The schedule should list each match as a pair of player identifiers. Players are numbered from 1 to N. Each pair should appear only once in the form (i, j) where i < j.

If there are fewer than 2 players, no matches will be played.

inputFormat

The input consists of a single integer N (where N ≥ 0), provided via standard input.

outputFormat

Output the total number of matches on the first line. If there are any matches, then output each match on a new line as two space-separated integers i and j representing a match between player i and player j, where i < j. All output should be printed to standard output.

## sample

4

6
1 2
1 3
1 4
2 3
2 4
3 4

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