There are N cities numbered from 1 to N (1 ≤ N ≤ 200) and M two-way roads connect them. There are at most one road between two cities. In summer holiday, members of DSAP Group want to make some traveling tours. Each tour is a route passes K different cities (K > 2) T₁, T₂, …, T_K and return to T₁. Your task is to help them make T tours such that:

1. Each of these T tours has at least a road that does not belong to (T−1) other tours.
2. T is maximum.

The first line of input contains N and M separated with white spaces. Then follow by M lines, each has two number H and T which means there is a road connect city H and city T.

You must output an integer number T — the maximum number of tours. If T > 0, then T lines followed, each describe a tour. The first number of each line is K — the amount of different cities in the tour, then K numbers which represent K cities in the tour.

If there are more than one solution, you can output any of them.