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 JAVA):

Solution:
public class Main {
    public static void main(String[] args) throws Exception {
        var sc = new FastScanner();
        var pw = new FastPrintStream();
        solve(sc, pw);
        sc.close();
        pw.flush();
        pw.close();
    }

    public static void solve(FastScanner sc, FastPrintStream pw) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        var scc = new SCC(n);
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            scc.addEdge(a, b);
        }
        int[][] g = scc.build();
        int k = g.length;
        pw.println(k);
        for (int i = 0; i < k; i++) {
            int l = g[i].length;
            pw.print(l);
            for (int j = 0; j < l; j++) {
                pw.print(' ').print(g[i][j]);
            }
            pw.println();
        }
    }
}

class SCC {

    static class Edge {
        int from, to;
        public Edge(int from, int to) {
            this.from = from; this.to = to;
        }
    }

    final int n;
    int m;
    final java.util.ArrayList<Edge> unorderedEdges;
    final int[] start;
    final int[] ids;
    boolean hasBuilt = false;

    public SCC(int n) {
        this.n = n;
        this.unorderedEdges = new java.util.ArrayList<>();
        this.start = new int[n + 1];
        this.ids = new int[n];
    }

    public void addEdge(int from, int to) {
        unorderedEdges.add(new Edge(from, to));
        start[from + 1]++;
        this.m++;
    }

    public int id(int i) {
        if (!hasBuilt) {
            throw new UnsupportedOperationException(
                "Graph hasn't been built."
            );
        }
        return ids[i];
    }
    
    public int[][] build() {
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        Edge[] orderedEdges = new Edge[m];
        int[] count = new int[n + 1];
        System.arraycopy(start, 0, count, 0, n + 1);
        for (Edge e : unorderedEdges) {
            orderedEdges[count[e.from]++] = e;
        }
        int nowOrd = 0;
        int groupNum = 0;
        int k = 0;
        // parent
        int[] par = new int[n];
        int[] vis = new int[n];
        int[] low = new int[n];
        int[] ord = new int[n];
        java.util.Arrays.fill(ord, -1);
        // u = lower32(stack[i]) : visiting vertex
        // j = upper32(stack[i]) : jth child
        long[] stack = new long[n];
        // size of stack
        int ptr = 0;
        // non-recursional DFS
        for (int i = 0; i < n; i++) {
            if (ord[i] >= 0) continue;
            par[i] = -1;
            // vertex i, 0th child.
            stack[ptr++] = 0l << 32 | i;
            // stack is not empty
            while (ptr > 0) {
                // last element
                long p = stack[--ptr];
                // vertex
                int u = (int) (p & 0xffff_ffffl);
                // jth child
                int j = (int) (p >>> 32);
                if (j == 0) { // first visit
                    low[u] = ord[u] = nowOrd++;
                    vis[k++] = u;
                }
                if (start[u] + j < count[u]) { // there are more children
                    // jth child
                    int to = orderedEdges[start[u] + j].to;
                    // incr children counter
                    stack[ptr++] += 1l << 32;
                    if (ord[to] == -1) { // new vertex
                        stack[ptr++] = 0l << 32 | to;
                        par[to] = u;
                    } else { // backward edge
                        low[u] = Math.min(low[u], ord[to]);
                    }
                } else { // no more children (leaving)
                    while (j --> 0) {
                        int to = orderedEdges[start[u] + j].to;
                        // update lowlink
                        if (par[to] == u) low[u] = Math.min(low[u], low[to]);
                    }
                    if (low[u] == ord[u]) { // root of a component
                        while (true) { // gathering verticies
                            int v = vis[--k];
                            ord[v] = n;
                            ids[v] = groupNum;
                            if (v == u) break;
                        }
                        groupNum++; // incr the number of components
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            ids[i] = groupNum - 1 - ids[i];
        }
        
        int[] counts = new int[groupNum];
        for (int x : ids) counts[x]++;
        int[][] groups = new int[groupNum][];
        for (int i = 0; i < groupNum; i++) {
            groups[i] = new int[counts[i]];
        }
        for (int i = 0; i < n; i++) {
            int cmp = ids[i];
            groups[cmp][--counts[cmp]] = i;
        }
        hasBuilt = true;
        return groups;
    }
}

class FastPrintStream implements AutoCloseable {
    private static final int BUF_SIZE = 1 << 15;
    private final byte[] buf = new byte[BUF_SIZE];
    private int ptr = 0;
    private final java.lang.reflect.Field strField;
    private final java.nio.charset.CharsetEncoder encoder;

    private java.io.OutputStream out;

