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 8.8.3) (judge verdict: Accepted)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

newUF n = VUM.replicate n (-1 :: Int)

root uf x = do
    p <- VUM.read uf x
    if p < 0
        then return x
        else do
            r <- root uf p
            VUM.write uf x r
            return r

same uf x y = liftM2 (==) (root uf x) (root uf y)

unite uf x y = do
    px <- root uf x
    py <- root uf y
    when (px /= py) $ do
        sx <- VUM.read uf px
        sy <- VUM.read uf py
        let (par, chld) = if sx < sy then (px, py)　else (py, px)
        VUM.write uf chld par
        VUM.write uf par (sx + sy) 

size uf x = do
    px <- root uf x
    s <- VUM.read uf px
    return $ abs s

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    [n,m] <- getIntList
    ps <- zip [0..] . map pred <$> getIntList
    xy <- replicateM m $ do
        [x,y] <- getIntList
        return (x-1,y-1)
    uf <- newUF n
    forM_ xy $ \(x,y) -> do
        unite uf x y
    ans <- sum <$> mapM (\(i,p) -> do
                       b <- same uf i p
                       return (if b then 1 else 0)) ps
    print ans