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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.TreeMap;

public class Main {

  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    int[] A = in.nextIntArray(N);
    int[] B = new int[N];
    System.arraycopy(A, 0, B, 0, N);
    Arrays.sort(B);
    UnionFind uf = new UnionFind(N);
    for (int i = 0; i < N; i++) {
      int x = Arrays.binarySearch(B, A[i]);
      uf.unite(x, i);
    }

    TreeMap<Integer, ArrayList<Integer>> map = new TreeMap<>();
    for (int i = 0; i < N; i++) {
      ArrayList<Integer> list = map.getOrDefault(uf.find(i), new ArrayList<>());
      list.add(i);
      map.put(uf.find(i), list);
    }

    out.println(map.size());
    for (ArrayList<Integer> list : map.values()) {
      out.print(list.size());
      for (int i : list) {
        out.print(" " + (i + 1));
      }
      out.println();
    }


  }

  class UnionFind {

    // par[i]：データiが属する木の親の番号。i == par[i]のとき、データiは木の根ノードである
    private int[] par;
    // sizes[i]：根ノードiの木に含まれるデータの数。iが根ノードでない場合は無意味な値となる
    private int[] sizes;

    // 木の数
    private int size;

    UnionFind(int n) {
      par = new int[n];
      sizes = new int[n];
      size = n;
      Arrays.fill(sizes, 1);
      // 最初は全てのデータiがグループiに存在するものとして初期化
      for (int i = 0; i < n; i++) {
        par[i] = i;
      }
    }

    /**
     * データxが属する木の根を得る
     */
    int find(int x) {
      if (x == par[x]) {
        return x;
      }
      return par[x] = find(par[x]);  // 根を張り替えながら再帰的に根ノードを探す
    }

    /**
     * 2つのデータx, yが属する木をマージする。 マージが必要なら true を返す
     */
    boolean unite(int x, int y) {
      // データの根ノードを得る
      x = find(x);
      y = find(y);

      // 既に同じ木に属しているならマージしない
      if (x == y) {
        return false;
      }

      // xの木がyの木より大きくなるようにする
      if (sizes[x] < sizes[y]) {
        int tx = x;
        x = y;
        y = tx;
      }

      // xがyの親になるように連結する
      par[y] = x;
      sizes[x] += sizes[y];
      sizes[y] = 0;  // sizes[y]は無意味な値となるので0を入れておいてもよい

      size--;
      return true;
    }

    /**
     * 2つのデータx, yが属する木が同じならtrueを返す
     */
    boolean isSame(int x, int y) {
      return find(x) == find(y);
    }

    /**
     * データxが含まれる木の大きさを返す
     */
    int partialSizeOf(int x) {
      return sizes[find(x)];
    }

    /**
     * 木の数を返す
     */
    int size() {
      return size;
    }
  }

  public static void main(String[] args) {
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(System.out);
    new Main().solve(in, out);
    out.close();
  }

  private static class FastScanner {

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) {
        return buffer[ptr++];
      } else {
        return -1;
      }
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
        ptr++;
      }
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) {
        throw new 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 *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextInt();
      }
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextLong();
      }
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) {
        array[i] = next();
      }
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) {
        array[i] = next().toCharArray();
      }
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}