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 Perl6 (rakudo-star 2016.01) (judge verdict: Runtime Error)


class Algorithm::SetUnion::Node {
has Int $.size is rw;
has Int $.parent is rw;
};

class Algorithm::SetUnion {
has $.size;
has Algorithm::SetUnion::Node @.nodes;

submethod BUILD(:$!size) {
    loop (my $i = 0; $i < $!size; $i++) {
	@!nodes.push(Algorithm::SetUnion::Node.new(parent => $i, size => 1));
    }
}

method union(Int $left-index, Int $right-index) returns Bool:D {
    my $left-root = self.find($left-index);
    my $right-root = self.find($right-index);
    return False if ($left-root == $right-root);
    
    if (@!nodes[$left-root].size < @!nodes[$right-root].size) {
	@!nodes[$left-root].parent = $right-root;
	@!nodes[$right-root].size = @!nodes[$left-root].size + @!nodes[$right-root].size;
    } else {
	@!nodes[$right-root].parent = $left-root;
	@!nodes[$left-root].size = @!nodes[$left-root].size + @!nodes[$right-root].size;
    }
    return True;
}

method find(Int $index) returns Int:D {
    my $root = $index;
    my $current = $index;
    while (@!nodes[$root].parent != $root) {
	$root = @!nodes[$root].parent;
    }
    while (@!nodes[$current].parent != $current) {
	my $save = @!nodes[$current].parent;
	@!nodes[$current].parent = $root;
	$current = $save;
    }
    return $root;
}
}

my ($N, $M) = get.words>>.Int;
my @nums = get.words>>.Int;
my $su = Algorithm::SetUnion.new(:size($N));
for ^$M {
my ($p, $q) = get.words>>.Int;
$su.union($p-1,$q-1);
}

my @ok;
my $pos = 0;
for @nums {
@ok[$su.find($_)].push($pos);
$pos++;
}
$pos = 0;
my $ans = 0;
for @nums {
  for @ok[$pos] -> $ok_num {
      $ans++ if @nums[$pos] == $ok_num;
  }
}
say $ans;