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.BufferedWriter;
		import java.io.IOException;
		import java.io.OutputStreamWriter;
		import java.io.ObjectInputStream.GetField;
		import java.math.BigInteger;
		import java.util.ArrayList;
		import java.util.Arrays;
		import java.util.Collections;
		import java.util.HashMap;
		import java.util.HashSet;
		import java.util.InputMismatchException;
		import java.util.LinkedList;
	import java.util.PriorityQueue;
	import java.util.Queue;
		import java.util.Stack;
		import java.util.TreeMap;
		import java.util.TreeSet;
public	class Q2 {
			static int MOD = 1000000007;
			static boolean b[];
			static boolean boo[][];
			static ArrayList<Integer>[] amp, amp2;
			static HashMap<ArrayList<Integer>,Integer> ts1 = new HashMap<>();
			static int sum[][],dist[][];
			static long ans = 0;
			static int p = 0;
			static int color[][];
			static FasterScanner sc = new FasterScanner();
			static Queue<Integer> q = new LinkedList<>();
			static Queue<Pair> qu = new LinkedList<>();
			static ArrayList<Pair>[][] arr;
			static ArrayList<Graph>[] amp1;
			static ArrayList<Integer> parent = new ArrayList<>();
			static BufferedWriter log;
			static HashMap<Long,Long> hm;
			static TreeSet<Long> ts = new TreeSet<>();
			static Stack<Integer> s = new Stack<>();
			static Pair prr[];
			static char ch[][];
			static int prime[];
			static long d,x,y;
			static int n,k,m;
			public static void main(String[] args) throws IOException {
				log = new BufferedWriter(new OutputStreamWriter(System.out));
				int n = sc.nextInt();
				int arr[] = sc.nextIntArray(n);
				if(n==1) System.out.println(1);
				else{
					amp = (ArrayList<Integer>[]) new ArrayList[n];
					for(int i =0 ;i<n;i++) amp[i] = new ArrayList<>();
					for(int i = 0;i<n;i++){
						amp[arr[i]-1].add(i);
						amp[i].add(arr[i]-1);
					}
					b = new boolean[n];
					for(int i =0 ;i<n;i++){
						if(!b[i]){
							ans++;
							dfs(i);
						}
					}
					System.out.println(ans);
				}
				log.close();
			}
			public static void dfs(int x){
				b[x] = true;
				for(int i =0 ;i<amp[x].size();i++){
					if(!b[amp[x].get(i)]){
						dfs(amp[x].get(i));
					}
				}
			}
			public static void bfs(int x){
				b[x] = true;
				q.add(x);
				while(!q.isEmpty()){
					ans++;
					int y = q.poll();
					for(int i = 0;i<amp[y].size();i++) {
						if(!b[amp[y].get(i)]){
							q.add(amp[y].get(i));
							b[amp[y].get(i)] = true;
							prime[amp[y].get(i)] = y;
						}
						else{
							if(amp[y].get(i)!=prime[y]) p++;
						}
					}
				}
			}
			public static void toThread(String[] args) throws Exception {
		    	new Thread(null, new Runnable() {
					public void run() {
						try {
							//InputReader(System.in);
					       // pw = new PrintWriter(System.out);
					        //soln();
					        //pw.close();
							//soln();
						} catch (Exception e) {
							e.printStackTrace();
						}
					}
				}, "1", 1 << 26).start();
		    }
			public static long mod(int x, int y){
				long ans = 1;
				while(y>0){
					if(y%2==1){
						ans = ((ans%MOD)*(x%MOD))%MOD;
						y-=1;
					}
					else{
						x = (int) (((x%MOD)*(x%MOD))%MOD);
						y = y/2;
					}
				}
				return ans;
			}
			public static void dfs2(int x, int y){
				boo[x][y] = true;
				ans++;
				if(ans==(p-k)){
					return;
				}
				for(Pair e:arr[x][y]){
					if(!boo[e.u][e.v]){
						dfs2(e.u,e.v);
						if(ans==(p-k)){
							return;
						}
					}
				}
			}
		/*	public static void dfs(int x){
				b[x] = true;
				for(int i =0 ;i<amp[x].size();i++){
					if(!b[amp[x].get(i)]){
						dfs(amp[x].get(i));
					}
				}
				
