WonderTeam

The Brasileiro Championship features $n$ football teams. Every team plays every other team twice — once at home and once away. A win is worth 3 points, a draw gives each of the two teams 1 point, and a loss is worth 0 points.

When all matches are over, the teams are ranked by their total points. The rank of a team with $p$ points is defined as one plus the number of teams that have strictly more than $p$ points, so several teams may share the same rank.

Besides the champion (the team or teams ranked first), a WonderTeam is also selected whenever one exists. A WonderTeam is a team that satisfies all three of the following conditions, and satisfies each of them strictly (no other team ties its value):

• it has the strictly highest number of wins,
• it has scored the strictly highest number of goals,
• it has conceded the strictly lowest number of goals.

A WonderTeam is defined only when a single team satisfies all three conditions strictly.

Determine the worst (that is, the largest) rank a WonderTeam can possibly have.

The input consists of several test cases. Each test case is a single line containing $n$ ($1 \le n \le 50$), the number of teams in the league. The input ends with a line containing $0$.

For each test case, print on its own line the worst possible rank of the WonderTeam.