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)

n,m = gets.chomp.split(" ").map(&:to_i)
p = gets.chomp.split(" ").map{|i|i.to_i-1}
edge = m.times.map{gets.chomp.split(" ").map{|i|i.to_i-1}}
ans = Array.new(n){|i|i}
mori = Hash.new{|h,k|h[k] = [k]}
edge.each do |i,j|
  if ans[i] != ans[j]
    if mori[ans[i]].size < mori[ans[j]].size
      k,l = i,j
    else
      k,l = j,i
    end
    temp = ans[k]
    mori[ans[k]].each do |o|
      ans[o] = ans[l]
      mori[ans[l]] << o
    end
    mori.delete(temp)
  end
end
temp = 0
mori.each do |k,arr|
  count = Hash.new(0)
  arr.each do |i|
    if p[i] != i
      count[i] += 1
      count[p[i]] += 1
    end
  end
  temp += count.values.count(2)
end
for i in 0..n-1
  if p[i] == i
    temp += 1
  end
end
puts temp