TOWER

There are empty plastic glasses numbered 1 to N, which can be stacked one inside another, standing on the table.

You are given a sequence of moves a→b. A move a→b means you take the whole bunch containing glass a and place it onto the bunch containing glass b, merging the two bunches into one. If a equals b, or glasses a and b are already in the same bunch, the move does nothing.

For example, with 7 glasses and the moves 1→3, 2→6, 3→6, 4→7, and 4→2, the table changes as follows:

                                                                        4
                                                                        7
                                                    1         1         1
                                                    3         3         3
                    1             1     2           2         2 4       2
1 2 3 4 5 6 7 --> 2 3 4 5 6 7 --> 3 4 5 6 7 --> 4 5 6 7 --> 5 6 7 --> 5 6

The moves must be applied in the given order.

You may insert one extra move, called the zero move, to be performed before the first given move. Choose the zero move so that, after all moves are applied, the largest bunch contains as many glasses as possible.

The first line contains two integers N and M (2 ≤ N ≤ 10000, 0 ≤ M ≤ 100000): the number of glasses on the table and the number of moves.

Each of the next M lines contains two integers a and b representing the move a→b.

Print a single integer: the maximum possible number of glasses in the largest bunch after applying the best zero move followed by all the given moves.