Problem:
Score : 200 points

Problem Statement

There are N rabbits, numbered 1 through N.

The i-th (1≤i≤N) rabbit likes rabbit a_i.
Note that no rabbit can like itself, that is, a_i≠i.

For a pair of rabbits i and j (i＜j), we call the pair (i，j) a friendly pair if the following condition is met.

Rabbit i likes rabbit j and rabbit j likes rabbit i.

Calculate the number of the friendly pairs.

Constraints

2≤N≤10^5

1≤a_i≤N

a_i≠i

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the number of the friendly pairs.

Sample Input 1

4
2 1 4 3

Sample Output 1

2

There are two friendly pairs: (1，2) and (3，4).

Sample Input 2

3
2 3 1

Sample Output 2

0

There are no friendly pairs.

Sample Input 3

5
5 5 5 5 1

Sample Output 3

1

There is one friendly pair: (1，5).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {

    private static String getPairID(int i1, int i2){
        return (i1<i2)? String.valueOf(i1) + "-" + String.valueOf(i2) : String.valueOf(i2) + "-" + String.valueOf(i1);
    }
    
    public static void main(String[] args) {
       Scanner scanner = new Scanner(System.in);
       
       int N = scanner.nextInt();
       int[] ar1 = new int[N];
       
       for (int i=0;i<N;i++){
        ar1[i] = scanner.nextInt();
       }
       
       int pairCount = 0;
       
       LinkedList<String> pairList = new LinkedList<>();
       for (int i=0;i<N;i++){
           String pairID = getPairID(i+1, ar1[i]);
           if (pairList.contains(pairID)){
               pairCount++;
           }
           else{
               pairList.add(pairID);
           }
       }       
      System.out.print(pairCount);
    }
}