There are n (n is even) players, conveniently labelled 1, 2, ...n. These players will play m rounds of games. In each round of games, the players are split into two teams of n/2 players each. Two players x < y are said to have played against each other if they were on different teams for one of the m games. You are given three arguments: n, m, games. Your task is to check that for all pairs of players 1 <= x, y <= n, player x has played against y. games is a 2-dimensional list that represents the m rounds of games among n players. Write a function check(n, m, games) that takes in 3 arguments. Inputs It is guaranteed that n, m are integers and 1 <= n <= 20,000, 1 <= m <= 30. It is also guaranteed that n is even. games is a 2 dimensional list with m rows and n columns, where games[i] is a permutation of 1,2,3,...,n representing round number i. In particular for round i, games[i][0], games[i][1], games[i][n/2-1] is on one team, games[i][n/2], games[i][n/2+1], games[i][n-1] is on the other team. Outputs check(n, m, games) should return a boolean, True if and only if all pairs of players have played against each other in the m rounds of games. Examples check(2, 1, [[1, 2]]) = True check(4, 2, [[1, 2, 3, 4], [4, 3, 1, 2]]) = False check(4, 2, [[1, 2, 3, 4], [1, 3, 2, 4]]) = True check(6, 6, [[1, 6, 3, 4, 5, 2], [6, 4, 2, 3, 1, 5], [4, 2, 1, 5, 6, 3], [4, 5, 1, 6, 2, 3], [3, 2, 5, 1, 6, 4], [2, 3, 6, 4, 1, 5]]) = True check(6, 6, [[3, 1, 4, 5, 6, 2], [5, 3, 2, 4, 1, 6], [5, 3, 6, 4, 2, 1], [6, 5, 3, 2, 1, 4], [5, 4, 1, 2, 6, 3], [4, 1, 6, 2, 5, 3]]) = False

def check(n, m, games):
    result = {}
    for round in games:
        for idx in range(n//2):
            team1 = round[idx]
            team2 = round[n//2 + idx]
            if team1 not in result:
                result[team1] = set([team2])
            else:
                result[team1].add(team2)
    new_result = result.values()
    if len(new_result) != n//2:
        return False
    for item in new_result:
        if len(item) != n//2-1:
            return False
    return True