			}*/
			static void findFactors(ArrayList<Integer> primeDivisors, ArrayList<Integer> multiplicity, int currentDivisor, long currentResult) {
			    if (currentDivisor == primeDivisors.size()) {
			        ts.add(currentResult);
			        return;
			    }
			    for (int i = 0; i <= multiplicity.get(currentDivisor); ++i) {
			        findFactors(primeDivisors, multiplicity, currentDivisor + 1, currentResult);
			        currentResult *= primeDivisors.get(currentDivisor);
			    }
			}
			public static void seive(long n){
				b = new boolean[(int) (n+1)];
				Arrays.fill(b, true);
				b[0] =false;
				b[1] = true;
				for(int i = 2;i*i<=n;i++){
					if(b[i]){
						for(int p = 2*i;p<=n;p+=i){
							b[p] = false;
						}
					}
				}
				for(int i = 0;i<n;i++) if(b[i]) parent.add(i);
			}
			public static void factors(int n){
				b = new boolean[n+1];
				prime = new int[n+1];
				Arrays.fill(b, true);
				b[0] =false;
				b[1] = false;
				for(int i = 2;i*i<=n;i++){
					if(b[i]){
						prime[i] = i;
						for(int p = 2*i;p<=n;p+=i){
							if(b[p]){
							b[p] = false;
							prime[p] = i;
							}
						}
					}
				}
				for(int i = 2;i<=n;i++){
					if(b[i]) prime[i] = i;
				}
			}
			public static void buildWeightedGraph(int m){
				for(int i = 0; i<m;i++){
					int x = sc.nextInt(), y = sc.nextInt(), w = sc.nextInt();
					amp1[--x].add(new Graph(--y,w));
					amp1[y].add(new Graph(x,w));
				}
			}
			public static void extendedEuclidian(long a, long b){
				if(b == 0) {
			        d = a;
			        x = 1;
			        y = 0;
			    }
			    else {
			        extendedEuclidian(b, a%b);
			        int temp = (int) x;
			        x = y;
			        y = temp - (a/b)*y;
			    }
			}
			private static void permutation(String prefix, String str) {
			    int n = str.length();
			   // if (n == 0) ts.add(prefix);
			  //  else {
			        for (int i = 0; i < n; i++)
			            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
			   //}
			}
			public static char give(char c1,char c2){
				if(c1!='a' && c2!='a') return 'a';
				if(c1!='b' && c2!='b') return 'b';
				return 'c';
			}
			static class Graph{
				int vertex;
				long weight;
				Graph(int v,int w){
					vertex = v;
					weight = w;
				}
			}
			public static void buildTree(int n){
				int arr[] = sc.nextIntArray(n);
				for(int i = 0;i<n;i++){
					int x = arr[i]-1;
					amp[i+1].add(x);
					amp[x].add(i+1);
				}
			}
			
				
			public static void buildGraph(int n){
				
				for(int i =0;i<n;i++){
					int x = sc.nextInt(), y = sc.nextInt();
					amp[--x].add(--y);
					amp[y].add(x);
				}
			}
				
			
			static class Pair implements Comparable<Pair> {
				int u;
				int v;
				int z;
				public Pair(){
					
				}
				public Pair(int u, int v) {
					this.u = u;
					this.v = v;
				}
				
				public int hashCode() {
					int hu = (int) (u ^ (u >>> 32));
					int hv = (int) (v ^ (v >>> 32));
					return 31*hu + hv;
				}
		
				public boolean equals(Object o) {
					Pair other = (Pair) o;
					return (u == other.u && v == other.v);
				}
		
				public int compareTo(Pair other) {
					return Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)) : (Integer.compare(v, other.v));
				}
				
