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 PHP (7.4.4) (judge verdict: Accepted)

<?php

class UnionFind
{
    private $parents;

    public function __construct($n)
    {
        $this->parents = array_fill(0, $n, -1);
    }

    public function root($a)
    {
        if ($this->parents[$a] < 0) {
            return $a;
        }

        $this->parents[$a] = $this->root($this->parents[$a]);

        return $this->parents[$a];
    }

    public function size($a)
    {
        return -1 * $this->parents[$this->root($a)];
    }

    public function connect($a, $b)
    {
        $ra = $this->root($a);
        $rb = $this->root($b);
        if ($ra == $rb) {
            return false;
        }

        if ($this->size($ra) > $this->size($rb)) {
            $this->parents[$ra] += $this->parents[$rb];
            $this->parents[$rb] = $ra;
        } else {
            $this->parents[$rb] += $this->parents[$ra];
            $this->parents[$ra] = $rb;
        }
        return true;
    }

    public function isConnect($a, $b)
    {
        return $this->root($a) == $this->root($b);
    }

    public function show()
    {
        print_r($this->parents);
    }
}

fscanf(STDIN, "%d %d", $N, $M);
$P = array_map('intval', explode(' ', trim(fgets(STDIN))));
for ($i = 0; $i < $N; ++$i) {
    --$P[$i];
}

$X = [];
$Y = [];
for ($i = 0; $i < $M; ++$i) {
    fscanf(STDIN, "%d %d", $x, $y);
    --$x;
    --$y;
    $X[] = $x;
    $Y[] = $y;
}

$uni = new UnionFind($N);
for ($i = 0; $i < $M; ++$i) {
    $uni->connect($P[$X[$i]], $P[$Y[$i]]);
}

$cnt = 0;
for ($i = 0; $i < $N; ++$i) {
    if ($uni->isConnect($i, $P[$i])) {
        ++$cnt;
    }
}

echo $cnt, PHP_EOL;