Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
E. Counter Attack

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBerland has managed to repel the flatlanders' attack and is now starting the counter attack.

Flatland has *n* cities, numbered from 1 to *n*, and some pairs of them are connected by bidirectional roads. The Flatlandian maps show roads between cities if and only if there is in fact no road between this pair of cities (we do not know whether is it a clever spy-proof strategy or just saving ink). In other words, if two cities are connected by a road on a flatland map, then there is in fact no road between them. The opposite situation is also true: if two cities are not connected by a road on a flatland map, then in fact, there is a road between them.

The berlanders got hold of a flatland map. Now Vasya the Corporal is commissioned by General Touristov to find all such groups of flatland cities, that in each group of cities you can get from any city to any other one, moving along the actual roads. Also the cities from different groups are unreachable from each other, moving along the actual roads. Indeed, destroying such groups one by one is much easier than surrounding all Flatland at once!

Help the corporal complete this task and finally become a sergeant! Don't forget that a flatland map shows a road between cities if and only if there is in fact no road between them.

Input

The first line contains two space-separated integers *n* and *m* (1 ≤ *n* ≤ 5·10^{5}, 0 ≤ *m* ≤ 10^{6}) — the number of cities and the number of roads marked on the flatland map, correspondingly.

Next *m* lines contain descriptions of the cities on the map. The *i*-th line contains two integers *a*_{i} and *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}) — the numbers of cities that are connected by the *i*-th road on the flatland map.

It is guaranteed that each pair of cities occurs in the input no more than once.

Output

On the first line print number *k* — the number of groups of cities in Flatland, such that in each group you can get from any city to any other one by flatland roads. At the same time, the cities from different groups should be unreachable by flatland roads.

On each of the following *k* lines first print *t*_{i} (1 ≤ *t*_{i} ≤ *n*) — the number of vertexes in the *i*-th group. Then print space-separated numbers of cities in the *i*-th group.

The order of printing groups and the order of printing numbers in the groups does not matter. The total sum *t*_{i} for all *k* groups must equal *n*.

Examples

Input

4 4

1 2

1 3

4 2

4 3

Output

2

2 1 4

2 2 3

Input

3 1

1 2

Output

1

3 1 2 3

Note

In the first sample there are roads only between pairs of cities 1-4 and 2-3.

In the second sample there is no road between cities 1 and 2, but still you can get from one city to the other one through city number 3.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/21/2021 00:15:22 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|