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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
// D
class UnionFind
{
    private $par; // par[$i]:$iの親 自分が根の場合は自身のindexとなる
    private $size;

    function __construct($n)
    {
        for ($i = 0; $i < $n; $i++) {
            $this->par[$i] = $i; // 最初は全てが根
            $this->size[$i] = 1;
        }
    }

    function root($x)
    { // 根を返す
        if ($this->par[$x] === $x) return $x; // 根の場合
        return $this->par[$x] = $this->root($this->par[$x]); // 全ての枝の親を根にしながら再帰処理
    }

    function unite($x, $y)
    { // $xと$yの木を併合
        $ix = $this->root($x);
        $iy = $this->root($y);
        if ($ix === $iy) return;
        if ($this->size[$ix] < $this->size[$iy]) list($ix, $iy) = [$iy, $ix];
        $this->size[$ix] += $this->size[$iy];
        $this->par[$iy] = $ix; // $yの根を$xの根に付ける
    }

    function isSame($x, $y)
    { // $xと$yの根が同じか
        return $this->root($x) === $this->root($y);
    }

    function size($x)
    {
        return $this->size[$this->root($x)];
    }
}

fscanf(STDIN, '%d %d', $n, $m);
$p = array_map('intval', explode(' ', trim(fgets(STDIN))));

$tree = new UnionFind($n);

for ($i  = 0; $i < $m; $i++) {
    fscanf(STDIN, '%d %d', $x, $y);
    $x--;
    $y--; // 0 ~ $n-1に合わせる
    $tree->unite($x, $y);
}

$cnt = 0;
for ($i = 0; $i < $n; $i++) {
    if ($i === $p[$i] - 1 || $tree->isSame($i, $p[$i] - 1)) $cnt++;
}

echo $cnt . PHP_EOL;