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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

struct SCC {
public:
    int num;

    SCC(vector<vector<int>>& G) : G(G), comp(G.size(), -1), visited(G.size()), G_rev(G.size()) {
        for (int u = 0; u < G.size(); u++) {
            for (int v : G[u]) G_rev[v].push_back(u);
        }

        for (int v = 0; v < G.size(); v++) dfs(v);
        reverse(order.begin(), order.end());
        num = 0;
        for (int v : order) if (comp[v] == -1) rdfs(v, num++);
    }

    int operator[](int k) const {
        return comp[k];
    }

private:
    vector<vector<int>> G, G_rev;
    vector<int> comp, order;
    vector<bool> visited;

    void dfs(int u) {
        if (visited[u]) return;
        visited[u] = true;
        for (int v : G[u]) dfs(v);
        order.push_back(u);
    }

    void rdfs(int u, int c) {
        if (comp[u] != -1) return;
        comp[u] = c;
        for (int v : G_rev[u]) rdfs(v, c);
    }
};

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int N, M;
    cin >> N >> M;
    vector<vector<int>> G(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        G[a].push_back(b);
    }
    SCC scc(G);
    cout << scc.num << "\n";
    vector<vector<int>> v(scc.num);
    for (int i = 0; i < N; i++) v[scc[i]].push_back(i);
    for (int i = 0; i < scc.num; i++) {
        cout << v[i].size();
        for (int j : v[i]) cout << " " << j;
        cout << "\n";
    }
}