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.awt.List;
import java.io.*;
import java.lang.*;
	
public class code1
	{
 
		public static void main(String[] args)
		{
			InputReader in = new InputReader(System.in);
			PrintWriter pw = new PrintWriter(System.out);
			
			//Code starts..
		
		
			
			
			int n = in.nextInt();
			int[] a = new int[n];
			int[] srt = new int[n];
			for(int i=0; i<n; i++)
			{
				a[i] = in.nextInt();
				srt[i] = a[i];
			}
			
			Arrays.sort(srt);
			HashMap<Integer, Integer> map = new HashMap<>();
			for(int i=0; i<n; i++)
			{
				map.put(srt[i], i);
			}
			int[] cng = new int[n];
			
			
			for(int i=0; i<n; i++)
				cng[i] = map.get(a[i]);
			
			int[] set = new int[n];
			int count = 1;
			for(int i=0; i<n; i++)
			{
				if(set[i]==0)
				{
					set[i] = count;
					int j = cng[i];
					while(j!=i)
					{
						set[j] = count;
						j = cng[j];
					}
					count++;
					
				}
				
			}
			ArrayList<Integer>[] list = new ArrayList[count];
			for(int i=0; i<count; i++)
				list[i] = new ArrayList<>();
			
			for(int i=0; i<n; i++)
				list[set[i]].add(i+1);
			
			pw.println(count-1);
			for(int i=1; i<count; i++)
			{
				pw.print(list[i].size()+" ");
				for(int j=0; j<list[i].size(); j++)
					pw.print(list[i].get(j)+" ");
				 pw.println();
			}
				
			
			
			
			//Code ends....
			
			pw.flush();
			pw.close();
		}
	
		
		static class InputReader 
		{
			 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) 
			{
				this.stream = stream;
			}
	 
			public int snext() 
			{
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) 
				{
					curChar = 0;
					try 
					{
						snumChars = stream.read(buf);
					} 
					catch (IOException e) 
					{
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public int nextInt() 
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-')
			    {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) 
			{
				int a[] = new int[n];
				for (int i = 0; i < n; i++) 
				{
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() 
			{
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}
	 
			public boolean isSpaceChar(int c) 
			{
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) 
			{
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter
		    {
				public boolean isSpaceChar(int ch);
			}
		}
		public static long c = 0;
		
		public static long mod = 1000000007;
		public static int d;
		public static int p;
		public static int q;
		public static boolean flag;
		public static long INF= Long.MAX_VALUE;
		
		public static long fun(int[] a, int[] b, int m,int n) {
			long result =0;
			for(int i=0; i<m; i++)
				for(int j=0; j<m; j++)
				{
					long[] fib  = new long[Math.max(2, n+2)];
					fib[1] = a[i];
					fib[2] = b[j];
					for(int k=3; k<=n; k++)
						fib[k] = (fib[k-1]%mod + fib[k-2]%mod)%mod;
					result = (result%mod + fib[n]%mod)%mod;
				}
			
			return result;
			
		}
		
		
		public static double slope(pair p1, pair p2)
		{
			double m = INF;
			if((p1.x - p2.x)!=0)
			m =  p1.y - p2.y/(p1.x - p2.x); 
			
			
			return Math.abs(m);
			
		}
		
		
		public static int count(String[] s, int f)
		{
			int count = 0;
			int n = s[0].length();
			
			if(f==1)
			{
			for(int i = 0; i<n; i++)
			{
				for(int j=0; j<n; j++)
				{
					if(i%2==0)
					{
						if(j%2==0 && s[i].charAt(j)=='0')
							count++;
						if(j%2==1 && s[i].charAt(j)=='1')
							count++;
					}
					if(i%2==1)
					{
						if(j%2==1 && s[i].charAt(j)=='0')
							count++;
						if(j%2==0 && s[i].charAt(j)=='1')
							count++;
					}
					
