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: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int N = sc.nextInt();
		int M = sc.nextInt();
		int[] p = new int[N];
		List<Integer>[] adj = new List[N];
		for (int i = 0; i < adj.length; i++) {
			adj[i] = new ArrayList<>();
		}
		for (int i = 0; i < p.length; i++) {
			p[i] = sc.nextInt() - 1;
		}
		int a, b;
		for (int i = 0; i < M; i++) {
			a = sc.nextInt() - 1;
			b = sc.nextInt() - 1;
			adj[a].add(b);
			adj[b].add(a);
		}
		int ans = 0;
		int[] vis = new int[N];
		int id = 1;
		for (int i = 0; i < N; i++) if (vis[i] == 0) {
			Deque<Integer> cola = new ArrayDeque<>();
			Set<Integer> got = new HashSet<>();
			cola.addFirst(i);
			vis[i] = id;
			while (!cola.isEmpty()) {
				int cur = cola.removeFirst();
				got.add(p[cur]);
				for (int vec : adj[cur]) {
					if (vis[vec] == 0) {
						vis[vec] = id;
						cola.addLast(vec);
					}
				}
			}
			for (int val : got) {
				if (vis[val] == id) ans++;
			}
			id++;
		}
		System.out.println(ans);
	}
}