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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.util.Vector;

public class Main {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int N, M;
        N = scan.nextInt();
        M = scan.nextInt();
        Vector<Integer> p = new Vector<>();

        for(int i = 0; i < N; ++i) p.addElement(scan.nextInt());

        Union_Find tree = new Union_Find();

        tree.init(N + 1);

        for(int i = 0; i < M; ++i) tree.unite(scan.nextInt(), scan.nextInt());

        int ans = 0;

        for(int i = 0; i < N; ++i) if(tree.same(i + 1, p.get(i))) ++ans;

        System.out.println(ans);
    }
}

class Union_Find {
    private Vector<Integer> par = new Vector<>();
    private Vector<Integer> rank = new Vector<>();

    public void init(int n) {
        for(int i = 0; i < n; ++i) {
            par.addElement(i);
            rank.addElement(0);
        }
    }

    public int root(int x) {
        return par.get(x).equals(x) ? x : par.set(x, root(par.get(x)));
    }

    public boolean same(int x, int y) {
        return root(x) == root(y);
    }

    public void unite(int x, int y) {
        x = root(x);
        y = root(y);

        if(x == y) return;

        if(rank.get(x) < rank.get(y)) {
            par.set(x, y);
        } else {
            par.set(y, x);
            if(rank.get(x).equals(rank.get(y))) rank.set(x, rank.get(x) + 1);
        }
    }
}