				public String toString() {
					return "[u=" + u + ", v=" + v + "]";
				}
			}
			static class SegmentTree{
				long st[][];
				char ch[];
				boolean lazy[];
				SegmentTree(String str, int n){
					int size = 4*n;
					ch = str.toCharArray();
					st = new long[size][2];
					lazy = new boolean[size];
					build(ch,0,n-1,0);
				}
				long[] build(char str[], int ss, int se, int si){
					if(ss==se){
						if(str[ss]=='>') st[si][0] = 1;
						else st[si][1] = 1;
						return st[si];
					}
					int mid = (ss+se)/2;
					long temp1[] = build(str,ss,mid,si*2+1);
					long temp2[] = build(str,mid+1,se,si*2+2);
					st[si][0] = temp1[0]+temp2[0];
					st[si][1] = temp1[1]+temp2[1];
					return st[si];
				}
				void updateRange(int node, int start, int end, int l, int r, boolean val)
				{
				//	System.out.println(lazy[node]+" "+node);
				    if(lazy[node])
				    { 
				        // This node needs to be updated
				    	long temp = st[node][0];
				    	st[node][0] = st[node][1];
				    	st[node][1] = temp; // Update it
				        if(start != end)
				        {
				            lazy[node*2+1] = lazy[node];                  // Mark child as lazy
				            lazy[node*2+2] = lazy[node];                // Mark child as lazy
				        }
				        lazy[node] = false;                                  // Reset it
				    }
				    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
				        return;
				    if(start >= l && end <= r)
				    {
				        // Segment is fully within range
				    	if(val){
				    	long temp = st[node][0];
				    	st[node][0] = st[node][1];
				    	st[node][1] = temp;
				        if(start != end)
				        {
				            // Not leaf node
				        	lazy[node*2+1] = val;                  // Mark child as lazy
				            lazy[node*2+2] = val; 
				        }
				    	}
				        return;
				    }
				    int mid = (start + end) / 2;
				    updateRange(node*2+1, start, mid, l, r, val);        // Updating left child
				    updateRange(node*2 + 2, mid + 1, end, l, r, val);   // Updating right child
				    st[node][0] = st[node*2+1][0] + st[node*2+2][0];
				    st[node][1] = st[node*2+1][1] + st[node*2+2][1];// Updating root with max value 
				}
				long[] queryRange(int node, int start, int end, int l, int r)
				{
				    if(start > end || start > r || end < l)
				        return new long[]{0,0};         // Out of range
				    if(lazy[node])
				    {
				    	long temp = st[node][0];
				    	st[node][0] = st[node][1];
				    	st[node][1] = temp; // Update it
				        if(start != end)
				        {
				            lazy[node*2+1] = lazy[node];                  // Mark child as lazy
				            lazy[node*2+2] = lazy[node];                // Mark child as lazy
				        }
				        lazy[node] = false;                  // Reset it
				    }
				    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
				        return st[node];
				    int mid = (start + end) / 2;
				    long p1[] = queryRange(node*2+1, start, mid, l, r);         // Query left child
				    long p2[] = queryRange(node*2 + 2, mid + 1, end, l, r); // Query right child
				    p1[0]+=p2[0];
				    p1[1]+=p2[1];
				    return p1;
				}

				/*long get(int qs, int qe, int ss, int se, int si){
					if(qe<ss || qs>se){
						return 0;
					}
					if(qs<=ss && qe>=se) return st[si]*power(2,qe-se,3);
					int mid = (ss+se)/2;
		            return (((get(qs,qe,ss,mid,2*si+1))%3*power(2,Math.min(qe-mid, se-mid),3))%3+(get(qs,qe, mid+1, se, 2*si+2))%3)%3;
				}
				void update(char str[],int ss,int se,int si,int idx){
					if(ss==se){
						st[si] = 1;
						str[idx] = 1;
					}
					else{
						int mid = (ss+se)/2;
						if(ss<=idx && idx<=mid) update(str,ss,mid,2*si+1,idx);
						else update(str,mid+1,se,2*si+2,idx);
						st[si] = (((st[2*si+1]*power(2,se-mid,3))%3+st[2*si+2])%3)%3;
					}
				}*/
				void print(){
					for(int i = 0;i<st.length;i++){
						System.out.print(st[i][0]+" "+st[i][1]);
						System.out.println("----------------------");
					}
				}
			}
			static int convert(int x){
				int cnt = 0;
				String str = Integer.toBinaryString(x);
				//System.out.println(str);
				for(int i = 0;i<str.length();i++){
					if(str.charAt(i)=='1'){
						cnt++;
					}
				}
				int ans = (int) Math.pow(3, 6-cnt);
				return ans;
			}
			static class Node2{
				Node2 left = null;
				Node2 right = null;
				Node2 parent = null;
				int data;
			}
			static class BinarySearchTree{
				Node2 root = null;
				int height = 0;
				int max = 0;
				int cnt = 1;
				ArrayList<Integer> parent = new ArrayList<>();
				HashMap<Integer, Integer> hm = new HashMap<>();
				public void insert(int x){
					Node2 n = new Node2();
					n.data = x;
					if(root==null){
						root = n;
					}
					else{
						Node2 temp = root,temp2 = null;
						while(temp!=null){
							temp2 = temp;
							if(x>temp.data) temp = temp.right;
							else temp = temp.left;
						}
						if(x>temp2.data) temp2.right = n;
						else temp2.left = n;
						n.parent = temp2;
						parent.add(temp2.data);
					}
				}
				public Node2 getSomething(int x, int y, Node2 n){
					if(n.data==x || n.data==y) return n;
					else if(n.data>x && n.data<y) return n;
					else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
					else return getSomething(x,y,n.left);
				}
				public Node2 search(int x,Node2 n){
					if(x==n.data){
						max = Math.max(max, n.data);
						return n;
					}
					if(x>n.data){
						max = Math.max(max, n.data);
						return search(x,n.right);
					}
					else{
						max = Math.max(max, n.data);
						return search(x,n.left);
					}
				}
				public int getHeight(Node2 n){
					if(n==null) return 0;
					height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
					return height;
				}
			}
			static long findDiff(long[] arr, long[] brr, int m){
				int i = 0, j = 0;
				long fa = 1000000000000L;
				while(i<m && j<m){
					long x = arr[i]-brr[j];
					if(x>=0){
						if(x<fa) fa = x;
						j++;
					}
					else{
						if((-x)<fa) fa = -x;
						i++;
					}
				}
				return fa;
			}
			public static long max(long x, long y, long z){
				if(x>=y && x>=z) return x;
				if(y>=x && y>=z) return y;
				return z;
			}
			
