Problem:
Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 ≤ i ≤ N) such that p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

Find the maximum possible number of i such that p_i = i after operations.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.
Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation.

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad (replicateM)
import Data.Set hiding (foldl, map, filter)
import qualified Data.Set as Set
import Data.Maybe

addPair :: [Set Int] -> (Int, Int) -> [Set Int]
addPair ls (x, y) = case (searchLinkedSets x y ls) of
    (Nothing, Nothing, r) -> (fromList [x, y]):r
    (Just(xs), Nothing, r) -> (insert y xs):r
    (Nothing, Just(ys), r) -> (insert x ys):r
    (Just(xs), Just(ys), r) -> (union xs ys):r

searchLinkedSets :: Int -> Int -> [Set Int] -> (Maybe(Set Int), Maybe(Set Int), [Set Int])
searchLinkedSets x y ls = foldl (search' x y) (Nothing, Nothing, []) ls
    where
        search' x y (Nothing, Nothing, ls) s | (member x s) && (member y s) = (Just s, Just s, ls)
        search' x y (Nothing, ys, ls) s | member x s = (Just s, ys, ls)
        search' x y (xs, Nothing, ls) s | member y s = (xs, Just s, ls)
        search' _ _ (xs, ys, ls) s             = (xs, ys, s:ls)

linkedSets :: [(Int, Int)] -> [Set Int]
linkedSets = foldl addPair []

equals :: [Int] -> [(Int, Int)] -> Int
equals l pairs = noNeedToMove + (sum $ map countIn linkedSets')
    where
        linkedSets' = linkedSets pairs
        countIn s = length $ filter ismember pickuped
            where
                ismember x = member x s
                at i = l !! (i - 1)
                pickuped = map at $ toList s
        linkedElements = unions linkedSets'
        notLinked x = notMember x linkedElements
        noNeedToMove = length $ filter notLinked $ map (\(_, x)->x) $ filter (\(i, x) -> i == x) $ zip [1..] l

main = do
    [n, m] <- (map read . words) <$> getLine
    l <- (map read . words) <$> getLine
    pairs <- map (map read . words) <$> replicateM m getLine --  :: IO [[Int]]
    print $ equals l $ map (\[x,y]->(x,y)) pairs