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 codeforces;

import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

/**
 * Created by brkuma on 1/18/2017.
 */

public class PolandBallAndForest {
    private static final int WHITE = 0;
    private static final int GREY = 1;
    private static final int BLACK = 2;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        PolandBallAndForest solver = new PolandBallAndForest();
        solver.solve(in, out);
        out.flush();
        out.close();
    }

    public void solve(InputReader in, PrintWriter out) {
        // Main Code goes here
        int n = in.nextInt();
        List<List<Integer>> graph = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            graph.add(new ArrayList<>());
        }
        for (int u = 0; u < n; u++) {
            int v = in.nextInt() - 1;
            graph.get(u).add(v);
            graph.get(v).add(u);
        }

        int[] color = new int[n];
        Arrays.fill(color, WHITE);
        int ret = 0;
        for (int i = 0; i < n; i++) {
            if (color[i] == WHITE) {
                ret++;
                dfs(graph, color, i);
            }
        }
        out.println(ret);
    }
    private void dfs(List<List<Integer>> graph, int[]colors, int vertex) {
        if (colors[vertex] != WHITE) {
            return;
        }
        colors[vertex] = GREY;
        for(int v : graph.get(vertex)) {
            if (colors[v] == WHITE) {
                dfs(graph, colors, v);
            }
        }
        colors[vertex] = BLACK;
    }
    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String nextString() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

    }


    static class ArrayUtils {
        public static void fill(int[][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                Arrays.fill(f[i], value);
            }
        }

    }
}