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.ST
import Data.Array.ST

createDjs :: Int -> ST s (STArray s Int Int)
createDjs n = do newArray (1, n) (-1)

findDjs :: STArray s Int Int -> Int -> ST s Int
findDjs arr x = do
    x' <- readArray arr x
    if x' < 0
        then
            return x
        else
            do
                x'' <- findDjs arr x'
                writeArray arr x x''
                return x''

mergeDjs :: STArray s Int Int -> Int -> Int -> ST s ()
mergeDjs arr x y = do
    nx <- readArray arr x
    ny <- readArray arr y
    if nx > ny
        then do
            writeArray arr x y
            writeArray arr y (nx + ny)
        else do
            writeArray arr y x
            writeArray arr x (nx + ny)

addDjs :: STArray s Int Int -> [Int] -> ST s ()
addDjs arr [x, y] = do
    x' <- findDjs arr x
    y' <- findDjs arr y
    if x' == y'
        then
             return()
        else
            do
                mergeDjs arr x' y'

movable :: STArray s Int Int -> (Int, Int) -> ST s Int
movable arr (x, y) = do
    x' <- findDjs arr x
    y' <- findDjs arr y
    return $ if x' == y' then 1 else 0

equals :: Int -> [Int] -> [[Int]] -> Int
equals n p edges = runST $ do
    arr <- createDjs n
    mapM_ (addDjs arr) edges
    movable_list <- mapM (movable arr) $ zip [1..] p
    return $ sum movable_list


main :: IO ()
main = do
    [n, m] <- map read . words <$> getLine :: IO [Int]
    p <- map read . words <$> getLine :: IO [Int]
    edges <- mapM (\_->map read . words <$> getLine) [1..m] :: IO [[Int]]
    putStrLn $ show $  equals n p edges