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 UnionFindTree
  def initialize(n)
    @parent = (0..n).to_a
    @rank = Array.new(n+1, 0)
  end
     
  def find(x)
    return x if @parent[x] == x
    return @parent[x] = find(@parent[x])
  end
     
  def unite(a, b)
    a = find(a)
    b = find(b)
    return if a == b
    if @rank[a] < @rank[b]
      @parent[a] = b
    else
      @parent[b] = a
      @rank[a] += 1 if @rank[a] == @rank[b]
    end
  end
  
  def same?(a, b)
    find(a) == find(b)
  end
end

N, M = gets.split.map(&:to_i)

a = gets.split.map(&:to_i)
b = Array.new(N+1)
a.each.with_index(1) do |x, i|
  b[x] = i
end

uf = UnionFindTree.new(N)
M.times do
  x, y = gets.split.map(&:to_i)
  uf.unite(x, y)
end

cnt = 0
(1..N).reverse_each do |i|
  if b[i] == i
    cnt += 1
    next
  end
  
  x = i;
  y = b[i];
  if uf.same?(x, y)
    cnt += 1
  end
end
puts cnt