				}
			}
			}
			else
			{
			
			 count = 0;
			
			for(int i = 0; i<n; i++)
			{
				for(int j=0; j<n; j++)
				{
					if(i%2==1)
					{
						if(j%2==0 && s[i].charAt(j)=='0')
							count++;
						if(j%2==1 && s[i].charAt(j)=='1')
							count++;
					}
					if(i%2==0)
					{
						if(j%2==1 && s[i].charAt(j)=='0')
							count++;
						if(j%2==0 && s[i].charAt(j)=='1')
							count++;
					}
					
				}
			}
 
			}	
				
		
			return count;
			
			
			
		}
				
		public static  int gcd(int p2, int p22)
		{
		    if (p2 == 0)
		        return (int) p22;
		    return gcd(p22%p2, p2);
		}
		
			
	
		
		
		public static int findGCD(int arr[], int n)
		{
		    int result = arr[0];
		    for (int i=1; i<n; i++)
		        result = gcd(arr[i], result);
		 
		    return result;
		}
		
	
 
		public static void nextGreater(long[] a, int[] ans)
		{
			
			Stack<Integer> stk = new Stack<>();
			stk.push(0);
			
			
			for(int i=1; i<a.length; i++)
			{
				
				if(!stk.isEmpty())
				{
				int s = stk.pop();
				while(a[s]<a[i])
				{
					ans[s] = i;
					if(!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if(a[s]>=a[i])
					stk.push(s);
				}
				
				stk.push(i);
				
			}
			return;
			
		}
		
		public static void nextGreaterRev(long[] a, int[] ans)
		{
			
			int n = a.length;
			int[] pans = new int[n];
			Arrays.fill(pans, -1);
			long[] arev = new long[n];
			for(int i=0; i<n; i++)
				arev[i] = a[n-1-i];
			
			Stack<Integer> stk = new Stack<>();
			stk.push(0);
			
			
			for(int i=1; i<n; i++)
			{
				
				if(!stk.isEmpty())
				{
				int s = stk.pop();
				while(arev[s]<arev[i])
				{
					pans[s] = n - i-1;
					if(!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if(arev[s]>=arev[i])
					stk.push(s);
				}
				
				stk.push(i);
				
			}
			
			//for(int i=0; i<n; i++)
				//System.out.print(pans[i]+" ");
			
			for(int i=0; i<n; i++)
				ans[i] = pans[n-i-1];
			
			
			
			return;
			
		}
		
		
		public static void nextSmaller(long[] a, int[] ans)
		{
			
			Stack<Integer> stk = new Stack<>();
			stk.push(0);
			
			
			for(int i=1; i<a.length; i++)
			{
				
				if(!stk.isEmpty())
				{
				int s = stk.pop();
				while(a[s]>a[i])
				{
					ans[s] = i;
					if(!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if(a[s]<=a[i])
					stk.push(s);
				}
				
				stk.push(i);
				
			}
			return;
			
		}
		
		
		
		
	    public static long lcm(int[] numbers) {
	        long lcm = 1;
	        int divisor = 2;
	        while (true) {
	            int cnt = 0;
	            boolean divisible = false;
	            for (int i = 0; i < numbers.length; i++) {
	                if (numbers[i] == 0) {
	                    return 0;
	                } else if (numbers[i] < 0) {
	                    numbers[i] = numbers[i] * (-1);
	                }
	                if (numbers[i] == 1) {
	                    cnt++;
	                }
	                if (numbers[i] % divisor == 0) {
	                    divisible = true;
	                    numbers[i] = numbers[i] / divisor;
	                }
	            }
	            if (divisible) {
	                lcm = lcm * divisor;
	            } else {
	                divisor++;
	            }
	            if (cnt == numbers.length) {
	                return lcm;
	            }
	        }
	    }
		public static long fact(long n) {
			
			long factorial = 1;
			 for(int i = 1; i <= n; i++)
		        {
		            factorial *= i;
		        }
			 return factorial;
		}
		
public static void factSieve(int[] a, int n) {
			
			
			for(int i=2; i<=n; i+=2)
				a[i] = 2;
			
			
			for(int i=3; i<=n; i+=2)
			{
				if(a[i]==0)
				{
					a[i] = i;
					
					for(int j=i; j*i<=n; j++)
					{
						a[i*j] = i;	
					}
				}
			}
			
			int k = 1000;
			while(k!=1)
			{
				System.out.print(a[k]+" ");
				k /= a[k];
				
