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:
import java.util.*;
import java.io.*;
import java.math.*;
public class Main {
	public static long mod= (long) (1e9 +7);
	static int p[];
	public static void main(String args[]) throws IOException
	{
		InputReader s= new InputReader(System.in);
		OutputStream outputStream= System.out;
		PrintWriter out= new PrintWriter(outputStream);
		int n= s.nextInt();
		p= new int[n+1];
		createSets(n);
		for(int i=1;i<=n;i++){
			unite(s.nextInt(),i);
		}
		int cnt[]= new int[n+1];
		for(int i=1;i<=n;i++){
			cnt[root(i)]++;
		}
		int ans=0;
		for(int i=1;i<=n;i++){
			if(cnt[i]!=0)
				ans++;
		}
		out.println(ans);
		out.close();
	}
	public static int[] createSets(int size) {
	    //int[] p = new int[size];
	    for (int i = 1; i <= size; i++)
	      p[i] = i;
	    return p;
	  }

	  public static int root(int x) {
	    return x == p[x] ? x : (p[x] = root(p[x]));
	  }

	  public static void unite(int a, int b) {
	    a = root(a);
	    b = root(b);
	    if (a != b)
	      p[a] = b;
	  }

//- See more at: http://www.java2novice.com/java-interview-programs/is-prime-number/#sthash.Cixh6tEc.dpuf
	static long combinations(long n,long r){   // O(r)
		if(r==0 || r==n) return 1;
		r= Math.min(r, n-r);
		long ans=n;  // nC1=n;
		for(int i=1;i<r;i++){
			ans= ans*(n-i);
			ans= ans/(i+1);
		}
		return ans;
		
	}
	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	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 void catalan_numbers(int n) {
		long catalan[]= new long[n+1];
	    catalan[1] = 1;
	    for (int i = 2; i <= n; i++) {
	        for (int j = 1; j <= i - 1; j++) {
	            catalan[i] = catalan[i] + ((catalan[j]) * catalan[i - j]);
	        }
	    }
	}
	
	static ArrayList<Integer> primeFactors(int n)   // O(sqrt(n))
	{
	    // Print the number of 2s that divide n
		ArrayList<Integer> arr= new ArrayList<>();
	    while (n%2 == 0)
	    {
	        arr.add(2);
	        n = n/2;
	    }
	 
	    // n must be odd at this point.  So we can skip one element (Note i = i +2)
	    for (int i = 3; i <= Math.sqrt(n); i = i+2)
	    {
	        // While i divides n, print i and divide n
	        while (n%i == 0)
	        {
	            arr.add(i);
	            n = n/i;
	        }
	    }
	    // This condition is to handle the case when n is a prime number
	    // greater than 2
	    if (n > 2)
	        arr.add(n);
	    
	    return arr;
	}
 
	public static long expo(long a, long b){
		if (b==0)
	        return 1;
	    if (b==1)
	        return a;
	    if (b==2)
	        return a*a;
 
	    if (b%2==0){
	            return expo(expo(a,b/2),2);
	    }
	    else{
	        return a*expo(expo(a,(b-1)/2),2);
	    }
	}
	static class Pair implements Comparable<Pair>
	{
		int f;
		int s;
		int t;
		Pair(int ii, int cc, int dd)
		{
			f=ii;
			s=cc;
			t=dd;
		}
		
		public int compareTo(Pair o) 
		{
			return Integer.compare(this.f, o.f);
		}
		
	}
	
	public static int[] sieve(int N){    // O(n*log(logn))
		int arr[]= new int[N+1];
		for(int i=2;i<=Math.sqrt(N);i++){
			if(arr[i]==0){
				for(int j= i*i;j<= N;j= j+i){
					arr[j]=1;
				}
			}
		}
		return arr;
		// All the i for which arr[i]==0 are prime numbers.
	}
	static long gcd(long a,long b){       // O(logn)
		if(b==0) return a;
		return gcd(b,a%b);
	}
	
	static final class InputReader{
        private final InputStream stream;
        private final byte[] buf=new byte[1024];
        private int curChar;
        private int Chars;
        public InputReader(InputStream stream){this.stream=stream;}
        private int read()throws IOException{
            if(curChar>=Chars){
                curChar=0;
                Chars=stream.read(buf);
                if(Chars<=0)
                    return -1;
            }
            return buf[curChar++];
        }
        public final int nextInt()throws IOException{return (int)nextLong();}
        public final long nextLong()throws IOException{
            int c=read();
            while(isSpaceChar(c)){
                c=read();
                if(c==-1) throw new IOException();
            }
            boolean negative=false;
            if(c=='-'){
                negative=true;
                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 negative?(-res):(res);
        }
        public final int[] nextIntBrray(int size)throws IOException{
            int[] arr=new int[size];
            for(int i=0;i<size;i++)arr[i]=nextInt();
            return arr;
        }
        public final String nextString()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        public final String nextLine()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(c!='\n'&&c!=-1);
            return res.toString();
        }
        private boolean isSpaceChar(int c){
            return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
        }
    }
}