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.*;

public class Codeforces {
    
    InputStream is;
    PrintWriter out;
    String INPUT = "";

//----------------------------------------------------------------------------------------------------//
    void solve() {
        int n=ni();
        int a[]=new int[n];
        Dsu dsu=new Dsu(n);
        for (int i = 0; i < n; i++) {
            a[i]=ni()-1;
            dsu.union(i, a[i]);
        }
        Set<Integer> set = new HashSet<Integer>();
        for (int i = 0; i < n; i++) {
            set.add(dsu.root(i));
        }
        out.print(set.size());
    }

//----------------------------------------------------------------------------------------------------//
    boolean isPrime(int n) {
        if (n <= 1) {
            return false;
        }
        for (int i = 2; i <= (int) Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
    
    Vector<Integer> sieveOfEratosthenes(int n) {
        boolean[] prime = new boolean[n + 1];
        for (int i = 0; i < n; i++) {
            prime[i] = true;
        }
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int j = p * p; j <= n; j += p) {
                    prime[j] = false;
                }
            }
        }
        Vector<Integer> v = new Vector<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                v.add(i);
            }
        }
        return v;
    }
    
    void swap(int a[], int l, int r) {
        int temp = a[l];
        a[l] = a[r];
        a[r] = temp;
    }
    
    long nCr(int n, int k) {
        long C[] = new long[k + 1];
        // nC0 is 1 
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = Math.min(i, k); j > 0; j--) {
                C[j] = C[j] + C[j - 1];
            }
        }
        return C[k];
    }
    
    public int gcd(int s, int l) {
        if (s == 0) {
            return l;
        }
        
        return gcd(l % s, s);
    }
    
    public HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        // Create a list from elements of HashMap 
        List<Map.Entry<Integer, Integer>> list
                = new LinkedList<>(hm.entrySet());

        //->change o1,o2 for reverseorder
        Collections.sort(list, (Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) -> (o1.getValue()).compareTo(o2.getValue()));

        // put data from sorted list to hashmap  
        HashMap<Integer, Integer> temp = new LinkedHashMap<>();
        list.forEach((aa) -> {
            temp.put(aa.getKey(), aa.getValue());
        });
        return temp;
    }
    
    void run() throws Exception {
        is = System.in;//oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }
    
    public static void main(String[] args) throws Exception {
        new Codeforces().run();
    }
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    
    private void tr(Object... o) {
        if (!oj) {
            System.out.println(Arrays.deepToString(o));
            
        }
    }
    
    class Pair {

        /*SORTING PAIRS BY COMPARING Y OF PAIR.
    Pair[] p=new Pair[n];
    p[i]=new Pair(i,ni());
    Arrays.sort(p,( p1, p2) -> {return p1.y-p2.y;});
         */
        int x;
        int y;
        
        Pair(int u, int v) {
            x = u;
            y = v;
        }
        
        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Pair)) {
                return false;
            }
            Pair key = (Pair) o;
            return x == key.x && y == key.y;
        }
        
        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
        
    }

    class Dsu {

        int par[];
        int size[];

        Dsu(int n) {
            par = new int[n];
            size = new int[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
                size[i] = 1;
            }
        }

        int root(int i) {
            if (i == par[i]) {
                return i;
            }
            return par[i] = root(par[i]);
        }

        boolean find(int p, int q) {
            return root(p) == root(q);
        }

        void union(int p, int q) {
            int a = root(p);
            int b = root(q);
            if (a == b) {
                return;
            }
            if (size[a] > size[b]) {
                par[b] = a;
                size[a] += size[b];
            } else {
                par[a] = b;
                size[b] += size[a];
            }
        }
        
    }
}
//isPrime(int)
//Vector<Integer> sieveOfEratosthenes(int n){PRIME NO <=n}
//swap(arr,i,j)
//HashMap sortByValue(map);
//long comb=nCr(5,2);
//int gcd(s,l);
//Pair p=new Pair(x,y);
// Dsu dsu=new Dsu(n);