			}
		}
	
		
		public static int lowerLimit(int[] a, int n) {
			int ans = 0;
			
			int ll = 0;
			int rl = a.length-1;
		//	System.out.println(a[rl]+" "+n);
			if(a[0]>n)
				return 0;
			if(a[0]==n)
				return 1;
			else if(a[rl]<=n)
				return rl+1;
		
			while(ll<=rl)
			{
				
				int mid = (ll+rl)/2;
				if(a[mid]==n)
				{
					ans = mid + 1;
					break;
				}
				
				else if(a[mid]>n)
				{
					rl = mid-1;
					
				}
				else
				{
					ans = mid+1;
					ll = mid+1;
				}
			}
			
			return ans; 
		}
		
		
		public static long choose(long total, long choose){
		    if(total < choose)
		        return 0;
		    if(choose == 0 || choose == total)
		        return 1;
		    return (choose(total-1,choose-1)+choose(total-1,choose))%mod;
		}
		
		public static int[] suffle(int[] a,Random gen)
		{
			int n = a.length;
			for(int i=0;i<n;i++)
			{
				int ind = gen.nextInt(n-i)+i;
				int temp = a[ind];
				a[ind] = a[i];
				a[i] = temp;
			}
			return a;
		}
		
		public static int floorSearch(int arr[], int low, int high, int x)
		{
		    if (low > high)
		        return -1;
		 
		    if (x > arr[high])
		        return high;
		    int mid = (low+high)/2;
		 
		 
		    if (mid > 0 && arr[mid-1] < x && x < arr[mid])
		        return mid-1;
		 
		    if (x < arr[mid])
		        return floorSearch(arr, low, mid-1, x);
		 
		    return floorSearch(arr, mid+1, high, x);
		}
		
		
		public static void swap(int a, int b){
			int temp = a;
			a = b;
			b = temp;
		}
		public static ArrayList<Integer> primeFactorization(int n)
		{
			ArrayList<Integer> a =new ArrayList<Integer>();
			for(int i=2;i*i<=n;i++)
			{
				while(n%i==0)
				{
					a.add(i);
					n/=i;
				}
			}
			if(n!=1)
				a.add(n);
			return a;
		}
		
		
		public static void sieve(boolean[] isPrime,int n)
		{
			for(int i=1;i<n;i++)
				isPrime[i] = true;
			
			isPrime[0] = false;
			isPrime[1] = false;
			
			for(int i=2;i*i<n;i++)
			{
				if(isPrime[i] == true)
				{
					for(int j=(2*i);j<n;j+=i)
						isPrime[j] = false;
				}
			}
		}
		
		public static int lowerbound(ArrayList<Long> net, long c2) {
			int i=Collections.binarySearch(net, c2);
			if(i<0)
				i = -(i+2);
			return i;
			
			
		}
		public static int uperbound(ArrayList<Long> net, long c2) {
			int i=Collections.binarySearch(net, c2);
			if(i<0)
				i = -(i+1);
			return i;
			
			
		}
		
		
		public static int GCD(int a,int b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static long GCD(long a,long b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static void extendedEuclid(int A,int B)
		{
			if(B==0)
			{
				d = A;
				p = 1 ;
				q = 0;
			}
			else
			{
				extendedEuclid(B, A%B);
				int temp = p;
				p = q;
				q = temp - (A/B)*q;
			}
		}
		
		public static long LCM(long a,long b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int LCM(int a,int b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int binaryExponentiation(int x,int n)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		
		public static int[] countDer(int n)
	    {
	        int der[] = new int[n + 1];
	     
	        der[0] = 1;
	        der[1] = 0;
	        der[2] = 1;
	     
	        for (int i = 3; i <= n; ++i)
	            der[i] = (i - 1) * (der[i - 1] + der[i - 2]);
	     