			
			static long modInverse(long a, long mOD2){
			            return  power(a, mOD2-2, mOD2);
			}
			static long power(long x, long y, long m)
			{
			    if (y == 0)
			        return 1;
			    long p = power(x, y/2, m) % m;
			    p = (p * p) % m;
			 
			    return (y%2 == 0)? p : (x * p) % m;
			}
			static long power2(long x,BigInteger y,long m){
				long ans = 1;
				BigInteger two = new BigInteger("2");
				while(y.compareTo(BigInteger.ZERO)>0){
					if(y.getLowestSetBit()==y.bitCount()){
						x = (x*x)%MOD;
						y = y.divide(two);
					}
					else{
						ans = (ans*x)%MOD;
						y = y.subtract(BigInteger.ONE);
					}
				}
				return ans;
			}
			static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
				BigInteger ans = new BigInteger("1");
				BigInteger one  = new BigInteger("1");
				BigInteger two  = new BigInteger("2");
				BigInteger zero  = new BigInteger("0");
				while(y.compareTo(zero)>0){
					//System.out.println(y);
					if(y.mod(two).equals(one)){
						ans = ans.multiply(x).mod(m);
						y = y.subtract(one);
					}
					else{
						x = x.multiply(x).mod(m);
						y = y.divide(two);
					}
				}
				return ans;
			}
			static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
			{
			    if (y.equals(0))
			        return (new BigInteger("1"));
			    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
			    p = (p.multiply(p)).mod(m);
			 
			    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
			}
			
			
			public static long gcd(long n, long m){
				if(m!=0) return gcd(m,n%m);
				else return n;
			}
			
			
			public static class FasterScanner {
				private byte[] buf = new byte[1024];
				private int curChar;
				private int numChars;
		 
				public int read() {
					if (numChars == -1)
						throw new InputMismatchException();
					if (curChar >= numChars) {
						curChar = 0;
						try {
							numChars = System.in.read(buf);
						} catch (IOException e) {
							throw new InputMismatchException();
						}
						if (numChars <= 0)
							return -1;
					}
					return buf[curChar++];
				}
		 
				public String nextLine() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					StringBuilder res = new StringBuilder();
					do {
						res.appendCodePoint(c);
						c = read();
					} while (!isEndOfLine(c));
					return res.toString();
				}
		 
				public String nextString() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					StringBuilder res = new StringBuilder();
					do {
						res.appendCodePoint(c);
						c = read();
					} while (!isSpaceChar(c));
					return res.toString();
				}
		 
				public long nextLong() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					int sgn = 1;
					if (c == '-') {
						sgn = -1;
						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 res * sgn;
				}
		 
				public int nextInt() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					int sgn = 1;
					if (c == '-') {
						sgn = -1;
						c = read();
					}
					int res = 0;
					do {
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = read();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
			        
			    public int[] nextIntArray(int n) {
			        return nextIntArray(n, 0);
			    }
			    
			    public int[] nextIntArray(int n, int off) {
			    	int[] arr = new int[n + off];
			    	for (int i = 0; i < n; i++) {
			    		arr[i + off] = nextInt();
			    	}
			    	return arr;
			    }
			    
			    public long[] nextLongArray(int n) {
			    	return nextLongArray(n, 0);
			    }
		        
				public long[] nextLongArray(int n, int off) {
				    long[] arr = new long[n + off];
				    for (int i = 0; i < n; i++) {
				        arr[i + off] = nextLong();
				    }
				    return arr;
				}
		 
			    private boolean isSpaceChar(int c) {
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
		 
				private boolean isEndOfLine(int c) {
					return c == '\n' || c == '\r' || c == -1;
				}
			}
		}