Football League

A football league has $n$ teams, where $n$ is even. During the season every team plays every other team exactly once, so there are $n(n-1)/2$ matches in total.

The season is divided into $n-1$ turns. In each turn every team plays exactly one match, so a turn consists of $n/2$ matches.

Every match is played at the home stadium of one of the two opponents: one team plays at home and the other plays away.

Ideally each team would alternate between home and away matches. However, it is not always possible to build a schedule in which no team ever plays two consecutive matches at the same venue (home-home or away-away).

Whenever a team plays two consecutive matches both at home, or both away, that counts as one break. For example, if a team's venues in consecutive turns are away, home, home, home, home, away, this contributes three breaks (there are three consecutive home-home pairs).

Over all valid schedules for the whole season, determine the minimum possible total number of breaks, counted across all teams and all turns.

The only line of input contains one even integer $n$ ($2 \le n \le 1000$) — the number of teams.

Output a single integer: the minimum possible total number of breaks over the whole season, that is, the minimum total number of situations in which some team plays two consecutive matches both at home or both away, minimized over all valid schedules.