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:
class Digraph:
    """重み[なし]有向グラフを生成する.

    """

    #入力定義
    def __init__(self,vertex=[]):
        self.vertex=set(vertex)

        self.edge_number=0
        self.vertex_number=len(vertex)

        self.adjacent_out={v:set() for v in vertex} #出近傍(vが始点)
        self.adjacent_in={v:set() for v in vertex} #入近傍(vが終点)

    #頂点の追加
    def add_vertex(self,*adder):
        for v in adder:
            if v not in self.vertex:
                self.adjacent_in[v]=set()
                self.adjacent_out[v]=set()

                self.vertex_number+=1
                self.vertex.add(v)

    #辺の追加
    def add_edge(self,From,To):
        for v in [From,To]:
            if v not in self.vertex:
                self.add_vertex(v)

        if To not in self.adjacent_in[From]:
            self.edge_number+=1

        self.adjacent_out[From].add(To)
        self.adjacent_in[To].add(From)

    #辺を除く
    def remove_edge(self,From,To):
        for v in [From,To]:
            if v not in self.vertex:
                self.add_vertex(v)

        if To in self.adjacent_out[From]:
            self.adjacent_out[From].remove(To)
            self.adjacent_in[To].remove(From)
            self.edge_number-=1

    #頂点を除く
    def remove_vertex(self,*vertexes):
        for  v in vertexes:
            if v in self.vertex:
                self.vertex_number-=1

                for u in self.adjacent_out[v]:
                    self.adjacent_in[u].remove(v)
                    self.edge_number-=1
                del self.adjacent_out[v]

                for u in self.adjacent_in[v]:
                    self.adjacent_out[u].remove(v)
                    self.edge_number-=1
                del self.adjacent_in[v]

    #Walkの追加
    def add_walk(self,*walk):
        N=len(walk)
        for k in range(N-1):
            self.add_edge(walk[k],walk[k+1])

    #Cycleの追加
    def add_cycle(self,*cycle):
        self.add_walk(*cycle)
        self.add_edge(cycle[-1],cycle[0])

    #頂点の交換
    def __vertex_swap(self,p,q):
        self.vertex.sort()

    #グラフに頂点が存在するか否か
    def vertex_exist(self,v):
        return v in self.vertex

    #グラフに辺が存在するか否か
    def edge_exist(self,From,To):
        if not(self.vertex_exist(From) and self.vertex_exist(To)):
            return False
        return To in self.adjacent_out[From]

    #近傍
    def neighbohood(self,v):
        if not self.vertex_exist(v):
            return []
        return list(self.adjacent[v])

    #出次数
    def out_degree(self,v):
        if not self.vertex_exist(v):
            return 0

        return len(self.adjacent_out[v])

    #入次数
    def in_degree(self,v):
        if not self.vertex_exist(v):
            return 0

        return len(self.adjacent_in[v])

    #次数
    def degree(self,v):
        if not self.vertex_exist(v):
            return 0

        return self.out_degree(v)-self.in_degree(v)

    #頂点数
    def vertex_count(self):
        return len(self.vertex)

    #辺数
    def edge_count(self):
        return self.edge_number

    #頂点vを含む連結成分
    def connected_component(self,v):
        pass

#Topologycal Sort
def Topological_Sort(D):
    from collections import deque

    X={v:D.in_degree(v) for v in D.vertex}
    Q=deque([v for v in D.vertex if X[v]==0])

    S=[]
    while Q:
        u=Q.pop()
        S.append(u)
        for v in D.adjacent_out[u]:
            X[v]-=1
            if X[v]==0:
                Q.append(v)

    return S

#強連結成分に分解
def Strongly_Connected_Component_Decomposition(D,Mode=0):
    """有向グラフDを強連結成分に分解

    Mode:
    0(Defalt)---各強連結成分の頂点のリスト
    1        ---各頂点が属している強連結成分の番号
    2        ---0,1の両方

    ※0で帰ってくるリストは各強連結成分に関してトポロジカルソートである.
    """
    import sys
    from collections import deque

    T={x:-1 for x in D.vertex}
    Q=deque([])

    def f(v):
        T[v]=0
        for w in D.adjacent_out[v]:
            if T[w]==-1:
                f(w)

        Q.appendleft(v)
        T[v]=len(Q)
    x=D.vertex.pop()
    D.vertex.add(x)

    RT=sys.getrecursionlimit()
    sys.setrecursionlimit(3*10**5)
    for v in D.vertex:
        if T[v]==-1:
            f(v)
    sys.setrecursionlimit(RT)

    T={x:-1 for x in D.vertex}
    C=[]
    p=0

    for v in Q:
        if T[v]==-1:
            T[v]=p
            P=[v]
            R=deque([v])

            while R:
                u=R.popleft()
                for w in D.adjacent_in[u]:
                    if T[w]==-1:
                        T[w]=p
                        R.append(w)
                        P.append(w)
            C.append(P)
            p+=1

    if Mode==1:
        return T
    elif Mode==2:
        return (C,T)
    else:
        return C
#================================================
N,M=map(int,input().split())
D=Digraph(list(range(N)))

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

C=Strongly_Connected_Component_Decomposition(D)

X=[""]*(len(C))
for i in range(len(C)):
    X[i]="{} {}".format(len(C[i])," ".join(map(str,C[i])))

print(len(C))
print("\n".join(X))