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 Go (1.6) (judge verdict: Accepted)

package main
 
import (
  "bufio"
  "os"
  "strconv"
  "strings"
  "fmt"
  "sort"
)
 
var reader = bufio.NewReaderSize(os.Stdin, 1000000)
var writer = bufio.NewWriter(os.Stdout)
func NextLine() string {
  var line, buffer []byte
  var isPrefix bool = true
  var err error
  for isPrefix {
    line, isPrefix, err = reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer, line...)
  }
  return string(buffer)
}
func NextInt() int {
  var n int
  n, _ = strconv.Atoi(NextLine())
  return n
}
func NextIntVec() []int {
  L := strings.Split(NextLine(), " ")
  N := make([]int, len(L))
  for i := range N {
    N[i], _ = strconv.Atoi(L[i])
  }
  return N
}
func Write(s interface{}) {
  fmt.Fprintln(writer, s)
}
func Output() {
  _ = writer.Flush()
}

func Find (R *[]int, i int) int {
  if (*R)[i] == i { return i }
  (*R)[i] = Find(R, (*R)[i])
  return (*R)[i]
}

func Union (R *[]int, i, j int) {
  Ri := Find(R, i)
  Rj := Find(R, j)
  if Ri < Rj {
    (*R)[Rj] = Ri
  } else {
    (*R)[Ri] = Rj
  }
}

func Intersection(S1, S2 *[]int) int {
  cnt := 0
  i := 0
  j := 0
  for i < len((*S1)) && j < len((*S2)) {
    if (*S1)[i] < (*S2)[j] {
      i += 1
    } else if (*S1)[i] == (*S2)[j] {
      i += 1
      j += 1
      cnt += 1
    } else {
      j += 1
    }
  }
  return cnt
}

func main() {
  NM := NextIntVec()
  P := NextIntVec()
  R := make([]int, NM[0])
  for i := range R {
    R[i] = i
  }
  for i := 0; i < NM[1]; i++ {
    XY := NextIntVec()
    Union(&R, XY[0] - 1, XY[1] - 1)
  }
  S := make([][][]int, NM[0])
  for i := range S {
    S[i] = make([][]int, 2)
    S[i][0] = make([]int, 0)
    S[i][1] = make([]int, 0)
  }
  for i, _ := range R {
    Find(&R, i)
    S[R[i]][0] = append(S[R[i]][0], P[i] - 1)
    S[R[i]][1] = append(S[R[i]][1], i)
  }
  cnt := 0
  for i, s := range S {
    sort.Ints(S[i][0])
    cnt += Intersection(&s[0], &s[1])
  }
  fmt.Println(cnt)
}