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 Ruby (2.3.3) (judge verdict: Accepted)

class UnionFind
  def initialize(n)
    @root = Array.new(n)
    @rank = Array.new(n)
    @size = Array.new(n)
    (0...n).each do |i|
      @root[i] = i
      @rank[i] = 0
      @size[i] = 1
    end
  end

  def find(x)
    if @root[x] == x
      x
    else
      @root[x] = find(@root[x])
    end
  end

  def unite(x, y)
    x_root = find(x)
    y_root = find(y)
    return if x_root == y_root

    if @rank[x_root] < @rank[y_root]
      @root[x_root] = y_root
      @size[y_root] += @size[x_root]
    else
      @root[y_root] = x_root
      @size[x_root] += @size[y_root]
      if @rank[x_root] == @rank[y_root]
        @rank[x_root] += 1
      end
    end
    nil
  end

  def size(x)
    x_root = find(x)
    @size[x_root]
  end

  def same?(x, y)
    find(x) == find(y)
  end
end

N, M = gets.split.map(&:to_i)
ps = gets.split.map(&:to_i)
xys = M.times.map { gets.split.map(&:to_i) }

uf = UnionFind.new(N + 1)
xys.each do |(x, y)|
  uf.unite(x, y)
end
ans = 0
ps.each.with_index do |n, i|
  i += 1
  if n == i || uf.same?(i, n)
    ans += 1
  end
end
puts ans