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)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Applicative
import Control.Monad.Fix
import Control.Monad.ST
import Data.Int
import Data.Foldable
import Data.List
import Data.Graph
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import Debug.Trace

solve :: Int -> Int -> VU.Vector Int -> VU.Vector (Int, Int) -> Int
solve !n !m !pn !xys = sum $ map
  (\idxs -> countPairs (sort idxs) (sort $ map (pn VU.!) idxs))
  componentGroups
 where
  graph           = buildG (0, n - 1) (VU.toList xys)

  componentGroups = map group $ components graph
    where group (Node !n !fs) = n : concat (map group fs)

  countPairs xs ys = go xs ys 0
   where
    go _  [] !acc = acc
    go [] _  !acc = acc
    go (x : xs) (y : ys) !acc | x == y = go xs ys (acc + 1)
                              | x > y  = go (x : xs) ys acc
                              | x < y  = go xs (y : ys) acc

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  (n, m) <-
    (\vec -> (vec VU.! 0, vec VU.! 1)) . VU.unfoldrN 2 readInt <$> B.getLine
  pn  <- VU.map (\n -> n - 1) . VU.unfoldrN n readInt <$> B.getLine
  xys <-
    VU.replicateM m
    $   (\vec -> (vec VU.! 0 - 1, vec VU.! 1 - 1))
    .   VU.unfoldrN 2 readInt
    <$> B.getLine
  print $ solve n m pn xys