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In a tournament, there are n teams T1, T2, ..., Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 and T2, T2 and T3, ..., Tn–1 and Tn and Tn and T1.
No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?