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)

{-# OPTIONS_GHC -O #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ViewPatterns #-}

import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Storable as V
import qualified Data.Vector.Storable.Mutable as MV
import qualified Data.IntMap as M
import qualified Data.Set as S

findUF :: MV.IOVector Int -> Int -> IO Int
findUF uf x = do
    p <- MV.unsafeRead uf x
    if p == -1
        then return x
        else do
                f <- findUF uf p
                MV.unsafeWrite uf x f
                return f

gp :: M.IntMap (S.Set Int, S.Set Int) -> V.Vector Int -> MV.IOVector Int -> Int -> Int -> IO (M.IntMap (S.Set Int, S.Set Int))
gp am _ _ n i | n==i = return am
gp am ps uf n i = do
    -- index iのroot (0..)
    ri <- findUF uf i
    let r = if ri == -1 then i else ri
    -- root indexをキーとして、(index, pi)をグルーピング
    let um = case M.lookup r am of
                Just (gis, gps) -> M.insert r (S.insert i gis, S.insert (ps V.! (i-1)) gps) am
                Nothing -> M.insert r (S.singleton i, S.singleton $ ps V.! (i-1)) am
    --
    gp um ps uf n (i+1)

main = do
    [n,m] <- map read.words <$> getLine

    -- 順列読込 / ByteString -> Vector.Storable
    ps <- V.unfoldr (B.readInt.B.dropWhile (==' ')) <$> B.getLine

    -- (xi, yi)をUnionFind -> Vector.Storable.Mutable
    uf <- MV.replicate (n+1) (-1)
    replicateM_ m $ do
        [x,y] <- unfoldr (B.readInt.B.dropWhile (==' ')) <$> B.getLine
        px <- findUF uf x
        py <- findUF uf y
        when (px /= py) $ MV.unsafeWrite uf py px
    
    -- UnionFind木の根をkeyとして、(indexのSet, PiのSet)のMap
    ms <- gp M.empty ps uf (MV.length uf) 1

    -- Mapの各keyについて、indexのSetとPiのSetの重複の数の合計
    print $ sum $ M.map (\(s1,s2) -> intnum s1 s2) ms

-- setの重複の数
intnum s1 s2 = length $ S.intersection s1 s2