When a few students of the Ural State University finished their sport career,
the university encountered a lot of problems in team composition.
Veterans of sports programming decided to play their role and create
the most successful team in the history of the Ural SU.

Veterans assumed that success of a team strongly depends on the number
of friends in the ACM community the members of this team have. After
more discussions they developed the *criterion of success*: all
three members of the team should have the same number of friends.

Unfortunately, the veterans failed to compose a team, as it turned out
that there were no three programmers in the Ural SU that together satisfied
this criterion.

You should use this information to determine which students are friends
of each other.

### Input

The first line contains a single integer *n*
(3 ≤ *n* ≤ 200), which is the number of students
in the Ural SU participating in programming contests.

### Output

If the veterans' calculations are correct, the first line should contain
an integer *k*, which is the number of pairs of students that are
friends of each other. The following *k* lines should contain these
pairs. Students should be numbered 1 through *n*. If a problem has
multiple correct answers, output any of them.

If the veterans are wrong and the problem has no solution, output
a single line containing a number −1.

### Sample

**Problem Author: **Ivan Burmistrov

**Problem Source: **XV Open USU Championship