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: Accepted)

import Control.Arrow
import Data.List
import qualified Data.ByteString.Char8 as B
import Control.Monad
import Control.Monad.Primitive
import qualified Data.Vector as V 
import qualified Data.Vector.Mutable as VM
import Control.Monad.ST
import Data.Foldable

main :: IO ()
main = breads >>= main'
    where
        main' nm = breads >>= main'' nm
        main'' [n, m] ps = replicateM m breads >>= print . solve n m ps

solve :: Int -> Int -> [Int] -> [[Int]] -> Int
solve n m ps xys = runST solveST
    where
        solveST :: ST s Int
        solveST = initTree >>= count
        initTree :: ST s (UFTree s)
        initTree = makeTreeM n >>= (\t -> t <$ mapM_ (\[x, y] -> unionNodesM (x - 1) (y - 1) t) xys)
        count uft = foldlM ff 0 $ zip [0..] ps
            where
                ff acc (i, p) = check acc <$> isSameM i (p - 1) uft 
                check acc b
                    | b = acc + 1
                    | otherwise = acc
            

newtype UFTree s = UFTree (VM.MVector s (Int, Int))

makeTreeM :: (PrimMonad m) => Int -> m (UFTree (PrimState m))
makeTreeM n = UFTree <$> V.unsafeThaw vec
    where
        vec = V.fromListN n $ zip (repeat 0) [0..]

findRootM :: (PrimMonad m) => Int -> UFTree (PrimState m) -> m Int
findRootM v t@(UFTree vs) = VM.unsafeRead vs v >>= checkRoot
    where
        checkRoot (_, root)
            | v == root = return v
            | otherwise = findRootM root t
            
unionNodesM :: (PrimMonad m) => Int -> Int -> UFTree (PrimState m) -> m ()
unionNodesM a b t@(UFTree vs) = mapM (flip findRootM t) [a, b] >>= checkRoot
    where
        checkRoot [c, d]
            | c == d = return ()
            | otherwise = mapM (VM.unsafeRead vs) [c, d] >>= checkRank c d 
        checkRank c d [ra, rb]
            | ra < rb = VM.unsafeModify vs (second (const d)) c
            | ra > rb = VM.unsafeModify vs (second (const c)) d
            | otherwise = VM.unsafeModify vs (\(x, _) -> (x + 1, c)) d
            
isSameM :: (PrimMonad m) => Int -> Int -> UFTree (PrimState m) -> m Bool
isSameM a b t = (==) <$> findRootM a t <*> findRootM b t
        

breads :: IO [Int]
breads = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine