Given an undirected graph with $N$ vertices and $M$ edges. The $i$-th edge is $(a_i, b_i)$. This graph may not be simple. Please decompose this graph into three-edge-connected components.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $0 \leq a_i, b_i < N$

Input

$N$ $M$

• $a_0$ $b_0$
• $a_1$ $b_1$
• :
• $a_{M - 1}$ $b_{M - 1}$

Output

Print the number of three-edge-connected components $K$ in the first line. Following $K$ lines, print as follows. $l$ is the number of vertices of the three-edge-connected component and $v_i$ is a vertex index.

• $l$ $v_0$ $v_1$ ... $v_{l-1}$

If there are multiple solutions, print any of them.

Examples

Input 1

4 5
0 2
0 1
3 0
2 1
2 3

Output 1

3
2 0 2
1 1
1 3

Input 2

13 21
4 5
8 7
12 3
3 10
1 5
10 2
0 0
11 4
2 12
9 1
9 0
7 8
7 6
9 1
8 2
12 10
11 0
8 6
3 2
5 9
4 11

Output 2

6
1 0
3 1 9 5
4 2 12 3 10
2 4 11
1 6
2 7 8