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:
import sys
sys.setrecursionlimit(10**9)
def SCC(G):
  D=[]
  C=[len(G)-1]
  U=[1]*len(G)
  def DFS(x):
    if U[x]:
      U[x]=0
      for i in range(len(G[x])):
        DFS(G[x][i])
      D.append(x)
  
  for i in range(len(G)):
    if U[i]:
      DFS(i)
  GR=[[] for i in range(len(G))]
  for i in range(N):
    for j in range(len(G[i])):
      GR[G[i][j]].append(i)
  R=[]
  U=[1]*len(G)
  def DFSR(x):
    if U[x]:
      R[-1].append(x)
      U[x]=0
      for i in range(len(GR[x])):
        DFSR(GR[x][i])
  
  for i in range(len(G)-1,-1,-1):
    if U[D[i]]:
      R.append([])
      DFSR(D[i])
  return R

S=sys.stdin.readlines()
N,M=map(int,S[0].split())
G=[[] for i in range(N)]
a,b=0,0
for i in range(M):
  a,b=map(int,S[i+1].split())
  G[a].append(b)
P=SCC(G)
print(len(P))
for i in range(len(P)):
  print(*([len(P[i])]+P[i]))