    public FastPrintStream(java.io.OutputStream out) {
        this.out = out;
        java.lang.reflect.Field f;
        try {
            f = java.lang.String.class.getDeclaredField("value");
            f.setAccessible(true);
        } catch (NoSuchFieldException | SecurityException e) {
            f = null;
        }
        this.strField = f;
        this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
    }

    public FastPrintStream(java.io.File file) throws java.io.IOException {
        this(new java.io.FileOutputStream(file));
    }

    public FastPrintStream(java.lang.String filename) throws java.io.IOException {
        this(new java.io.File(filename));
    }

    public FastPrintStream() {
        this(System.out);
        try {
            java.lang.reflect.Field f = java.io.PrintStream.class.getDeclaredField("autoFlush");
            f.setAccessible(true);
            f.set(System.out, false);
        } catch (IllegalAccessException | IllegalArgumentException | NoSuchFieldException e) {
            // ignore
        }
    }

    public FastPrintStream println() {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) '\n';
        return this;
    }

    public FastPrintStream println(java.lang.Object o) {
        return print(o).println();
    }

    public FastPrintStream println(java.lang.String s) {
        return print(s).println();
    }

    public FastPrintStream println(char[] s) {
        return print(s).println();
    }

    public FastPrintStream println(char c) {
        return print(c).println();
    }

    public FastPrintStream println(int x) {
        return print(x).println();
    }

    public FastPrintStream println(long x) {
        return print(x).println();
    }

    public FastPrintStream println(double d, int precision) {
        return print(d, precision).println();
    }

    private FastPrintStream print(byte[] bytes) {
        int n = bytes.length;
        if (ptr + n > BUF_SIZE) {
            internalFlush();
            try {
                out.write(bytes);
            } catch (java.io.IOException e) {
                throw new RuntimeException();
            }
        } else {
            System.arraycopy(bytes, 0, buf, ptr, n);
            ptr += n;
        }
        return this;
    }

    public FastPrintStream print(java.lang.Object o) {
        return print(o.toString());
    }

    public FastPrintStream print(java.lang.String s) {
        if (strField == null) {
            return print(s.getBytes());
        } else {
            try {
                return print((byte[]) strField.get(s));
            } catch (IllegalAccessException e) {
                return print(s.getBytes());
            }
        }
    }

    public FastPrintStream print(char[] s) {
        try {
            return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
        } catch (java.nio.charset.CharacterCodingException e) {
            byte[] bytes = new byte[s.length];
            for (int i = 0; i < s.length; i++) {
                bytes[i] = (byte) s[i];
            }
            return print(bytes);
        }
    }

    public FastPrintStream print(char c) {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) c;
        return this;
    }

    public FastPrintStream print(int x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(long x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(double d, int precision) {
        if (d < 0) {
            print('-');
            d = -d;
        }
        d += Math.pow(10, -d) / 2;
        print((long) d).print('.');
        d -= (long) d;
        for(int i = 0; i < precision; i++){
            d *= 10;
            print((int) d);
            d -= (int) d;
        }
        return this;
    }

    private void internalFlush() {
        try {
            out.write(buf, 0, ptr);
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            out.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static int len(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }

    private static int len(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
}

class FastScanner implements AutoCloseable {
    private final java.io.InputStream in;
    private final byte[] buf = new byte[2048];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(java.io.InputStream in) {
        this.in = in;
    }

    public FastScanner() {
        this(System.in);
    }

    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {
            buflen = in.read(buf);
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
        return buflen > 0;
    }

    private int readByte() {
        return hasNextByte() ? buf[ptr++] : -1;
    }

    public boolean hasNext() {
        while (hasNextByte() && !(32 < buf[ptr] && buf[ptr] < 127)) ptr++;
        return hasNextByte();
    }

    private StringBuilder nextSequence() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        for (int b = readByte(); 32 < b && b < 127; b = readByte()) {
            sb.appendCodePoint(b);
        }
        return sb;
    }

    public String next() {
        return nextSequence().toString();
    }

    public String next(int len) {
        return new String(nextChars(len));
    }

    public char nextChar() {
        if (!hasNextByte()) throw new java.util.NoSuchElementException();
        return (char) readByte();
    }

    public char[] nextChars() {
        StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (32 < b && b < 127 && i < len) {
            s[i++] = (char) b; b = readByte();
        }
        if (i != len) {
            throw new java.util.NoSuchElementException(
                String.format("Next token has smaller length than expected.", len)
            );
        }
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n = n * 10 + b - '0';
            } else if (b == -1 || !(32 < b && b < 127)) {
                return minus ? -n : n;
            } else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {
        return Math.toIntExact(nextLong());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public void close() {
        try {
            in.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }
}