//iterates to the next permutation lexicographically
NPlayersBijection NPlayersBijection::operator++()
{
    for(int e=playersPartition1.size()-1; e >= 0; e--)
    {
        for(int k=playersPartition1[e].size()-2; k>=0; k--)
        {
            if(playersBijection[playersPartition1[e][k] ] < playersBijection[playersPartition1[e][k+1] ])
            {
                for(int l=playersPartition1[e].size()-1; l>k; l--)
                {
                    if(playersBijection[playersPartition1[e][k] ] < playersBijection[playersPartition1[e][l] ])
                    {
                        swap(playersBijection[playersPartition1[e][k] ], playersBijection[playersPartition1[e][l] ]);

                        for(int i=k+1, j=playersPartition1[e].size()-1; i<=j; i++, j--)
                            swap(playersBijection[playersPartition1[e][i] ], playersBijection[playersPartition1[e][j] ]);

                        if(isIdentity(e))
                            break;
                        else
                            return *this;
                    }
                }
                break;
            }
        }

        //resets the current partition to the identity
        for(int p=0; p<(int)playersPartition1[e].size(); p++)
            playersBijection[playersPartition1[e][p] ] = identity[playersPartition1[e][p] ];
    }

    return *this;
};