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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(){
	int N = 100000;
	scanf("%d\n", &N);
	int usagi[100000];
	int flag[100000] = {0};
	for (size_t i = 0; i < N; i++) {
		scanf("%d", &usagi[i]);
	}
	int count = 0;
	for (size_t i = 0; i < N; i++) {
		if(flag[i])
			continue;
		for (size_t j = i+1; j < N; j++) {
			if(flag[j])
				continue;
			if (usagi[i] == i)
				break;
			if(count >= N/2)
				break;
			if(usagi[i] == j+1 && usagi[j] == i+1){
				count++;
				flag[i] = 1;
				flag[j] = 1;
				break;
			}



		}
	}
	printf("%d\n", count);
	return 0;
}