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:
N,M = map(int,input().split())
AB = [tuple(map(int,input().split())) for i in range(M)]

import sys
sys.setrecursionlimit(10**8)
class Scc:
    def __init__(self,n):
        self.n = n
        self.edges = []

    def add_edge(self,fr,to):
        assert 0 <= fr < self.n
        assert 0 <= to < self.n
        self.edges.append((fr, to))

    def scc(self):
        csr_start = [0] * (self.n + 1)
        csr_elist = [0] * len(self.edges)
        for fr,to in self.edges:
            csr_start[fr + 1] += 1
        for i in range(1,self.n+1):
            csr_start[i] += csr_start[i-1]
        counter = csr_start[:]
        for fr,to in self.edges:
            csr_elist[counter[fr]] = to
            counter[fr] += 1

        self.now_ord = self.group_num = 0
        self.visited = []
        self.low = [0] * self.n
        self.ord = [-1] * self.n
        self.ids = [0] * self.n
        def _dfs(v):
            self.low[v] = self.ord[v] = self.now_ord
            self.now_ord += 1
            self.visited.append(v)
            for i in range(csr_start[v], csr_start[v+1]):
                to = csr_elist[i]
                if self.ord[to] == -1:
                    _dfs(to)
                    self.low[v] = min(self.low[v], self.low[to])
                else:
                    self.low[v] = min(self.low[v], self.ord[to])
            if self.low[v] == self.ord[v]:
                while 1:
                    u = self.visited.pop()
                    self.ord[u] = self.n
                    self.ids[u] = self.group_num
                    if u==v: break
                self.group_num += 1
        for i in range(self.n):
            if self.ord[i] == -1: _dfs(i)
        for i in range(self.n):
            self.ids[i] = self.group_num - 1 - self.ids[i]

        groups = [[] for _ in range(self.group_num)]
        for i in range(self.n):
            groups[self.ids[i]].append(i)
        return groups

scc = Scc(N)
for a,b in AB:
    scc.add_edge(a,b)
ans = scc.scc()
print(len(ans))
for row in ans:
    print(*[len(row)] + row)