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 (2.7.1) (judge verdict: Wrong Answer)

class Unionfind
  attr_accessor(:par, :size)

  def initialize(n)
    @par = Array.new(n+1)
    (n+1).times do |i|
      @par[i] = i
    end
    @size = Array.new(n+1,1)
  end

  def root(x)
    while @par[x] != x
      x = @par[@par[x]]
      @par[x] = @par[@par[x]]
    end
    x
  end

  def unite(x,y)
    rx = root(x)
    ry = root(y)
    if rx != ry
      @size[ry] += size(rx)
      @par[rx] = ry
    end
  end

  def same(x,y)
    return root(x)==root(y)
  end

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

end

n,m = gets.chomp.split(" ").map(&:to_i)
p = gets.chomp.split(" ").map(&:to_i)
x = []
y = []
tree = Unionfind.new(n)
m.times do |i|
  x,y = gets.chomp.split(" ").map(&:to_i)
  tree.unite(x,y)
end
cnt = 0
1.upto(n) do |i|
  if i == p[i]
    cnt += 1
  elsif tree.same(p[i-1],i)
    cnt += 1
  end
end
puts cnt