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: Time Limit Exceeded)

de = false
require 'set'
n, m = gets.chomp.split().map(&:to_i)
q = gets.chomp.split().map(&:to_i)

mark = Array.new(n+1, nil)
s = []
sorig = []
m.times do
  x, y = gets.chomp.split().map(&:to_i)
  if mark[x].nil? && mark[y].nil?
    s.push Set.new([x,y])
    sorig.push Set.new([q[x-1],q[y-1]])
    mark[x] = s.size-1
    mark[y] = s.size-1
  elsif mark[x].nil? && !mark[y].nil?
    mark[x] = mark[y]
    s[mark[y]].add x
    sorig[mark[y]].add q[x-1]
  elsif !mark[x].nil? && mark[y].nil?
    mark[y] = mark[x]
    s[mark[x]].add y
    sorig[mark[x]].add q[y-1]
  else
    # marge y to x
    s[mark[x]].merge(s[mark[y]])
    sorig[mark[x]].merge(sorig[mark[y]])
    s[mark[y]].each do |i|
      mark[i] = mark[x]
    end
    p ['hoge', x, y] if de
    p ['hoge', mark[x], mark[y]] if de
    p ['hoge', s[mark[x]], s[mark[y]]] if de
  end
  p ['m', mark] if de
  p ['s', s] if de
end

p ['m', mark] if de
p ['s', s] if de
p ['so', sorig] if de

ans = 0
1.upto(n) do |i|
  if q[i-1] == i
    p ['same',i] if de
    ans += 1
  elsif  mark[i] && sorig[mark[i]].include?(i)
    p [s[mark[i]], i] if de
    ans += 1
  end
end

puts ans