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.*;
import java.math.BigDecimal;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.logging.SimpleFormatter;


public class Main1 {

    static  class pair implements Comparable<pair>{
        int a ,ind ;

        pair(int a , int ind){
            this.a = a ;
            this.ind = ind ;
        }

        @Override
        public int compareTo(pair o) {
            if (this.a == o.a)
                return this.ind - o.ind ;
            return this.a - o.a ;
        }
    }

    static StringBuilder sb= new StringBuilder() ;

    static void printer(ArrayList<Integer> list) {
        sb.append(list.size() + " ") ;
        for (int i = 0; i <list.size() ; i++) {
            sb.append(list.get(i) + " ") ;
        }
        sb.append("\n") ;
    }

    public static void main(String[] args) {

        try {
            FastScanner in = new FastScanner();
            PrintWriter out = new PrintWriter(System.out);


            int n = in.nextInt() ;
            pair a[] = new pair[n];
            for (int i = 0; i <n ; i++) {
                a[i] = new pair(in.nextInt() , i) ;
            }
            Arrays.sort(a);
            int tt = 0 ;

            boolean vis[] = new boolean[n] ;

            for (int i = 0; i <n ; i++) {
                if (!vis[i]){
                    tt++ ;
                    ArrayList<Integer> lst = new ArrayList<>() ;
                    while (!vis[i]){
                        vis[i] = true ;
                        lst.add(i+1) ;
                        i = a[i].ind ;
                    }
                    printer(lst);
                }
            }


            System.out.println(tt);
            System.out.print(sb);











            out.flush();
            out.close();
        } catch (Exception e) {
            return;
        }

    }


    static int findLCA(int a, int b, int par[][], int depth[]) {
        if (depth[a] > depth[b]) {
            a = a ^ b;
            b = a ^ b;
            a = a ^ b;
        }
        int diff = depth[b] - depth[a];
        for (int i = 19; i >= 0; i--) {
            if ((diff & (1 << i)) > 0) {
                b = par[b][i];
            }
        }
        if (a == b)
            return a;
        for (int i = 19; i >= 0; i--) {
            if (par[b][i] != par[a][i]) {
                b = par[b][i];
                a = par[a][i];
            }
        }
        return par[a][0];
    }

    static int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static void formArrayForBinaryLifting(int n, int par[][]) {
        for (int j = 1; j < 20; j++) {
            for (int i = 0; i < n; i++) {
                if (par[i][j - 1] == -1)
                    continue;
                par[i][j] = par[par[i][j - 1]][j - 1];
            }
        }
    }


    static void sort(int ar[]) {
        int n = ar.length;
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }


    private static int countDigits(long l) {
        if (l >= 1000000000000000000L) return 19;
        if (l >= 100000000000000000L) return 18;
        if (l >= 10000000000000000L) return 17;
        if (l >= 1000000000000000L) return 16;
        if (l >= 100000000000000L) return 15;
        if (l >= 10000000000000L) return 14;
        if (l >= 1000000000000L) return 13;
        if (l >= 100000000000L) return 12;
        if (l >= 10000000000L) return 11;
        if (l >= 1000000000L) return 10;
        if (l >= 100000000L) return 9;
        if (l >= 10000000L) return 8;
        if (l >= 1000000L) return 7;
        if (l >= 100000L) return 6;
        if (l >= 10000L) return 5;
        if (l >= 1000L) return 4;
        if (l >= 100L) return 3;
        if (l >= 10L) return 2;
        return 1;
    }


    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                //            boolean success = false;
                //            if (stringBuilderValueField != null) {
                //                try {
                //                    char[] value = (char[]) stringBuilderValueField.get(cache);
                //                    os.write(value, 0, cache.length());
                //                    success = true;
                //                } catch (Exception e) {
                //                }
                //            }
                //            if (!success) {
                os.append(cache);
                //            }
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }


        long nextLong() {
            return Long.parseLong(next());
        }
    }


}