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 (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

class UnionFind(n: Int) {
  private val pare = Array.ofDim[Int](n)
  private val rk = Array.ofDim[Int](n)

  (0 until n).foreach(i => {
    pare(i) = i
    rk(i) = i
  })

  def find(x: Int): Int = {
    if (x == pare(x)) x
    else {
      pare(x) = find(pare(x))
      pare(x)
    }
  }

  def unite(x: Int, y: Int): Unit = {
    val xx: Int = find(x)
    val yy: Int = find(y)
    if (xx != yy) {
      if (rk(xx) < rk(yy)) pare(xx) = yy
      else pare(yy) = xx
      if (rk(xx) == rk(yy)) rk(xx) += 1
    }
  }

  def same(x: Int, y: Int): Boolean = {
    find(x) == find(y)
  }
}

object Main {
  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)

    val N, M = sc.nextInt
    val p = Array.ofDim[Int](N+1)
    (1 to N).foreach(i => {
      p(i) = sc.nextInt
    })

    val uf = new UnionFind(N+1)
    (1 to M).foreach(_ => {
      val x, y = sc.nextInt
      uf.unite(x, y)
    })

    var ans = 0
    (1 to N).foreach(i => {
      if (uf.same(p(i), i)) ans += 1
    })

    println(ans)
  }
}