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)

# util functions
class UnionFind
  def initialize(n) # n: number of elements in the forest
    @par  = []
    @rank = []
    @vs   = []
    n.times do |i|
      @par[i] = i
      @rank[i] = 0
      @vs[i] = 1
    end
  end
  attr_accessor :par, :rank, :vs

  def find(x)
    raise "x = #{x} is out of range 0..#{@par.size - 1}" unless @par[x]
    if @par[x] == x
      return x
    else
      return find( @par[x] )
    end
  end

  def unite( x, y )
    xrt = find(x)
    yrt = find(y)
    return if xrt == yrt

    if @rank[xrt] > @rank[yrt]
      @par[yrt] = xrt
      @vs[xrt] += @vs[yrt]
    else
      @par[xrt] = yrt
      @vs[yrt] += @vs[xrt]
      @rank[yrt] += 1 if @rank[xrt] == @rank[yrt]
    end
  end

  def same( x, y ) # returns true/false
    return find( x ) == find( y )
  end

end # UnionFind

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

def printd(str)
  print str if $debugFlag
end

# input
inputs = []
lc = 0
while l = $stdin.gets do
  if false
    inputs << l.chomp.split(" ").map(&:to_s)
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

nn = inputs[0][0]
$lst = inputs[1]

# body
if $debugFlag
end

uf = UnionFind.new(nn)

for i in 2..inputs.size-1
  uf.unite($lst[inputs[i][0]-1]-1, $lst[inputs[i][1]-1]-1);
end

ans = 0;
for j in 0..nn-1
  ans += 1 if uf.same(j, $lst[j] - 1) or j == $lst[j]-1
end

puts ans