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
input = sys.stdin.readline

def dfs_numbering(st, M, V, ANS, cnt, v):
    ST = [st]
    while len(ST) > 0:
        i = ST[-1]
        if ANS[i] == -1:
            V[i] = v
            end = 1
            for x in M[i]:
                if V[x] == -1:
                    ST.append(x)
                    end = 0
            if end == 1:
                ST.pop()
                ANS[i] = cnt
                cnt += 1
        else:
            ST.pop()
    return cnt

class scc():
    def __init__(self, n):
        self.n = n
        self.M = [[] for i in range(n)]
        self.IM = [[] for i in range(n)]

    def add_edge(self, frm, to):
        self.M[frm].append(to)
        self.IM[to].append(frm)

    def scc_list(self):
        n = self.n
        V = [-1] * n
        ANS = [-1] * n

        cnt = 0
        for i in range(n):
            if V[i] == -1:
                cnt = dfs_numbering(i, self.M, V, ANS, cnt, 0)

        ANS1 = [[ANS[i], i] for i in range(n)]
        ANS1.sort(reverse=True)

        V = [-1] * n
        ANS = [-1] * n
        v = 0
        for i in range(n):
            if V[ANS1[i][1]] == -1:
                dfs_numbering(ANS1[i][1], self.IM, V, ANS, 0, v)
                v += 1

        FANS = [[] for i in range(v)]
        for i in range(n):
            FANS[V[i]].append(i)

        return FANS

n, m = map(int,input().split())

S = scc(n)
for i in range(m):
    frm, to = map(int,input().split())
    S.add_edge(frm, to)
ANS = S.scc_list()

print(len(ANS))
for i in range(len(ANS)):
    print(len(ANS[i]), end=" ")
    print(*ANS[i])