You are given a directed graph with $N$ vertices and $M$ edges, not necessarily simple. The $i$-th edge is oriented from the vertex $a_i$ to the vertex $b_i$. Divide this graph into strongly connected components and print them in their topological order.

Input is given from Standard Input in the following format:
$N\ M$
$a_0\ b_0$
$a_1\ b_1$
$\vdots$
$a_{M - 1}\ b_{M - 1}$

Print $1+K$ lines, where $K$ is the number of strongly connected components. Print $K$ on the first line. Print the information of each strongly connected component in next $K$ lines in the following format, where $l$ is the number of vertices in the strongly connected component and $v_i$ is the index of the vertex in it.
$l\ v_0\ v_1\ ...\ v_{l-1}$
Here, for each edge $(a_i, b_i)$, $b_i$ should not appear in earlier line than $a_i$.
If there are multiple correct output, print any of them.

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