Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

6 7
1 4
5 2
3 0
5 5
4 1
0 3
4 2

Sample Output 1

4
1 5
2 4 1
1 2
2 3 0

Solution in Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};

use petgraph::algo::kosaraju_scc;
use petgraph::graph::DiGraph;

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(u32, u32); m]
    }
    let mut thegraph = DiGraph::<(), ()>::from_edges(&ab);
    while thegraph.node_count() < n {
        thegraph.add_node(());
    }
    let scc_list = kosaraju_scc(&thegraph);
    let k = scc_list.len();
    println!("{}", k);
    for i in (0..k).rev() {
        let l = scc_list[i].len();
        print!("{}", l);
        for j in 0..l {
            print!(" {}", scc_list[i][j].index());
        }
        println!();
    }
}

use num_traits::{pow, One};
use std::ops::{Add, Div, Mul, Sub};

const MODULUS: usize = 1000000007;

#[derive(Clone, Copy, PartialEq, Debug)]
struct ModP(usize);

impl One for ModP {
    fn one() -> Self {
        return ModP(1);
    }
}
impl Add for ModP {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        return ModP((self.0 + rhs.0) % MODULUS);
    }
}
impl Sub for ModP {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        return ModP((self.0 + MODULUS - rhs.0) % MODULUS);
    }
}
impl Mul for ModP {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        return ModP((self.0 * rhs.0) % MODULUS);
    }
}
impl Div for ModP {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        if rhs.0 == 0 {
            panic!("Tried to divide by ModP(0)!");
        }
        let rhs_inv = pow(rhs, MODULUS - 2);
        return self * rhs_inv;
    }
}

// Number-theoretic transformation
// The length of f must be a power of 2
// and zeta must be a primitive f.len()th root of unity
// start and skip should be 0 and 1 respectively for the root invocation
// The inverse can be calculated by doing the same
// with the original zeta's inverse as zeta
// and dividing by f.len()
fn number_theoretic_transformation(
    f: &Vec<ModP>,
    start: usize,
    skip: usize,
    zeta: ModP,
) -> Vec<ModP> {
    let n = f.len() / skip;
    if n == 1 {
        return vec![f[start]];
    }
    let g0 = number_theoretic_transformation(f, start, skip * 2, zeta * zeta);
    let g1 = number_theoretic_transformation(f, start + skip, skip * 2, zeta * zeta);
    let mut pow_zeta = ModP(1);
    let mut g = Vec::new();
    for i in 0..n {
        g.push(g0[i % (n / 2)] + pow_zeta * g1[i % (n / 2)]);
        pow_zeta = pow_zeta * zeta;
    }
    return g;
}

// BIT from https://github.com/rust-lang-ja/atcoder-rust-base/blob/ja-all-enabled/examples/abc157-e-proconio.rs
// It requires commutativity so that "plus" operation works
use alga::general::{AbstractGroupAbelian, Additive, Operator};
use std::marker::PhantomData;
use std::ops::{RangeInclusive, RangeTo, RangeToInclusive};

struct FenwickTree<A, O> {
    partial_sums: Vec<A>,
    phantom_operator: PhantomData<O>,
}

impl<A: AbstractGroupAbelian<O>, O: Operator> FenwickTree<A, O> {
    fn new(n: usize) -> Self {
        Self {
            partial_sums: vec![A::identity(); n],
            phantom_operator: PhantomData,
        }
    }

    fn operate_to_index(&mut self, i: usize, x: &A) {
        let mut i1 = i + 1;
        while i1 <= self.partial_sums.len() {
            self.partial_sums[i1 - 1] = self.partial_sums[i1 - 1].operate(x);
            // add "the last nonzero bit" to i1
            i1 += 1 << i1.trailing_zeros();
        }
    }
}

trait RangeQuery<T> {
    type Output;
    fn query(&self, r: T) -> Self::Output;
}

impl<A: AbstractGroupAbelian<O>, O: Operator> RangeQuery<RangeToInclusive<usize>>
    for FenwickTree<A, O>
{
    type Output = A;
    fn query(&self, range: RangeToInclusive<usize>) -> A {
        let mut sum = A::identity();
        let mut i1 = range.end + 1;
        while i1 > 0 {
            sum = sum.operate(&self.partial_sums[i1 - 1]);
            i1 -= 1 << i1.trailing_zeros();
        }
        return sum;
    }
}

impl<A: AbstractGroupAbelian<O>, O: Operator> RangeQuery<RangeTo<usize>> for FenwickTree<A, O> {
    type Output = A;
    fn query(&self, range: RangeTo<usize>) -> A {
        if range.end == 0 {
            return A::identity();
        } else {
            return self.query(..=range.end - 1);
        }
    }
}

impl<A: AbstractGroupAbelian<O>, O: Operator> RangeQuery<RangeInclusive<usize>>
    for FenwickTree<A, O>
{
    type Output = A;
    fn query(&self, range: RangeInclusive<usize>) -> A {
        return self
            .query(..=*range.end())
            .operate(&self.query(..*range.start()).two_sided_inverse());
    }
}

use std::cell::Cell;

#[derive(Debug, Clone)]
struct EquivalenceRelation {
    parent: Vec<Cell<usize>>,
    rank: Vec<Cell<usize>>,
}

impl EquivalenceRelation {
    fn new(n: usize) -> Self {
        let mut parent = Vec::with_capacity(n);
        for i in 0..n {
            parent.push(Cell::new(i));
        }
        let rank = vec![Cell::new(0); n];
        return Self { parent, rank };
    }

    fn make_equivalent(&mut self, a: usize, b: usize) {
        let volume = self.parent.len();
        if a >= volume || b >= volume {
            panic!(
                "Tried to make {} and {} equivalent but there are only {} elements",
                a, b, volume
            );
        }
        let aa = self.find(a);
        let bb = self.find(b);
        if aa == bb {
            return;
        }
        let aarank = self.rank[aa].get();
        let bbrank = self.rank[bb].get();
        if aarank > bbrank {
            self.parent[bb].set(aa);
        // self.rank[aa] = aarank.max(bbrank + 1);
        } else {
            self.parent[aa].set(bb);
            self.rank[bb].set(bbrank.max(aarank + 1));
        }
    }

    fn find(&self, a: usize) -> usize {
        let volume = self.parent.len();
        if a >= volume {
            panic!("Tried to find {} but there are only {} elements", a, volume);
        }
        let b = self.parent[a].get();
        if b == a {
            return a;
        } else {
            let c = self.find(b);
            self.parent[a].set(c);
            return c;
        }
    }

    fn are_equivalent(&self, a: usize, b: usize) -> bool {
        return self.find(a) == self.find(b);
    }
}