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)
    @n = n
    @par = Array.new(@n)
    @chl = Hash.new{|h, k| h[k] = []}
    @par.map!.with_index{|x, i| @chl[i]; i}
  end
  def union(a, b)
    pa, pb = [@par[a], @par[b]]
    if pa < pb then
      absorb(a, b)
    elsif pa > pb then
      absorb(b, a)
    end
  end
  def each_group(&b)
    @chl.each{|k, v| b.call(k, v)}
  end
  
  private
  
  def absorb(pa, ch)
    par = @par[pa]
    chl = @par[ch]
    @chl[chl].each{|c|
      @chl[par] << c
      @par[c] = par
    }
    @chl.delete(chl)
    @chl[par] << chl
    @par[chl] = par
  end
end

N, M = gets.chomp.split(" ").map(&:to_i)
P = gets.chomp.split(" ").map(&:to_i)
U = UnionFind.new(N+1)
M.times{|i|
  x, y = gets.chomp.split(" ").map(&:to_i)
  U.union(x, y)
}

ans = 0
U.each_group{|k, v|
  v << k
  num = v.map{|pos| P[pos-1]}
  ans += (v & num).size
}

puts ans