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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define MOD 1000000007
#define INF 800000000
#define MAX 1000

int main(){
  int N;
  cin>>N;
  vector<int> a(N);
  vector<pair<int,int>> p(N);
  for(int i=0;i<N;i++){
    cin>>a.at(i);
    p.at(i).first=a.at(i);
    p.at(i).second=i+1;
  }
  sort(p.begin(),p.end());
  int ans=0;
  for(int i=0;i<N;i++){
    if(a.at(p.at(i).first-1)==p.at(i).second){
      ans++;
    }
  }
  cout<<ans/2<<endl;
}