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.io.PrintStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class CF755C {
	/**
	 * solution result
	 */
	public static class Answer {
		int n;
		public Answer(int n) {
			this.n = n;
		}

		@Override
		public String toString() {
			return Integer.toString(n);
		}
	};

	/**
	 * input parser
	 */
	public static class Input {
		int n;
		int pp[];
		public Input(Scanner sc) {
			n = sc.nextInt();
			pp = new int[n];
			for (int i=0; i<n; i++)
				pp[i] = sc.nextInt()-1;
		}
	};

	static int[][] graph(int pp[]) {
		Map<Integer, Set<Integer>> gg = new HashMap<>();
		for (int p=0; p<pp.length; p++) {
			Set<Integer> cf = gg.get(p);
			if (cf == null) {
				cf = new HashSet<>();
				gg.put(p, cf);
			}
			Set<Integer> cr = gg.get(pp[p]);
			if (cr == null) {
				cr = new HashSet<>();
				gg.put(pp[p], cr);
			}
			cf.add(pp[p]);
			cr.add(p);
		}
		int res[][] = new int[gg.size()][];
		for (int p=0; p<pp.length; p++) {
			int l = gg.get(p).size();
			res[p] = new int[l];
			int i = 0;
			for (int c:gg.get(p))
				res[p][i++] = c;
		}
		return res;
	}
	
	/**
	 * FIFO ringbuffer of ints
	 * sz should be 1 greater of what you want to store
	 * @author kokarev
	 */
	static class FifoInt {
		int head, tail;
		int sz;
		int emptyInd;	// what do we return if our Q is empty
		int buf[];
		FifoInt(int sz) {
			this(sz, -1);
		}
		FifoInt(int sz, int emptyInd) {
			this.emptyInd = emptyInd;
			this.sz = sz;
			buf = new int[sz];
		}
		int size() {
			return (head+sz-tail)%sz;
		}
		int avail() {
			return sz-size();
		}
		boolean put(int v) {
			int n = (head+1)%sz; 
			if (n != tail) {
				buf[head] = v;
				head = n;
				return true;
			} else {
				return false;
			}
		}
		int get() {
			if (tail != head) {
				int v = buf[tail];
				tail = (tail+1)%sz;
				return v;
			} else {
				return emptyInd;
			}
		}
	}

	/**
	 * Take a graph and return list of its connected components
	 * @param graph is given as a list of edges where graph[i][?] == j denotes edge i->j
	 * @return list of connected components meaning [n][v] - vertice v belongs to connected component number n 
	 */
	static int[][] connectedComponents(int graph[][]) {
		final int EMPTY = -1;
		FifoInt q = new FifoInt(graph.length+1, EMPTY);
		int vis[] = new int[graph.length];
		int cnts[] = new int[graph.length+1];
		int cnt = 0;
		for (int p=0; p<graph.length; p++) {
			if (vis[p] == 0) {
				cnt++;
				q.put(p);
				for (int v = q.get(); v != EMPTY; v = q.get()) {
					if (vis[v] == 0) {
						vis[v] = cnt;
						cnts[cnt]++;
						for (int c:graph[v])
							q.put(c);
					}
				}
			}
		}
		int res[][] = new int[cnt][];
		for (int i=0; i<res.length; i++)
			res[i] = new int[cnts[i+1]];
		Arrays.fill(cnts, 0);
		int c;
		for (int p=0; p<graph.length; p++) {
			c = vis[p]-1; 
			res[c][cnts[c]++] = p;
		}
		return res;
	}

	/**
	 * solver function
	 */
	public static Answer solve(Input in) {
		Answer ans = new Answer(connectedComponents(graph(in.pp)).length);
		return ans;
	}

	/**
	 * standard CodeForces executable mantra
	 */
	public static void proc(Scanner sc, PrintStream out) {
		Input in = new Input(sc);
		out.println(solve(in));
	}

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			proc(sc, System.out);
		}
	}
}