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.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.*;

public class Sorting_by_subsequence {
public static void main(String[] args){
 InputReader in=new InputReader(System.in);
 PrintWriter pw=new PrintWriter(System.out);
 int n=in.readInt();
 long[] arr=new long[n+1];
 Pair[] p =new Pair[n+1];
 ArrayList<Integer>[] gr=new ArrayList[n+1];
 p[0]=new Pair(0, Long.MIN_VALUE);
 for(int i=1;i<=n;i++){
	 p[i]=new Pair(i, in.readLong());
 }
Arrays.sort(p);

boolean[] visited=new boolean[n+1];
int count=0;
for(int i=1;i<=n;i++) {
	gr[i]=new ArrayList<Integer>();
	if(visited[p[i].x] == false) {
			count++;
		int s=p[i].x;
		gr[i].add(s);
		visited[s]=true;
		int id=p[i].x;
		while(p[id].x != s) {
			visited[p[id].x] =true;
			gr[i].add(p[id].x);
			id = p[id].x;
		}
	}
}
pw.println(count);
for(int i=1;i<=n;i++) {
	if(gr[i].size() !=0) {
	pw.print(gr[i].size()+" ");
	
	for(int j:gr[i]) {
		pw.print(j+" ");
	}
	pw.println();
	}
}
 pw.close();
}
static long fib(long n)
{
long F[][] = new long[][]{{1,1},{1,0}};
if (n == 0)
    return 0;
power(F, n-1);
 
   return F[0][0];
}
  
 /* Helper function that multiplies 2 matrices F and M of size 2*2, and
 puts the multiplication result back to F[][] */
static void multiply(long F[][], long M[][])
{
long x =  F[0][0]*M[0][0] + F[0][1]*M[1][0];
long y =  F[0][0]*M[0][1] + F[0][1]*M[1][1];
long z =  F[1][0]*M[0][0] + F[1][1]*M[1][0];
long w =  F[1][0]*M[0][1] + F[1][1]*M[1][1];
  
F[0][0] = x%1000000007;
F[0][1] = y%1000000007;
F[1][0] = z%1000000007;
F[1][1] = w%1000000007;
}


static void power(long F[][], long n)
{
long i;
long M[][] = new long[][]{{1,1},{1,0}};
 
// n - 1 times multiply the matrix to {{1,0},{0,1}}
for (i = 2; i <= n; i++)
    multiply(F, M);
}
static long modulo(long a,long b,long c) {
	long x=1;
	long y=a;
	while(b > 0){
		if(b%2 == 1){
			x=(x*y)%c;
		}
		y = (y*y)%c; // squaring the base
		b /= 2;
	}
	return  x%c;
}
static long gcd(long x, long y)
{
	if(x==0)
		return y;
	if(y==0)
		return x;
	long r=0, a, b;
	a = (x > y) ? x : y; // a is greater number
	b = (x < y) ? x : y; // b is smaller number
	r = b;
	while(a % b != 0)
	{
		r = a % b;
		a = b;
		b = r;
	}
	return r;
}
static class Pair implements Comparable<Pair>{
	int x;
	long y;
	Pair(int xx,long yy){
		x=xx;y=yy;
	}
	@Override
	public int compareTo(Pair o) {
		if(Long.compare(o.y, this.y)==0){
			return Integer.compare(this.x, o.x);
		}
		else{
			return Long.compare(this.y, o.y);
		}
	}
}
static  class InputReader
{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public InputReader(InputStream stream)
    {
        this.stream = stream;
    }
 
    public int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read(buf);
            } catch (IOException e)
            {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
 
    public int readInt()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public String readString()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do
        {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
    public String readLine() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }
    
 
    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    public boolean isSpaceChar(int c)
    {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next()
    {
        return readString();
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }
}
}