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: Runtime Error)

#require 'pp'
require 'set'


n, m = gets.chomp!.split(" ").map(&:to_i)
p_n = gets.chomp!.split(" ").map(&:to_i)
pairs = []
$groups = {}

m.times do |i|
    x, y = gets.chomp!.split(" ").map(&:to_i).minmax
    $groups[x] ||= {}
    $groups[x][y] = y
    $groups[y] ||= {}
    $groups[y][x] = x
end

def find(i, memo)
    v = $groups[i]
    $groups.delete(i)
    memo[i] = i

    v.keys.each do |k|
        if memo[k].nil?
            memo[k] = k
            find(k, memo)
        end
    end

    return memo
end

g = []
index = 0
m = {}
while $groups.empty?.!
    k, _ = $groups.first
    g[index] = find(k, {})
    g[index].each do |k, _|
        m[k] = index
    end  
    index += 1
end

#pp g
#pp m

count = 0
p_n.each.with_index(1) do |a, index|
    if m[index].nil?
        if a == index
            count += 1
        end
    elsif g[m[index]].include?(a)
        count += 1
    end
end

puts count