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: Accepted)

import qualified Data.IntMap as M              

main :: IO ()
main = do
    n  <- readLn
    as <- map read . words <$> getLine
    print $ solve n as

solve :: Int -> [Int] -> Int
solve n as = go mp0
  where
    mp0 = M.fromList $ zip [1 .. n] as

    go :: M.IntMap Int -> Int
    go mp = case M.minViewWithKey mp of
        Nothing -> 0
        Just ((k, a), mp') | M.lookup a mp' == Just k -> 1 + go mp'
                           | otherwise                -> go mp'