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)

require 'set'
require 'pp'
N, M = gets.chomp.split(" ").map(&:to_i)
p = gets.chomp.split(" ").map(&:to_i)
N.times do |i|
  p[i] -= 1
end
x = []
y = []
M.times do |i|
  a, b = gets.chomp.split(" ").map(&:to_i)
  x[i] = a - 1
  y[i] = b - 1
end

## union find tree

par = (0..N-1).to_a
def root(par, a)
  if par[a] == a
    a
  else
    par[a] = root(par, par[a])
  end
end
def same_group?(par, x, y)
  root(par, x) == root(par, y)
end
def unite(par, a, b)
  a = root(par, a)
  b = root(par, b)
  return if a == b
  par[a] = b
end

M.times do |i|
  unite(par, x[i], y[i])
end

# pp par

##

index_hash = Hash.new { Set.new }
value_hash = Hash.new { Set.new }
N.times do |i|
  root = root(par, p[i])
  index_set = index_hash[root]
  value_set = value_hash[root]
  index_set << i
  value_set << p[i]
  index_hash[root] = index_set
  value_hash[root] = value_set
end

# pp index_hash
# pp value_hash

ans = 0
index_hash.each do |root, index_set|
  hash_set = value_hash[root]
  ans += index_set.intersection(hash_set).size
end

puts ans