Problem: 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.

Constraints

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

Input

Input is given from Standard Input in the following format:


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


Output

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.

Example

Input

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


Output

4
1 5
2 4 1
1 2
2 3 0

Solution (in PYTHON3):

Solution:
from collections import deque

class StronglyConnectedComponents():
    def __init__(self, n):
        self.n = n
        self.graph = [[] for _ in range(n)]
        self.rev = [[] for _ in range(n)]

    def add_edge(self, fr, to):
        self.graph[fr].append(to)
        self.rev[to].append(fr)

    def scc_id(self):
        group = [0] * self.n
        order = []
        for s in range(self.n):
            if group[s]: continue
            stack = deque([s])
            group[s] = -1
            while stack:
                node = stack.pop()
                for adj in self.graph[node]:
                    if group[adj]: continue
                    group[adj] = -1
                    stack.append(node)
                    stack.append(adj)
                    break
                else:
                    order.append(node)
        cnt = 0
        for s in order[::-1]:
            if group[s] != -1: continue
            stack = deque([s])
            group[s] = cnt
            while stack:
                node = stack.pop()
                for adj in self.rev[node]:
                    if group[adj] != -1: continue
                    group[adj] = cnt
                    stack.append(adj)
            cnt += 1
        return group, cnt

    def scc(self):
        group, cnt = self.scc_id()
        res = [[] for _ in range(cnt)]
        for i, g in enumerate(group):
            res[g].append(i)
        return res

import sys
input = sys.stdin.buffer.readline

N, M = map(int, input().split())

scc = StronglyConnectedComponents(N)

for _ in range(M):
    a, b = map(int, input().split())
    scc.add_edge(a, b)

res = scc.scc()
print(len(res))

for r in res:
    print(len(r), *r)