Given a directed graph with $N$ vertices and $M$ edges. The $i$-th edge is $(a_i, b_i)$. This graph may not be simple.

Decompose this graph into SCCs and print them in topological order.

Constraints

• $1 \leq N \leq 500,000$
• $1 \leq M \leq 500,000$
• $0 \leq a_i, b_i < N$

Input

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

Output

The first line contains the number of SCCs $K$. The following $K$ lines contain the information for each SCC. $l$ is the number of vertices in the SCC, and $v_i$ are the vertex indices.

$l$ $v_0$ $v_1$ ... $v_{l-1}$

For each edge $(a_i, b_i)$, the line containing $b_i$ must not appear before the line containing $a_i$.

If there are multiple solutions, you may print any of them.

Examples

Input 1

6 7
1 4
5 2
3 0
5 5
4 1
0 3
4 2

Output 1

4
1 5
2 4 1
1 2
2 3 0