Round Robin Tournaments

Problem

The problem is to schedule a tournament of n teams over n-1 weeks, with each week divided into n/2 periods, and each period divided into two slots. The first team in each slot plays at home, whilst the second plays the first team away. A tournament must satisfy the following three constraints: every team plays once a week; every team plays at most twice in the same period over the tournament; every team plays every other team.

Input

The number of teams in the tournament

Output

Linear program

SAT

Assignment for boolean variables tiwjpk, i=1..n, j=1..n-1, k=1..n/2 (eg. t1w3p2)
tiwjpk = 1, if team i is playing on week j at perioid k.
tiwjpk = 0, othewise