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: Wrong Answer)

require 'set'

n, m = gets.chomp.split.map(&:to_i)
ps = gets.chomp.split.map(&:to_i)

aggs = []
m.times do
  a, b = gets.chomp.split.map(&:to_i)
  a_agg_i = nil
  b_agg_i = nil
  aggs.each_with_index do |agg, i|
    if agg.include?(a)
      a_agg_i = i
    end
    if agg.include?(b)
      b_agg_i = i
    end
    break if a_agg_i && b_agg_i
  end

  if a_agg_i && b_agg_i
    aggs[a_agg_i] |= aggs[b_agg_i]
    aggs.delete_at(b_agg_i)
  elsif a_agg_i
    aggs[a_agg_i].add b
  elsif b_agg_i
    aggs[b_agg_i].add a
  else
    aggs.push Set.new([a,b])
  end
end

agg_map = Array.new(n, nil)
aggs.each_with_index do |agg, i|
  agg.each do |a|
    agg_map[a-1] = i
  end
end

# p aggs.map{|a| a.to_a.sort}
# p agg_map

ans = 0
ps.each_with_index do |p, i|
  if p == i+1
    ans += 1
    next
  end

  next unless agg_map[i]
  agg = aggs[agg_map[i]]
  agg.each do |a|
    if ps[a-1] == i+1
      ans += 1
      break
    end
  end

=begin
  aggs.each do |agg|
    if agg.include?(i+1)
      agg.each do |a|
        if ps[a-1] == i+1
          ans += 1
          break
        end
      end
      break
    end
  end
=end
end

puts ans