Problem: You are given a sequence a1, a2, ..., an consisting of different integers. It is required to split this sequence into the maximum number of subsequences such that after sorting integers in each of them in increasing order, the total sequence also will be sorted in increasing order.

Sorting integers in a subsequence is a process such that the numbers included in a subsequence are ordered in increasing order, and the numbers which are not included in a subsequence don't change their places.

Every element of the sequence must appear in exactly one subsequence.

Input

The first line of input data contains integer n (1 ≤ n ≤ 105) — the length of the sequence.

The second line of input data contains n different integers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the elements of the sequence. It is guaranteed that all elements of the sequence are distinct.

Output

In the first line print the maximum number of subsequences k, which the original sequence can be split into while fulfilling the requirements.

In the next k lines print the description of subsequences in the following format: the number of elements in subsequence ci (0 < ci ≤ n), then ci integers l1, l2, ..., lci (1 ≤ lj ≤ n) — indices of these elements in the original sequence. 

Indices could be printed in any order. Every index from 1 to n must appear in output exactly once.

If there are several possible answers, print any of them.

Examples

Input

6
3 2 1 6 5 4


Output

4
2 1 3
1 2
2 4 6
1 5


Input

6
83 -75 -49 11 37 62


Output

1
6 1 2 3 4 5 6

Note

In the first sample output:

After sorting the first subsequence we will get sequence 1 2 3 6 5 4.

Sorting the second subsequence changes nothing.

After sorting the third subsequence we will get sequence 1 2 3 4 5 6.

Sorting the last subsequence changes nothing.

Solution (in JAVA):

Solution:
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

/**
 * http://codeforces.com/problemset/problem/844/C
 */
public class SortSub {
    InputStream is;
    PrintWriter out;
    String INPUT = "";

    long mod = 1000000007;


    int[] rank, parent;
    int n;

    // Returns representative of x's set
    int find(int x) {
        // Finds the representative of the set
        // that x is an element of
        if (parent[x] != x) {
            // if x is not the parent of itself
            // Then x is not the representative of
            // his set,
            parent[x] = find(parent[x]);

            // so we recursively call Find on its parent
            // and move i's node directly under the
            // representative of this set
        }
        return parent[x];
    }

    // Unites the set that includes x and the set
    // that includes x
    void union(int x, int y) {
        // Find representatives of two sets
        int xRoot = find(x), yRoot = find(y);

        // Elements are in the same set, no need
        // to unite anything.
        if (xRoot == yRoot)
            return;

        // If x's rank is less than y's rank
        if (rank[xRoot] < rank[yRoot])

            // Then move x under y  so that depth
            // of tree remains less
            parent[xRoot] = yRoot;

            // Else if y's rank is less than x's rank
        else if (rank[yRoot] < rank[xRoot])

            // Then move y under x so that depth of
            // tree remains less
            parent[yRoot] = xRoot;

        else // if ranks are the same
        {
            // Then move y under x (doesn't matter
            // which one goes where)
            parent[yRoot] = xRoot;

            // And increment the the result tree's
            // rank by 1
            rank[xRoot] = rank[xRoot] + 1;
        }
    }

    void solve() {
        n = ni();
        int[] ar = na(n);

        List<Integer> li = new ArrayList();
        for (int k : ar) {
            li.add(k);
        }

        Collections.sort(li);

        Map<Integer, Integer> pos = new HashMap();

        for (int i = 0; i < n; i++) {
            pos.put(li.get(i), i);
        }

        for (int i = 0; i < n; i++) {
            ar[i] = pos.get(ar[i]);
        }

        parent = new int[n];
        rank = new int[n];


        for (int i = 0; i < n; i++) {
            parent[i] = i;
        }
        for (int i = 0; i < n; i++) {
            if (ar[i] != i) {
                union(ar[i], i);
            }
        }
        Map<Integer, List<Integer>> map = new HashMap();
        for (int i = 0; i < n; i++) {
            int parent = find(i);
            map.putIfAbsent(parent, new ArrayList());
            map.get(parent).add(i+1);
        }
        out.println(map.size());
        map.values().forEach(list -> {
            out.print(list.size());
            list.forEach(item -> out.print(" " + item));
            out.println();
        });
    }

    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }

    public static void main(String[] args) throws Exception {
        new SortSub().run();
    }

    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static void tr(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
}