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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

class UnionFind[T] {

  private[this] var map = Map.empty[T, T];

  def addEdge(parent: T, child: T): Unit = {
    map = map + (child -> parent);
  }

  def fetchRoot(elem: T): T = {
    @scala.annotation.tailrec
    def sub(elem: T, pendings: List[(T, T)]): T = {
      map.get(elem) match {
        case None =>
          pendings.foreach { case (c, p) =>
            map = map + (c -> elem);
          }
          elem;
        case Some(p) =>
          sub(p, (elem, p) :: pendings);
      }
    }
    sub(elem, Nil);
  }

}

object Main extends App {
  val sc = new java.util.Scanner(System.in);
  val n, m = sc.nextInt();
  val ps = Array.fill(n)(sc.nextInt());
  val xys = Array.fill(m)((sc.nextInt(), sc.nextInt()));

  val unionFind = new UnionFind[Int];
  xys.foreach { case (x, y) =>
    val xr = unionFind.fetchRoot(x);
    val yr = unionFind.fetchRoot(y);
    unionFind.addEdge(yr, xr);
  }

  val answer = ps.zipWithIndex.count { case (p, i) =>
    unionFind.fetchRoot(p) == unionFind.fetchRoot(i + 1);
  }
  println(answer);
}