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 OCaml (4.02.3) (judge verdict: Accepted)

open Hashtbl
let n = Scanf.scanf " %d" (+) 0
let a_s = Array.init n @@ fun i -> Scanf.scanf " %d" @@ fun a -> min i @@ a - 1, max i @@ a - 1
let h = create n
let _ = Array.iteri (fun i a -> replace h a @@ try find h a + 1 with _ -> 1) a_s; fold (fun _ c s -> s + if c = 2 then 1 else 0) h 0 |> Printf.printf "%d\n"