	        // Return result for n
	        return der;
	    }
		
		
		 static long binomialCoeff(int n, int k)
		    {
		    long C[][] = new long[n+1][k+1];
		    int i, j;
		     
		        // Calculate  value of Binomial Coefficient in bottom up manner
		    for (i = 0; i <= n; i++)
		    {
		        for (j = 0; j <= Math.min(i, k); j++)
		        {
		            // Base Cases
		            if (j == 0 || j == i)
		                C[i][j] = 1;
		      
		            // Calculate value using previosly stored values
		            else
		                C[i][j] = C[i-1][j-1] + C[i-1][j];
		          }
		     }
		      
		    return C[n][k];
		    }
		
		public static long binaryExponentiation(long x,long n)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=(x%mod * x%mod)%mod;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modularExponentiation(int x,int n,int M)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long modularExponentiation(long x,long n,long M)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modInverse(int A,int M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		public static long modInverse(long A,long M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		
		public static boolean checkYear(int year)
	    {
			if (year % 400 == 0)
	            return true;
	     
	        if (year % 100 == 0)
	            return false;
	     
	        if (year % 4 == 0)
	            return true;
	        return false;
	    }
		
		public static boolean isPrime(int n)
		{
		    
		    if (n <= 1)  return false;
		    if (n <= 3)  return true;
		    
		    if (n%2 == 0 || n%3 == 0) 
		    	return false;
		 
		    for (int i=5; i*i<=n; i=i+6)
		    {
		        if (n%i == 0 || n%(i+2) == 0)
		           return false;
		    }
		    
		    return true;
		}
		
		static class pair implements Comparable<pair>
 
		{
			Integer x, y;
			pair(int x,int y)
			{
				this.x=x;
				this.y=y;
			}
			
			public int compareTo(pair o) {
				int result = x.compareTo(o.x);
				if(result==0)
					result = y.compareTo(o.y);
				
				return result;
			}  
			
			public String toString()
			{
				return x+" "+y;
			}
			
			public boolean equals(Object o)
			{
				if (o instanceof pair)
			    {
					pair p = (pair)o;
					return p.x == x && p.y == y ;
				}
				return false;
			}
			
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode();
			}
		}
	
		
		static class triplet implements Comparable<triplet>
		{
			Integer x,y,z;
			triplet(int x,int y,int z)
			{
				this.x = x;
				this.y = y;
				this.z = z;
			}
			
			public  int compareTo(triplet o)
			{
				int result = x.compareTo(o.x);
				if(result==0)
					result =  y.compareTo(o.y);
				if(result==0)
					result = z.compareTo(o.z);
 
				return result;
			}
			
			public boolean equlas(Object o)
			{
				if(o instanceof triplet)
				{
					triplet p = (triplet)o;
					return x==p.x && y==p.y && z==p.z;
				}
				return false;
			}
			
			public String toString()
			{
				return x+" "+y+" "+z;
			}
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode() + new Long(z).hashCode(); 
			}
		}
		
 
		
		
		
	
		static class node implements Comparable<node>
 
		{
			Integer x, y, z;
			node(int x,int y, int z)
			{
				this.x=x;
				this.y=y;
				this.z=z;
			}
			
			public int compareTo(pair o) {
				int result = x.compareTo(o.x);
				if(result==0)
					result = y.compareTo(o.y);
				if(result==0)
					result = z.compareTo(z); 
				return result;
			}
 
			@Override
			public int compareTo(node o) {
				// TODO Auto-generated method stub
				return 0;
			}  
		}
	}