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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List
import Data.Tuple
import GHC.Exts
    
main :: IO ()
main =
  fmap read getLine >>=
  \n -> fmap ((zipWith (,) [1..n]) . (map read) . words) getLine >>=
  \as -> putStrLn $ show $ solve as

solve :: [(Int,Int)] -> Int
solve as = sub (sortWith (fst) (map (\(x,y) -> if x <= y then (x,y) else (y,x)) as))

sub :: [(Int,Int)] -> Int
sub [] = 0
sub [a] = 0
sub (a1:a2:as)
  | a1 == a2 = 1 + (sub as)
  | otherwise = sub (a2:as)