Problem: PolandBall lives in a forest with his family. There are some trees in the forest. Trees are undirected acyclic graphs with k vertices and k - 1 edges, where k is some integer. Note that one vertex is a valid tree.

There is exactly one relative living in each vertex of each tree, they have unique ids from 1 to n. For each Ball i we know the id of its most distant relative living on the same tree. If there are several such vertices, we only know the value of the one with smallest id among those.

How many trees are there in the forest?

Input

The first line contains single integer n (1 ≤ n ≤ 104) — the number of Balls living in the forest.

The second line contains a sequence p1, p2, ..., pn of length n, where (1 ≤ pi ≤ n) holds and pi denotes the most distant from Ball i relative living on the same tree. If there are several most distant relatives living on the same tree, pi is the id of one with the smallest id.

It's guaranteed that the sequence p corresponds to some valid forest.

Hacking: To hack someone, you should provide a correct forest as a test. The sequence p will be calculated according to the forest and given to the solution you try to hack as input. Use the following format:

In the first line, output the integer n (1 ≤ n ≤ 104) — the number of Balls and the integer m (0 ≤ m < n) — the total number of edges in the forest. Then m lines should follow. The i-th of them should contain two integers ai and bi and represent an edge between vertices in which relatives ai and bi live. For example, the first sample is written as follows:
    
    
      
    5 3  
    1 2  
    3 4  
    4 5  
    

Output

You should output the number of trees in the forest where PolandBall lives.

Interaction

From the technical side, this problem is interactive. However, it should not affect you (except hacking) since there is no interaction.

Examples

Input

5
2 1 5 3 3

Output

2

Input

1
1


Output

1

Note

In the first sample testcase, possible forest is: 1-2 3-4-5. 

There are 2 trees overall.

In the second sample testcase, the only possible graph is one vertex and no edges. Therefore, there is only one tree.

Solution (in JAVA):

Solution:
 // package Jobeel;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
import java.util.Map.*;

public class codeforces {
	static 	PrintWriter pw=new PrintWriter(System.out);
	static int [] size,arr;
	static String [] words;
	public static int find(int i) {
		if(arr[i]==i) return i;
		else {
			int result=find(arr[i]);
			arr[i]=result;
			return result;
		}
	}
	
public static void union(int u,int v) {
		int root_u=find(u);
		int root_v=find(v);
		if (root_u==root_v) return;
		else if(size[root_u]>size[root_v]) {
			size[root_u]+=size[root_v];
			arr[root_v]=root_u;
		}else  {
			size[root_v]+=size[root_u];
			arr[root_u]=root_v;
		}
	}
 
public static void main(String [] args) throws IOException, InterruptedException {
		Scanner sc=new Scanner(System.in);
		 int x=sc.nextInt();
		 
		 arr=new int [x+1];
		 size=new int [x+1];
		 for(int i=1;i<=x;i++) {
			 arr[i]=i;
			 size[i]=1;
		 }
		 int [] list=sc.nextIntArray(x);
		 for(int i=0;i<x;i++) {
			 union(i+1, list[i]);
		 }
		 HashSet<Integer> set =new HashSet<>();
		 
		 for(int w:list) set.add(find(w));
		 pw.println(set.size());
		pw.flush();
		pw.close();
	}
	static class pair implements Comparable<pair>{
		String  name; int x,y ;
		
		
		public pair (int x,int y) {
			this.x=x; this.y=y;
		}
		public int compareTo(pair o) {
			if(!name.equals(o.name))
				return name.compareTo(o.name);
			return x-o.x;
		}
		public String toString() {
			return x+" "+y;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
		public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
        public HashMap<Integer, Integer> nextHashMap(int n) throws IOException{
        	HashMap<Integer, Integer> map =new HashMap<>();
        	for(int i=0;i<n;i++) {
        		int x=nextInt();
        		int b=map.getOrDefault(x, 0);
        		map.put(x, b+1);
        	}
        	return map;
        }
        public TreeMap<Integer, Integer> nextTreeMap(int n) throws IOException{
        	TreeMap<Integer, Integer> map =new TreeMap<>();
        	for(int i=0;i<n;i++) {
        		int x=nextInt();
        		int b=map.getOrDefault(x, 0);
        		map.put(x, b+1);
        		
        	}
        	return map;
        }
        public HashSet<Integer> nextHashSet (int n) throws IOException{
        	HashSet<Integer> set=new HashSet<>();
        	for(int i=0;i<n;i++) set.add(nextInt());
        	return set;
        }
        public TreeSet<Integer> nextTreeSet(int n) throws IOException{
        	TreeSet<Integer> set=new TreeSet<>();
        	for(int i=0;i<n;i++) set.add(nextInt());
        	return set;
        }
        public long[] nextLongArraySorted(int n) throws IOException {
        	long [] arr=nextLongArray(n);
        	Arrays.parallelSort(arr);
            return arr;
        }
        public int [] nextIntArraySorted(int n) throws IOException{
        	int [] arr=nextIntArray(n);
        	Arrays.parallelSort(arr);
        	return arr;
        }
	    public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	}