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.util.*;
import java.io.*;

public class Codeforces {

    InputStream is;
    PrintWriter out;
    String INPUT = "";

//----------------------------------------------------------------------------------------------------//\
    
    void solve() {
        int n=ni();
        int a[]=na(n);
        Map<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            map.put(a[i], i);
        }
       
        Arrays.sort(a);
        Dsu uf=new Dsu(n);
        boolean sorted=true;
        for (int i = 0; i < n; i++) {
            int j=map.get(a[i]);
            if(i!=j)sorted=false;
            uf.union(i,j);
        }
        map = new HashMap<>();
        int k=uf.count();
       ArrayList<ArrayList<Integer> > al =new ArrayList<>(k);
        int idx=0;
        for (int i = 0; i < n; i++) {
            int r=uf.root(i);
            if(!map.containsKey(r)){
                ArrayList<Integer> l = new ArrayList<Integer>();
                l.add(i+1);
                map.put(r, idx);
                al.add(idx,l);
                idx++;
            }
            else {
                int j=map.get(r);
                al.get(j).add(i+1);
            }
        }
        StringBuilder sb = new StringBuilder();
        sb.append(k);
        for (List<Integer> l : al) {
            sb.append("\n"+l.size()+" ");
            for (Integer x : l) {
                sb.append(x+" ");
            }
        }
        out.println(sb);
        /*if(sorted){
            out.println(n);
            for (int i = 1; i <=n; i++) {
                out.println(1+" "+i);
            }
            return;
        }
        Set<Integer> set = new HashSet<Integer>();
        List<List<Integer>> ll = new ArrayList<>();
        
        for (int i = 0; i < n; i++) {
            int r=uf.root(i);
            if(!set.contains(r)){
                set.add(r);
                List<Integer> al = new ArrayList<Integer>();
                for (int j = i; j < n; j++) {
                    if(uf.root(j)==r)al.add(j+1);
                }
                ll.add(al);
            }
        }
        out.println(ll.size());
        for (List<Integer> list : ll) {
            out.print(list.size()+" ");
            for (int l : list) {
                out.print(l+" ");
            }
            out.println();
        }*/
        
       
    }
//----------------------------------------------------------------------------------------------------//
    boolean isPrime(int n) {
        if (n <= 1) {
            return false;
        }
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }

    Vector<Integer> sieveOfEratosthenes(int n) {
        boolean[] prime = new boolean[n + 1];
        for (int i = 0; i < n; i++) {
            prime[i] = true;
        }
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int j = p * p; j <= n; j += p) {
                    prime[j] = false;
                }
            }
        }
        Vector<Integer> v = new Vector<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                v.add(i);
            }
        }
        return v;
    }

    void swap(int a[], int l, int r) {
        int temp = a[l];
        a[l] = a[r];
        a[r] = temp;
    }

    long nCr(int n, int k) {
        long C[] = new long[k + 1];
        // nC0 is 1 
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = Math.min(i, k); j > 0; j--) {
                C[j] = C[j] + C[j - 1];
            }
        }
        return C[k];
    }

    int gcd(int s, int l) {
        if (s == 0) {
            return l;
        }

        return gcd(l % s, s);
    }

    

    public HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        // Create a list from elements of HashMap 
        List<Map.Entry<Integer, Integer>> list
                = new LinkedList<>(hm.entrySet());

        //->change o1,o2 for reverseorder
        Collections.sort(list, (Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) -> (o1.getValue()).compareTo(o2.getValue()));

        // put data from sorted list to hashmap  
        HashMap<Integer, Integer> temp = new LinkedHashMap<>();
        list.forEach((aa) -> {
            temp.put(aa.getKey(), aa.getValue());
        });
        return temp;
    }

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

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

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

    private byte[] inbuf = new byte[1024];
    public 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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) {
            System.out.println(Arrays.deepToString(o));

        }
    }

    class Pair {

        /*SORTING PAIRS BY COMPARING Y OF PAIR.
    Pair[] p=new Pair[n];
    p[i]=new Pair(i,ni());
    Arrays.sort(p,( p1, p2) -> {return p1.y-p2.y;});
         */
        int x;
        int y;

        Pair(int u, int v) {
            x = u;
            y = v;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Pair)) {
                return false;
            }
            Pair key = (Pair) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

    }

    class Dsu {

        int par[];
        int size[];
        int cnt;
        Set<Integer> roots = new HashSet<>();

        //boolean belongs[];
        Dsu(int n) {
            cnt=n;//cnt=0;
            par = new int[n];
            size = new int[n];
            //belongs=new boolean[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
                size[i] = 1;
                //belongs[i]=false;
            }
        }

        int root(int i) {
            if (i == par[i]) {
                return i;
            }
            return par[i] = root(par[i]);
        }

        boolean find(int p, int q) {
            return root(p) == root(q);
        }

        void union(int p, int q) {
            
            int a = root(p);
            int b = root(q);
            
            if(a!=b){
                cnt--;
            }
            /*if(!belongs[p]&&!belongs[q])cnt++;
            else if(belongs[p]&&belongs[q]){
                if(a!=b)cnt--;
            }
            belongs[p]=belongs[q]=true;*/
            
            if (a == b)return;
            if (size[a] < size[b]) {
                int temp = a;
                a = b;
                b = temp;
            }
            par[b] = a;
            size[a] += size[b];
            roots.add(a);
            if(roots.contains(b))roots.remove(b);
        }
        Set<Integer> getRoots(){
            return roots;
        }
        int count() { 
            return cnt;
        }

    }
}
//isPrime(int)
//Vector<Integer> sieveOfEratosthenes(int n){PRIME NO <=n}
//swap(arr,i,j)
//HashMap sortByValue(map);
//long comb=nCr(5,2);
//int gcd(s,l);
//Pair p=new Pair(x,y);
// Dsu dsu=new Dsu(n);